SYSTEM AND METHOD FOR ESTIMATING TISSUE HEATING OF A TARGET ABLATION ZONE FOR ELECTRICAL-ENERGY BASED THERAPIES
Systems and methods are provided for modeling and for providing a graphical representation of tissue heating and electric field distributions for medical treatment devices that apply electrical treatment energy through one or a plurality of electrodes. In embodiments, methods comprise: providing one or more parameters of a treatment protocol for delivering one or more electrical pulses to tissue through a plurality of electrodes; modeling electric and heat distribution in the tissue based on the parameters; and displaying a graphical representation of the modeled electric and heat distribution. In another embodiment, a treatment planning module is adapted to generate an estimated target ablation zone based on a combination of one or more parameters for an irreversible electroporation protocol and one or more tissue-specific conductivity parameters.
The present application is a Continuation of U.S. patent application Ser. No. 14/558,631 filed Dec. 2, 2014, which published as U.S. Patent Application Publication No. US 2015/0088120 on Mar. 26, 2015. The '631 application is a Continuation-in-Part (CIP) of U.S. patent application Ser. No. 14/012,832, filed on Aug. 28, 2013, which published as U.S. Patent Application Publication No. 2013/0345697 on Dec. 26, 2013 and issued as U.S. Pat. No. 9,283,051 on Mar. 15, 2016. The '832 application relies on and claims the benefit of the filing date of U.S. Provisional Application No. 61/694,144, filed on Aug. 28, 2012. The '832 application is also a CIP of U.S. application Ser. No. 12/491,151, filed on Jun. 24, 2009, which '151 application published as U.S. Patent Application Publication No. 2010/0030211 on Feb. 4, 2010 and issued as U.S. Pat. No. 8,992,517 on Mar. 31, 2015. The '151 application relies on and claims the benefit of the filing dates of U.S. Provisional Patent Application Nos. 61/171,564, filed on Apr. 22, 2009, 61/167,997, filed on Apr. 9, 2009, and 61/075,216, filed on Jun. 24, 2008. The '151 application is also a CIP of U.S. patent application Ser. No. 12/432,295, filed on Apr. 29, 2009, which '295 application published as U.S. Patent Application Publication No. 2009/0269317 and issued as U.S. Pat. No. 9,598,691 on Mar. 21, 2017. The '295 application relies on and claims the benefit of the filing date of U.S. Provisional Patent Application No. 61/125,840, filed on Apr. 29, 2008. The '631 application also relies on and claims priority to and the benefit of the filing date of U.S. Provisional Application No. 61/910,655, filed Dec. 2, 2013. The disclosures of these patent applications are hereby incorporated by reference herein in their entireties.
FIELD OF THE INVENTIONThe present invention is related to medical therapies involving the administering of electrical treatment energy. More particularly, embodiments of the present invention provide systems and methods for modeling and providing a graphical representation of tissue heating and electric field for a medical treatment device that applies electrical treatment energy through a plurality of electrodes defining a target treatment area. Embodiments of the present invention also provide systems and methods providing a graphical representation of a target ablation zone based on one or more electrical conductivity parameters that are specific for the tissue to be treated.
DESCRIPTION OF RELATED ARTElectroporation-based therapies (EBTs) are clinical procedures that utilize pulsed electric fields to induce nanoscale defects in cell membranes. Typically, pulses are applied through minimally invasive needle electrodes inserted directly into the target tissue, and the pulse parameters are tuned to create either reversible or irreversible defects. Reversible electroporation facilitates the transport of molecules into cells without directly compromising cell viability. This has shown great promise for treating cancer when used in combination with chemotherapeutic agents or plasmid DNA (M. Marty et al., “Electrochemotherapy—An easy, highly effective and safe treatment of cutaneous and subcutaneous metastases: Results of ESOPE (European Standard Operating Procedures of Electrochemotherapy) study,” European Journal of Cancer Supplements, 4, 3-13, 2006; A. I. Daud et al., “Phase I Trial of Interleukin-12 Plasmid Electroporation in Patients With Metastatic Melanoma,” Journal of Clinical Oncology, 26, 5896-5903, Dec. 20 2008). Alternatively, irreversible electroporation (IRE) has been recognized as a non-thermal tissue ablation modality that produces a tissue lesion, which is visible in real-time on multiple imaging platforms (R. V. Davalos, L. M. Mir, and B. Rubinsky, “Tissue ablation with irreversible electroporation,” Ann Biomed Eng, 33, 223-31, February 2005; R. V. Davalos, D. M. Otten, L. M. Mir, and B. Rubinsky, “Electrical impedance tomography for imaging tissue electroporation,” IEEE Transactions on Biomedical Engineering, 51, 761-767, 2004; L. Appelbaum, E. Ben-David, J. Sosna, Y. Nissenbaum, and S. N. Goldberg, “US Findings after Irreversible Electroporation Ablation: Radiologic-Pathologic Correlation,” Radiology, 262, 117-125, Jan. 1, 2012). Because the mechanism of cell death does not rely on thermal processes, IRE spares major nerve and blood vessel architecture and is not subject to local heat sink effects when using a specific protocol that does not exceed the thermal damage threshold. (B. Al-Sakere, F. Andre, C. Bernat, E. Connault, P. Opolon, R. V. Davalos, B. Rubinsky, and L. M. Mir, “Tumor ablation with irreversible electroporation,” PLoS ONE, 2, e1135, 2007). These unique benefits have translated to the successful treatment of several surgically “inoperable” tumors (K. R. Thomson et al., “Investigation of the safety of irreversible electroporation in humans,” J Vasc Intery Radiol, 22, 611-21, May 2011; R. E. Neal II et al., “A Case Report on the Successful Treatment of a Large Soft-Tissue Sarcoma with Irreversible Electroporation,” Journal of Clinical Oncology, 29, 1-6, 2011; P. A. Garcia et al., “Non-thermal irreversible electroporation (N-TIRE) and adjuvant fractionated radiotherapeutic multimodal therapy for intracranial malignant glioma in a canine patient,” Technol Cancer Res Treat, 10, 73-83, 2011).
In EBTs, the electric field distribution is the primary factor for dictating defect formation and the resulting volume of treated tissue (J. F. Edd and R. V. Davalos, “Mathematical modeling of irreversible electroporation for treatment planning,” Technology in Cancer Research and Treatment, 6, 275-286, 2007 (“Edd and Davalos, 2007”); D. Miklavcic, D. Semrov, H. Mekid, and L. M. Mir, “A validated model of in vivo electric field distribution in tissues for electrochemotherapy and for DNA electrotransfer for gene therapy,” Biochimica et Biophysica Acta, 1523, 73-83, 2000). The electric field is influenced by both the geometry and positioning of the electrodes as well as the dielectric tissue properties. Because the pulse duration is typically much longer than the pulse rise/fall time, static solutions of the Laplace's equation incorporating only electric conductivity are sufficient for predicting the electric field distribution. In tissues with uniform conductivity, solutions can be obtained analytically for various needle electrode configurations if the exposure length is much larger than the separation distance (S. Corovic, M. Pavlin, and D. Miklavcic, “Analytical and numerical quantification and comparison of the local electric field in the tissue for different electrode configurations,” Biomed Eng Online, 6, 2007; R. Neal II et al., “Experimental Characterization and Numerical Modeling of Tissue Electrical Conductivity during Pulsed Electric Fields for Irreversible Electroporation Treatment Planning,” Biomedical Engineering, IEEE Transactions on, PP, 1-1, 2012 (“Neal et al., 2012”)). This is not often the case in clinical applications where aberrant masses with a diameter on the order of 1 cm are treated with an electrode exposure length of similar dimensions. Additionally, altered membrane permeability due to electroporation influences the tissue conductivity in a non-linear manner. Therefore numerical techniques may be used to account for any electrode configuration and incorporate a tissue-specific function relating the electrical conductivity to the electric field distribution (i.e. extent of electroporation).
Conventional devices for delivering therapeutic energy such as electrical pulses to tissue include a handle and one or more electrodes coupled to the handle. Each electrode is connected to an electrical power source. The power source allows the electrodes to deliver the therapeutic energy to a targeted tissue, thereby causing ablation of the tissue.
Once a target treatment area is located within a patient, the electrodes of the device are placed in such a way as to create a treatment zone that surrounds the treatment target area. In some cases, each electrode is placed by hand into a patient to create a treatment zone that surrounds a lesion. The medical professional who is placing the electrodes typically watches an imaging monitor while placing the electrodes to approximate the most efficient and accurate placement.
However, if the electrodes are placed by hand in this fashion, it is very difficult to predict whether the locations selected will ablate the entire treatment target area because the treatment region defined by the electrodes vary greatly depending on such parameters as the electric field density, the voltage level of the pulses being applied, size of the electrode and the type of tissue being treated. Further, it is often difficult or sometimes not possible to place the electrodes in the correct location of the tissue to be ablated because the placement involves human error and avoidance of obstructions such as nerves, blood vessels and the like.
Conventionally, to assist the medical professional in visualizing a treatment region defined by the electrodes, an estimated treatment region is generated using a numerical model analysis such as complex finite element analysis. One problem with such a method is that even a modest two dimensional treatment region may take at least 30 minutes to several hours to complete even in a relatively fast personal computer. This means that it would be virtually impossible to try to obtain on a real time basis different treatment regions based on different electrode positions.
In IRE treatments, the electric field distribution is the primary factor for dictating defect formation and the resulting volume of treated tissue (See J. F. Edd and R. V. Davalos, “Mathematical modeling of irreversible electroporation for treatment planning,” Technol Cancer Res Treat, vol. 6, pp. 275-286, 2007; D. Sel, et al., “Sequential finite element model of tissue electropermeabilization,” IEEE Trans Biomed Eng, vol. 52, pp. 816-27, May 2005). The electric field is influenced by both the geometry and positioning of the electrodes as well as the dielectric tissue properties. The application of an electric field across any conductive media will result in some degree of resistive losses in which energy is dissipated as heat. Though cell death in IRE is attributed to non-thermal mechanisms, it is possible to inadvertently elevate tissue temperatures above thermal damage thresholds if parameters are not chosen carefully. Since a major advantage of IRE is the ablation of tissue without deleterious thermal effects and the therapy is often applied in regions which cannot clinically sustain thermal injury, it is important to identify safe operating parameters. Transient heating of tissue in proximity to the electrode can result in the denaturing of the extracellular matrix, scar formation, or damage to local blood vessels and nerves. To avoid these effects, it is important to understand the extent and geometry of tissue heating.
Therefore, it would be desirable to provide an improved system and method to predict a treatment region that avoids electrical and thermal overexposure and damage in order to determine safe and effective pulse protocols for administering electrical energy based therapies, such IRE.
SUMMARY OF THE INVENTIONIn one embodiment, the invention provides a system for treating a tissue, which system applies electrical treatment energy through one or more electrodes, such as a plurality of electrodes, defining a target treatment area of the tissue. The system comprises a memory, a display device, a processor coupled to the memory and the display device, and a treatment planning module stored in the memory and executable by the processor. In one embodiment, the treatment planning module is adapted to generate an estimated heat distribution and/or electrical field distribution in the display device based on one or more parameters for an electrical energy based protocol, such as an irreversible electroporation (IRE) protocol. In another embodiment, the treatment planning module is adapted to generate an estimated target ablation zone based on a combination of one or more parameters for an electrical energy based protocol, such as an IRE-based protocol, and one or more tissue-specific conductivity parameters.
In another embodiment, the invention provides a method of treating a tissue with a medical treatment device that applies electrical treatment energy through a one or more or a plurality of electrodes defining a target treatment area of the tissue and comprises a display device. The method may be executed partially or completely using the system of the invention. In a specific embodiment, one or more steps are executed through the treatment planning module.
In embodiments, the treatment planning module can be used to determine a temperature distribution to determine tissue heating at or around a target ablation zone prior to or during treatment. The treatment planning module can be used to graphically display contour lines which represent a specific temperature of tissue heating. In one embodiment, the treatment planning module estimates the temperature rise within tissue due to Joule heating effects, and plots a contour line according to a temperature specified by a user. Further, the treatment planning module may further plot a contour line representing an electric field intensity such that temperature and electric field intensity can be correlated. The treatment planning module may plot the temperature distribution and electric field distribution for a bipolar and single needle electrodes. This capability may allow a user (e.g. treating physician) to determine heating to surrounding tissues during treatment planning and adjust parameters to prevent thermal damage to critical surrounding structures such as nerves and blood vessels. In one embodiment, the contour lines are Cassini oval approximations performed according to the equations and procedure in Example 7.
In embodiments, the treatment planning module can be used to provide the electric field distributions using different configurations of bipolar probes and include the dynamic change in electrical conductivity from the non-electroporated baseline tissue electrical conductivity. The treatment planning module may plot contour lines representing electric field distributions based on a specific combination of electrode length, separation distance, and applied voltage. The treatment planning module may incorporate the dynamic change in electrical conductivity from the baseline during treatment to account for treatment-related changes in conductivity for particular tissues such as liver, kidney, brain, etc. This capability may allow the treating physician to determine electric field distributions and zones of ablation based on the capacity for a specific target tissue to change in conductivity during treatment. In one embodiment, the contour lines are Cassini oval approximations performed according to the equations and procedure in Example 7.
In embodiments, the treatment planning module can be based on a parametric study of the dynamic conductivity curve so that variables related to the dynamic conductivity could be used to fit tissue specific behavior. In embodiments, the treatment planning module may provide input for one or more electrical conductivity parameters such as the baseline (e.g., non-electroporated) conductivity, change in conductivity, the transition zone (how rapidly the conductivity increases), the electric field at which the change in conductivity occurs, and the electric field at which irreversible electroporation occurs. These parameters may be experimentally derived for different tissues and stored in a database. This capability may allow the treating physician to account for different conductivity parameters as they apply to different target tissues when designing a treatment protocol. Thus, when considering a specific tissue, the treating physician may optimize the calculation of an ablation zone for that tissue by inputting one or more of the tissue-specific conductivity parameters for the tissue of interest.
The accompanying drawings illustrate certain aspects of embodiments of the present invention, and should not be used to limit or define the invention. Together with the written description the drawings serve to explain certain principles of the invention.
Further, the application file contains at least one drawing executed in color. Copies of the patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee.
Reference will now be made in detail to various exemplary embodiments of the invention. Embodiments described in the description and shown in the figures are illustrative only and are not intended to limit the scope of the invention. Changes may be made in the specific embodiments described in this specification and accompanying drawings that a person of ordinary skill in the art will recognize are within the scope and spirit of the invention.
Throughout the present teachings, any and all of the features and/or components disclosed or suggested herein, explicitly or implicitly, may be practiced and/or implemented in any combination, whenever and wherever appropriate as understood by one of ordinary skill in the art. The various features and/or components disclosed herein are all illustrative for the underlying concepts, and thus are non-limiting to their actual descriptions. Any means for achieving substantially the same functions are considered as foreseeable alternatives and equivalents, and are thus fully described in writing and fully enabled. The various examples, illustrations, and embodiments described herein are by no means, in any degree or extent, limiting the broadest scopes of the claimed inventions presented herein or in any future applications claiming priority to the instant application.
Embodiments of the invention include a method for visualization of heat and electric field distribution within a target treatment area, the method comprising: selecting as inputs an applied voltage, electrode spacing, and treatment duration corresponding to a desired treatment protocol for a target treatment area; using the inputs in a Cassini approximation of data, wherein the data comprises measured voltage, electrode spacing, and time of actual treatment protocols, and determining an expected temperature distribution and expected electric field distribution of the target treatment area; and displaying a graphical representation of a selected temperature and a selected electric field of the expected temperature and electric field distributions. Such methods can further comprise as inputs one or more of a baseline conductivity for the target treatment area, a change in conductivity for the target treatment area, or a conductivity for a specific tissue type.
Such methods can include a method of treatment planning for medical therapies involving administering electrical treatment energy, the method comprising: providing one or more parameters of a treatment protocol for delivering one or more electrical pulses to tissue through one or more or a plurality of electrodes; modeling heat distribution in the tissue based on the parameters; and displaying a graphical representation of the modeled heat distribution.
One embodiment of the present invention is illustrated in
For example, a treatment protocol according to the invention could include a one or more or a plurality of electrodes. According to the desired treatment pattern, the plurality of electrodes can be disposed in various positions relative to one another. In a particular example, a plurality of electrodes can be disposed in a relatively circular pattern with a single electrode disposed in the interior of the circle, such as at approximately the center. Any configuration of electrodes is possible and the arrangement need not be circular but any shape periphery can be used depending on the area to be treated, including any regular or irregular polygon shape, including convex or concave polygon shapes. The single centrally located electrode can be a ground electrode while the other electrodes in the plurality can be energized. Any number of electrodes can be in the plurality such as from about 1 to 20. Indeed, even 3 electrodes can form a plurality of electrodes where one ground electrode is disposed between two electrodes capable of being energized, or 4 electrodes can be disposed in a manner to provide two electrode pairs (each pair comprising one ground and one electrode capable of being energized). During treatment, methods of treating can involve energizing the electrodes in any sequence, such as energizing one or more electrode simultaneously, and/or energizing one or more electrode in a particular sequence, such as sequentially, in an alternating pattern, in a skipping pattern, and/or energizing multiple electrodes but less than all electrodes simultaneously, for example.
In the embodiment shown, each probe 22 includes either a monopolar electrode or bipolar electrodes having two electrodes separated by an insulating sleeve. In one embodiment, if the probe includes a monopolar electrode, the amount of exposure of the active portion of the electrode can be adjusted by retracting or advancing an insulating sleeve relative to the electrode. See, for example, U.S. Pat. No. 7,344,533, which is incorporated by reference herein in its entirety. The pulse generator 10 is connected to a treatment control computer 40 having input devices such as keyboard 12 and a pointing device 14, and an output device such as a display device 11 for viewing an image of a target treatment area such as a lesion 300 surrounded by a safety margin 301. The therapeutic energy delivery device 22 is used to treat a lesion 300 inside a patient 15. An imaging device 30 includes a monitor 31 for viewing the lesion 300 inside the patient 15 in real time. Examples of imaging devices 30 include ultrasonic, CT, MRI and fluoroscopic devices as are known in the art.
The present invention includes computer software (treatment planning module 54) which assists a user to plan for, execute, and review the results of a medical treatment procedure, as will be discussed in more detail below. For example, the treatment planning module 54 assists a user to plan for a medical treatment procedure by enabling a user to more accurately position each of the probes 22 of the therapeutic energy delivery device 20 in relation to the lesion 300 in a way that will generate the most effective treatment zone. The treatment planning module 54 can display the anticipated treatment zone based on the position of the probes and the treatment parameters. The treatment planning module 54 may also display a zone of temperature heating according to cutoff values inputted by the treating physician and correlate this with a value for the electric field distribution. The treatment planning module may also allow the treating physician to display the anticipated treatment zone, or target ablation zone, according to one or more tissue-specific conductivity parameters inputted by the treating physician. The conductivity parameters may include the baseline conductivity of the tissue to be treated, the ratio of the baseline conductivity to the maximum conductivity of the tissue that is reached during treatment, the rate at which the conductivity increases from the baseline to the maximum conductivity, and/or the electric field at which the conductivity changes during treatment.
The treatment planning module 54 can display the progress of the treatment in real time and can display the results of the treatment procedure after it is completed. This information can be displayed in a manner such that it can be used for example by a treating physician to determine whether the treatment was successful and/or whether it is necessary or desirable to re-treat the patient.
For purposes of this application, the terms “code”, “software”, “program”, “application”, “software code”, “computer readable code”, “software module”, “module” and “software program” are used interchangeably to mean software instructions that are executable by a processor. The “user” can be a physician or other medical professional. The treatment planning module 54 executed by a processor outputs various data including text and graphical data to the monitor 11 associated with the generator 10.
Referring now to
In one embodiment, the computer 40 is built into the voltage generator 10. In another embodiment, the computer 40 is a separate unit which is connected to the voltage generator through the communications link 52. In a preferred embodiment, the communication link 52 is a USB link. In one embodiment, the imaging device 30 is a standalone device which is not connected to the computer 40. In the embodiment as shown in
It should be noted that the software can be used independently of the pulse generator 10. For example, the user can plan the treatment in a different computer as will be explained below and then save the treatment parameters to an external memory device, such as a USB flash drive (not shown). The data from the memory device relating to the treatment parameters can then be downloaded into the computer 40 to be used with the generator 10 for treatment. Additionally, the software can be used for hypothetical illustration of zones of ablation, temperature thresholds or cutoffs, and electrical field thresholds or cutoffs for training purposes to the user on therapies that deliver electrical energy. For example, the data can be evaluated by a human to determine or estimate favorable treatment protocols for a particular patient rather than programmed into a device for implementing the particular protocol.
General treatment protocols for the destruction (ablation) of undesirable tissue through electroporation are known. They involve the insertion (bringing) electroporation electrodes to the vicinity of the undesirable tissue and in good electrical contact with the tissue and the application of electrical pulses that cause irreversible electroporation of the cells throughout the entire area of the undesirable tissue. The cells whose membrane was irreversible permeabilized may be removed or left in situ (not removed) and as such may be gradually removed by the body's immune system. Cell death is produced by inducing the electrical parameters of irreversible electroporation in the undesirable area.
Electroporation protocols involve the generation of electrical fields in tissue and are affected by the Joule heating of the electrical pulses. When designing tissue electroporation protocols it is important to determine the appropriate electrical parameters that will maximize tissue permeabilization without inducing deleterious thermal effects. It has been shown that substantial volumes of tissue can be electroporated with reversible electroporation without inducing damaging thermal effects to cells and has quantified these volumes (Davalos, R. V., B. Rubinsky, and L. M. Mir, Theoretical analysis of the thermal effects during in vivo tissue electroporation. Bioelectrochemistry, 2003. Vol. 61(1-2): p. 99-107).
The electrical pulses used to induce irreversible electroporation in tissue are typically larger in magnitude and duration from the electrical pulses required for reversible electroporation. Further, the duration and strength of the pulses for irreversible electroporation are different from other methodologies using electrical pulses such as for intracellular electro-manipulation or thermal ablation. The methods are very different even when the intracellular (nano-seconds) electro-manipulation is used to cause cell death, e.g. ablate the tissue of a tumor or when the thermal effects produce damage to cells causing cell death.
Typical values for pulse length for irreversible electroporation are in a range of from about 5 microseconds to about 62,000 milliseconds or about 75 microseconds to about 20,000 milliseconds or about 100 microseconds±10 microseconds. This is significantly longer than the pulse length generally used in intracellular (nano-seconds) electro-manipulation which is 1 microsecond or less—see published U.S. application 2002/0010491 published Jan. 24, 2002.
The pulse is typically administered at voltage of about 100 V/cm to 7,000 V/cm or 200 V/cm to 2000 V/cm or 300V/cm to 1000 V/cm about 600 V/cm for irreversible electroporation. This is substantially lower than that used for intracellular electro-manipulation which is about 10,000 V/cm, see U.S. application 2002/0010491 published Jan. 24, 2002.
The voltage expressed above is the voltage gradient (voltage per centimeter). The electrodes may be different shapes and sizes and be positioned at different distances from each other. The shape may be circular, oval, square, rectangular or irregular etc. The distance of one electrode to another may be 0.5 to 10 cm, 1 to 5 cm, or 2-3 cm. The electrode may have a surface area of 0.1-5 sq. cm or 1-2 sq. cm.
The size, shape and distances of the electrodes can vary and such can change the voltage and pulse duration used. Those skilled in the art will adjust the parameters in accordance with this disclosure to obtain the desired degree of electroporation and avoid thermal damage to surrounding cells.
Additional features of protocols for electroporation therapy are provided in U.S. Patent Application Publication No. US 2007/0043345 A1, the disclosure of which is hereby incorporated by reference in its entirety.
In one aspect, the systems and methods may have the capability for estimating a volume of tissue that will be heated at or above a cutoff value and a volume of tissue that will receive an electric field at or above a cutoff value for the above medical treatment device. The cut-off values may be user-specified values determined by a treating physician or technician. The systems and methods are provided so that the treating physician may recognize treatments that produce overheating in the vicinity of the electrodes of the treatment device. This additional capability of the treatment device may be based on the Joule heating equations of Example 8. The values may be plotted as contour lines which may be displayed with a graphical representation of the estimated treatment volume above. In one embodiment, the contour lines are Cassini oval approximations performed according to the equations and procedure in Example 7.
In another aspect, the systems and methods may have the additional capability for providing the electric field distributions using different configurations of bipolar probes and include the dynamic change in electrical conductivity from the baseline non-electroporated tissue. The systems and methods may allow a user to incorporate tissue-specific values for the dynamic change in conductivity in estimating a treatment volume. This additional capability is further described in Example 9. In one embodiment, the contour lines are Cassini oval approximations performed according to the equations and procedure in Example 7.
In another aspect, the systems and methods may have the additional capability for inputting or adjusting one or more variables related to the dynamic conductivity so that tissue-specific behavior can be accounted for when estimating a treatment volume. In embodiments, the treatment planning module may provide input for parameters such as the baseline conductivity, change in conductivity, the transition zone (how rapidly the conductivity increases), the electric field at which the change in conductivity occurs, and the electric field at which irreversible electroporation occurs. These parameters may allow the treating physician to fine-tune the ablation zone based on the conductivity characteristics of the target tissue. The present inventors have recognized that the conductivity characteristics of the tissue, such as baseline and maximum conductivities, should be determined before the therapy in order to determine safe and effective pulse protocols. This additional capability is further described in Example 10.
The numerical models and algorithms of the invention, as provided in the Examples, such as Cassini Oval equations of Example 7 and the Joule Heating Model equations of Example 8, can be implemented in a system for estimating a 3-dimensional treatment volume for a medical treatment device that applies treatment energy through one or more or a plurality of electrodes defining a treatment area. In one embodiment, the numerical models and algorithms are implemented in an appropriate computer readable code as part of the treatment planning module 54 of the system of the invention. Computing languages available to the skilled artisan for programming the treatment planning module 54 include general purpose computing languages such as the C and related languages, and statistical programming languages such as the “S” family of languages, including R and S-Plus. The computer readable code may be stored in a memory 44 of the system of the invention. A processor 46 is coupled to the memory 44 and a display device 11 and the treatment planning module 54 stored in the memory 44 is executable by the processor 46. Treatment planning module 54, through the implemented numerical models, is adapted to generate a graphical display of an estimated temperature or electric field or target ablation zone in the display device 11.
In one embodiment, the invention provides for a system for estimating and graphically displaying a thermal and/or electric field value for a medical treatment device that applies treatment energy through one or more or a plurality of electrodes 22 defining a treatment area, the system comprising a memory 44, a display device 11, a processor 46 coupled to the memory 44 and the display device 11, and a treatment planning module 54 stored in the memory 44 and executable by the processor 46, the treatment planning module 54 adapted to generate one or more isocontours representing a value of a temperature and/or electric field for display in the display device 11 based on modeling of the temperature distributions or electrical field distributions according to one or more parameters defining an electrical energy based protocol (e.g., irreversible electroporation). The results of modeling the temperature distributions and electrical field distributions may be stored in a database or calculated in real-time. The treatment planning module may generate the isocontours based on the modeling results.
In another embodiment, the invention provides for a system for estimating a target ablation zone for a medical treatment device that applies treatment energy through one or more or a plurality of electrodes 22 defining a treatment area, the system comprising a memory 44, a display device 11, a processor 46 coupled to the memory 44 and the display device 11, and a treatment planning module 54 stored in the memory 44 and executable by the processor 46, the treatment planning module 54 adapted to generate a target ablation zone in the display device 11 based on a combination of one or more parameters for a treatment protocol for irreversible electroporation and one or more tissue-specific conductivity parameters.
The foregoing description provides additional instructions and algorithms for a computer programmer to implement in computer readable code a treatment planning module 54 that may be executable through a processor 46 to generate an estimated temperature or electrical field for display in the display device 11 based on modeling of a tissue according to one or more parameters for electroporation, such as IRE. The computer readable code may also estimate a temperature value and an electric field value according to equations described in Example 8 and graphically display these value as contour lines in the display device. In one embodiment, the contour lines are Cassini oval approximations performed according to the equations and procedure in Example 7. The computer readable code may also provide for input on one or more conductivity parameters for estimating the target ablation zone as described in Examples 9 and 10.
The method of the invention fits data extracted from numerical simulations to both the ‘a’ and ‘b’ parameters from the Cassini Equation, providing the flexibility to match potentially any shape of electric field created by the specific pulse parameters employed. Also, as illustrated in
Additionally, by adding the cumulative effects of electrode pairs, the electric field and thermal contours of alternative multi-electrode arrangements of three or more probes can be determined. For example, a four single probe electrode box can be captured by calculating treatment regions based on each combination of electrode pairs for the fit according to the techniques described above. Thus, for example, if the four probe electrode box is configured for treatment using pulses that cycle through probe combinations 1-2, 3-4, 1-3, 2-4, 2-3 and 1-4 the approximation tool can find electric field and temperature contours for each probe combination, then superimpose the results to display the cumulative effect of that particular pulse protocol in the treatment region.
In one embodiment, the treatment planning module 54 provides for a method for modeling and graphical display of tissue heating according to a set of parameters defining a treatment protocol. In a specific embodiment, the set of parameters correspond to a treatment protocol for inducing irreversible electroporation in a tissue.
The treatment planning module 54 may provide one or more parameters of a treatment protocol for delivering one or more electrical pulses to a tissue through one or more or a plurality of electrodes.
The treatment planning module 54 may model a heat distribution in a tissue surrounding the one or more or the plurality of electrodes based on the one or more parameters.
The treatment planning module 54 may provide a graphical representation of the heat distribution based on the modeled heat distribution.
The treatment planning module 54 may allow a user to optionally modify one or more of the parameters of the treatment protocol through input devices 12, 14 based on the graphical representation of the heat distribution.
The treatment planning module 54 may be in operable connection with a controller 71 capable of delivering one or more electrical pulses to the tissue based on the one or more parameters stored in the treatment planning module 54.
The treatment planning module 54 may model the heat distribution in the tissue based on the Joule heating in the tissue.
The treatment planning module 54 may calculate the heat distribution as:
where ρ is the density, Cp is the heat capacity, k is the thermal conductivity, and Qjh are the resistive losses
where J is the induced current density
and σ is the tissue conductivity and E is the electric field
The treatment planning module may further calculate the resistive losses as
jh.Qrh=((jh.Jix+jh.Jex)*duty_cycle*jh.Ex+(jh.Jiy+jh.Jey)*duty_cycle*jh.Ey+(jh.Jiz+jh.Jez)*duty_cycle*jh.Ez)*)t<=90)+0*(t>90)
according to the Joule Heating Model described in Example 8.
The treatment planning module 54 may allow a user to specify a heat distribution value (i.e. temperature) and may provide a graphical representation of the temperature as an isocontour line.
The treatment planning module 54 may model an electric field distribution in a tissue surrounding the one or more or a plurality of electrodes based on the one or more parameters of the treatment protocol.
The treatment planning module 54 may provide a graphical representation of the electric field distribution based on the modeled electrical field distribution.
The treatment planning module may calculate the electric field distribution as:
∇2ϕ=0
where ϕ is the electric potential, this equation is solved with boundary conditions:
{right arrow over (n)}·{right arrow over (J)}=0 at the boundaries
ϕ=Vin at the boundary of the first electrode
ϕ=0 at the boundary of the second electrode
wherein {right arrow over (n)} is the normal vector to the surface, {right arrow over (J)} is the electrical current and Vin is the electrical potential applied.
The treatment planning module 54 may allow a user to specify a value for an electrical field distribution and provide a graphical representation of the electrical field distribution value as an isocontour line.
The treatment planning module 54 may display isocontour lines representing the heat and electrical field distributions by calculating a Cassini oval according to Example 7. The Cassini oval may be calculated by first modeling the temperature and electrical field distributions, storing the values in a database, and then calculating the specific Cassini oval based on parameters chosen by the user.
The treatment planning module 54 may allow a user to specify the one or more parameters of a treatment protocol including voltage, gap between electrodes, duration, pulse width, and electric field intensity.
Alternatively, or in addition, the treatment planning module 54 may allow a user to input one or more of the tissue-specific conductivity parameters described herein and model the electric field distribution and tissue heating. The treatment planning module 54 may then provide graphical representations of one or more values of the electrical field intensity and tissue temperature.
The treatment planning module 54 may provide a graphical representation of an electrical field distribution and a heat distribution through a variety of modes of operation. First, the treatment planning module 54 may model the electrical field distribution and heat distribution for each set of parameters that are entered through input devices 12, 14. Thus, every time the treating physician altered one or more parameters of the treatment protocol, the treatment planning module 54 software would model the electrical field and heat distributions according to those parameters and then graphically display them on the display device 11. In a second approach, the software would first run the modeling of the heat and electrical field distributions for a wide range of parameter combinations and store the resulting distributions in the database stored in memory 44. In this approach, when the treating physician enters a particular combination of parameters, the treatment planning module 54 retrieves the heat distribution and electrical field distribution from values stored in the database. These values are then used as a basis for Cassini oval calculations to determine specific contours for the particular combination of parameters. The Cassini oval calculations are performed according to the equations and procedure described in Example 7. The Cassini ovals are then graphically displayed on the display device 11 in real time. In embodiments, specific contours are provided according to values for temperature or electrical field intensity set by the user.
The treatment planning module 54 may model the heat and electric field distributions according to mathematical formulas. In a specific embodiment, the treatment planning module 54 may model the heat distribution and the electrical field distribution according to the formulas in Example 8.
In another embodiment, the invention provides a system for treating a tissue, which system applies electrical treatment energy through one or more or a plurality of electrodes defining a target treatment area of the tissue. The system comprises a computer 40 comprising: a memory 44, a display device 11, a processor 46 coupled to the memory 44 and the display device 11; and a treatment planning module 54 stored in the memory 44 and executable by the processor 46. In this embodiment, the treatment planning module 54 is adapted to: provide one or more parameters of a treatment protocol for delivering one or more electrical pulses to a tissue through one or more or a plurality of electrodes; model a heat distribution in a tissue surrounding the at least electrode based on the one or more parameters; provide a graphical representation of the heat distribution on the display device 11 based on the modeled heat distribution. The system further comprises input devices 12, 14 in operable connection with computer 40, which input devices are capable of modifying the one or more parameters of the treatment protocol in the treatment planning module 54. The system further comprises a generator 10 in operable connection with the computer through a controller 71, which controller 71 is capable of instructing the generator 10 to deliver the one or more electrical pulses to the target tissue through the one or more or the plurality of electrodes 22 based on the one or more parameters of the treatment protocol stored in the treatment planning module 54. The system may further comprise one or more databases stored in the memory 44 for storing the modeled heat distributions or modeled electric field distributions for a plurality of sets of parameters for a treatment protocol.
In another embodiment, the treatment planning module 54, in addition to providing one or more parameters of a treatment protocol for delivering one or more electrical pulses to a tissue through one or more or a plurality of electrodes, may also provide one or more conductivity parameters specific for the tissue to be treated.
The treatment planning module 54 may estimate the target ablation zone based on the one or more parameters of the treatment protocol and the one or more electrical flow characteristics. The treatment planning module may also display a graphical representation of the estimation in the display device 11.
The treatment planning module 54 may optionally allow for modification of one or more of the parameters of the treatment protocol through input devices 12, 14 based on the graphical representation of the target ablation zone.
Additionally, the treatment planning module 54 may be in operable communication with a controller 77 and provide one or more parameters to the controller for delivering one or more electrical pulses to the tissue.
The treatment planning module 54 may provide one or more parameters of a treatment protocol comprise voltage, gap between electrodes, duration, pulse width, and electric field intensity.
Additionally, the one or more conductivity parameters provided by the treatment planning module 54 may comprise the baseline conductivity of the tissue to be treated, the ratio of the baseline conductivity to the maximum conductivity of the tissue that is reached during treatment, the rate at which the conductivity increases from the baseline to the maximum conductivity, or the electric field at which the conductivity changes during treatment.
Additionally, one or more conductivity parameters for a plurality of tissues may be provided in a database stored in memory 44.
In another embodiment, the invention provides a system for treating a tissue, which system applies electrical treatment energy through one or more or a plurality of electrodes 22 defining a target treatment area of the tissue. The system may comprise a computer 40 comprising a memory 44, a display device 11, a processor 46 coupled to memory 44 and the display device 11, and a treatment planning module 54 stored in the memory 44 and executable by the processor 46. The treatment planning module 54 may be adapted to provide one or more parameters of a treatment protocol for delivering one or more electrical pulses to a tissue through one or more or a plurality of electrodes, provide one or more conductivity parameters specific for the tissue to be treated, estimate the target ablation zone and display a graphical representation of the estimation in the display device based on the one or more parameters of the treatment protocol and the one or more conductivity parameters. The system may further comprise input devices 12, 14 in operable connection with the computer 40, which input devices 12, 14 are capable of allowing a user to modify the one or more parameters of the treatment protocol in the treatment planning module 54. The system may further comprise a generator 10 in operable connection with the computer 40 through a controller 71, which controller 71 is capable of instructing the generator 10 to deliver the one or more electrical pulses to a tissue through the one or more or the plurality of electrodes 22 based on the one or more parameters of the treatment protocol stored in the treatment planning module 54. Additionally, the system may comprise a database of conductivity parameters for a plurality of tissues stored in the memory 44.
The systems of the invention may be further configured to include software for displaying a Graphical User Interface in the display device with various screens for input and display of information, including those for inputting various parameters or display of graphical representations of zones of temperature, electrical field, and ablation. Additionally, the Graphical User Interface (GUI) may allow a user to input one or more values related to an irreversible electroporation protocol and tissue-specific conductivity measurements through the use of text fields, check boxes, pull-downs, sliders, command buttons, tabs, and the like.
In one embodiment, the invention provides a method of treating a tissue with a medical treatment device that applies electrical treatment energy through one or more or a plurality of electrodes defining a target treatment area of the tissue and that comprises a display device. The method may comprise providing one or more parameters of a treatment protocol for delivering one or more electrical pulses to a tissue through one or more or a plurality of electrodes, modeling a heat distribution in a tissue surrounding the at least electrode based on the one or more parameters, displaying a graphical representation of the heat distribution based on the modeled heat distribution in the display device, modifying one or more of the parameters of the treatment protocol based on the graphical representation of the heat distribution, and implanting one or a plurality of electrodes in the tissue and delivering one or more electrical pulses to the tissue through the electrodes based on the one or more modified parameters.
In an exemplary implementation of the method, a treating physician identifies a target treatment area in a tissue of a patient. For example, the target treatment area may be a tumor that is unresectable by conventional surgical methods. The treating physician then uses input devices 12, 14 such as a keyboard or mouse to interact with the treatment planning module 54 to select and input one or more parameters for designing an irreversible electroporation treatment protocol for ablating the tumor. The treating physician then selects a temperature value to graphically display a temperature contour profile in the target treatment area on the display device 11. For example, the treating physician may select a value of 50° C. The treating physician then may correlate this temperature contour with imaging from the treatment area, by overlaying the temperature contour with the imaging on the display device 11. By visualizing the temperature contour relative to the imaging, the treating physician then may identify structures surrounding the treatment area such as nerves and blood vessels that may be subject to thermal damage. The treating physician then may modify the irreversible electroporation parameters so that the temperature contour no longer indicates that critical structures may be subject to overheating. Irreversible electroporation parameters that may be modified include the voltage, distance between electrodes, electrode diameter, period of treatment, pulse width, number of pulses, and electric field. Similarly, the treatment planning module 54 may allow the treating physician to visualize a temperature contour relative to an electric field contour. Through one or more iterations of adjustment of the irreversible electroporation parameters and visualization of the temperature contour and electric field contour on the display device, the treating physician may ultimately select a final set of irreversible electroporation parameters to be used for treatment. The treating physician may then implant a pair of electrodes at the target treatment area in the tissue and deliver a plurality of electrical pulses to the treatment area based on the final set of irreversible electroporation parameters.
Thus, one embodiment of the method may comprise one or more of: 1. identifying a target treatment area in a tissue of a patient; 2. selecting and inputting one or more parameters for designing an irreversible electroporation treatment protocol for the target treatment area; 3. selecting a temperature value to graphically display a temperature contour in a simulation of the target treatment area; 4. correlating the temperature contour with imaging from the treatment area; 5. Identifying structures within or surrounding the target treatment area such as nerves and blood vessels that may be subject to thermal damage based on the temperature contour; 6. modifying the irreversible electroporation parameters through one or more iterations so that the temperature contour no longer indicates that critical structures may be subject to overheating; 7. selecting a final set of irreversible electroporation parameters to be used for treatment; and 8. implanting a pair of electrodes at the target treatment area in the tissue and delivering a plurality of electrical pulses to the treatment area based on the final set of irreversible electroporation parameters.
The target treatment area may be imaged through a variety of imaging modalities including Computed Tomography (CT), Magnetic Resonance Imaging (MRI), Ultrasound, Positron Emission Tomography (PET), and the like. The imaging devices may be operably connected with the display device 11 so that results of the imaging may overlap or otherwise be available for comparison with the graphical display of the temperature and electric field contours.
In another embodiment, the invention provides a method of treating a tissue with a medical treatment device that applies electrical treatment energy through one or more or a plurality of electrodes defining a target treatment area of the tissue, which medical treatment device comprises a display device. The method may comprise providing one or more parameters of a treatment protocol for delivering one or more electrical pulses to a tissue through one or a plurality of electrodes, and one or more conductivity parameters specific for the tissue to be treated, estimating the target ablation zone and displaying a graphical representation of the estimation in the display device based on the one or more parameters of the treatment protocol and the one or more conductivity parameters, modifying one or more of the parameters of the treatment protocol based on the graphical representation of the target ablation zone, and implanting one or a plurality of electrodes in the tissue and delivering one or more electrical pulses to the tissue through the electrodes based on the one or more modified parameters. In the context of this specification, when referring to implanting an electrode, one or more of the electrode(s) can alternatively or in addition be placed near, or contact, or otherwise be operably disposed in a manner to administer electrical energy to the tissue.
In an exemplary implementation of the method, a treating physician identifies a target treatment area in a tissue of a patient. For example, the target treatment area may be a tumor that is unresectable by conventional surgical methods. The treating physician then uses input devices 12, 14 such as a keyboard or mouse to interact with the treatment planning module 54 to select and input one or more parameters for designing an irreversible electroporation treatment protocol for ablating the tumor. The treatment planning module 54 then graphically displays an ablation zone on the display device 11 based on the one or more parameters of the irreversible electroporation treatment protocol. The treating physician then selects one or more conductivity parameters based on the type of tissue to be treated. The one or more conductivity parameters may be tissue-specific values based on experimental data that is stored in a database in memory 44 or may be obtained by the physician and entered into the treatment planning module 54 using the keyboard or other input, such as a hands-free input. In embodiments, tissue-specific conductivity values may be provided for heart, kidney, liver, lung, spleen, pancreas, brain, prostrate, breast, small intestine, large intestine, and stomach.
The one or more conductivity parameters may include the baseline conductivity, change in conductivity, the transition zone (how rapidly the conductivity increases), the electric field at which the change in conductivity occurs, and the electric field at which irreversible electroporation occurs. After selecting the one or more conductivity parameters, the treatment planning module 54 may display a modified ablation zone on the display device 11 based on the tissue-specific conductivity characteristics inputted by the physician. The treating physician then may alter the one or more parameters of the irreversible electroporation protocol to modify the target ablation zone on the display device 11 to fit a desired area of treatment. The treating physician may then strategically place (e.g., implant) a pair of electrodes at the target treatment area in the tissue and deliver a plurality of electrical pulses to the treatment area based on the final set of irreversible electroporation parameters.
Thus, one embodiment of the method may comprise one or more of: 1. identifying a target treatment area in a tissue of a patient; 2. selecting and inputting one or more parameters for designing an irreversible electroporation treatment protocol for the target treatment area; 3. displaying a graphical representation of a target ablation zone on a display device; 4. selecting and inputting one or more conductivity characteristics based on the specific tissue to be treated; 5. displaying a modified graphical representation of the target ablation zone based on the tissue-specific conductivity characteristics; 6. modifying the one or more parameters of the irreversible electroporation protocol to fit a desired area of treatment; and 7. disposing/implanting a pair of electrodes at the target treatment area in the tissue and delivering a plurality of electrical pulses to the treatment area based on the modified IRE parameters.
As will be apparent to a skilled artisan, the systems and methods described above may be compatible with a variety of bi-polar and mono-polar probe combinations and configurations. Additionally, the calculations may be extended to not only display an electric field and temperature but also using that information to calculate an electrical damage and thermal damage component which take into account the time of exposure to the electric field and temperatures and can be tissue-specific such as for liver, kidney, etc. The systems and methods may be capable of displaying information such as “electric damage” or “thermal damage” once the electric field and temperature contours are determined, based on predetermined values for electric damage and thermal damage in the given tissue type. “Electric damage” and “thermal damage” regions can be visualized in place of or in combination with electric field and temperature as isocontour lines, shaded or highlighted areas, or other forms of graphical representation. In addition, the inclusion of tissue-specific in-vivo derived data including blood flow, metabolic heat generation, and one or more conductivity parameters such as tissue conductivity and ratios of changing conductivity can be included to reflect dynamic changes within a specific tissue type.
Additional details of the algorithms and numerical models disclosed herein will be provided in the following Examples, which are intended to further illustrate rather than limit the invention.
In Example 1, the present inventors provide a numerical model that uses an asymmetrical Gompertz function to describe the response of porcine renal tissue to electroporation pulses. However, other functions could be used to represent the electrical response of tissue under exposure to pulsed electric fields such as a sigmoid function, ramp, and/or interpolation table. This model can be used to determine baseline conductivity of tissue based on any combination of electrode exposure length, separation distance, and non-electroporating electric pulses. In addition, the model can be scaled to the baseline conductivity and used to determine the maximum electric conductivity after the electroporation-based treatment. By determining the ratio of conductivities pre- and post-treatment, it is possible to predict the shape of the electric field distribution and thus the treatment volume based on electrical measurements. An advantage of this numerical model is that it is easy to implement in computer software code in the system of the invention and no additional electronics or numerical simulations are needed to determine the electric conductivities. The system and method of the invention can also be adapted for other electrode geometries (sharp electrodes, bipolar probes), electrode diameter, and other tissues/tumors once their response to different electric fields has been fully characterized.
The present inventors provide further details of this numerical modeling as well as experiments that confirm this numerical modeling in Example 2. In developing this work, the present inventors were motivated to develop an IRE treatment planning method and system that accounts for real-time voltage/current measurements. As a result of this work, the system and method of the invention requires no electronics or electrodes in addition to the NANOKNIFE® System, a commercial embodiment of a system for electroporation-based therapies. The work shown in Example 2 is based on parametric study using blunt tip electrodes, but can be customized to any other geometry (sharp, plate, bipolar). The numerical modeling in Example 2 provides the ability to determine a baseline tissue conductivity based on a low voltage pre-IRE pulse (non-electroporating ˜50 V/cm), as well as the maximum tissue conductivity based on high voltage IRE pulses (during electroporation) and low voltage post-IRE pulse (non-electroporating ˜50 V/cm). Two numerical models were developed that examined 720 or 1440 parameter combinations. Results on IRE lesion were based on in vitro measurements. A major finding of the modeling in Example 2 is that the electric field distribution depends on conductivity ratio pre- and post-IRE. Experimental and clinical IRE studies may be used to determine this ratio. As a result, one can determine e-field thresholds for tissue and tumor based on measurements. The 3-D model of Example 2 captures depth, width, and height e-field distributions.
In Example 3, as a further extension of the inventors work, the inventors show prediction of IRE treatment volume based on 1000 V/cm, 750 v/cm, and 500 V/cm IRE thresholds as well as other factors as a representative case of the numerical modeling of the invention.
In Example 4, the inventors describe features of the Specific Conductivity and procedures for implementing it in the invention.
In Example 5, the inventors describe in vivo experiments as a reduction to practice of the invention.
In Example 6, the inventors describe how to use the ratio of maximum conductivity to baseline conductivity in modifying the electric field distribution and thus the Cassini oval equation.
In Example 7, the inventors describe the Cassini oval equation and its implementation in the invention.
In Example 8, the inventors describe mapping of electric field and thermal contours using a simplified data cross-referencing approach.
In Example 9, the inventors describe visualization of electric field distributions using different configurations of bipolar probes.
In Example 10, the inventors describe a method for determining the IRE threshold for different tissues according to one or more conductivity parameters.
In Example 11, the inventors describe correlating experimental and numerical IRE lesions using the bipolar probe.
EXAMPLES Example 1Materials And Methods
The tissue was modeled as a 10-cm diameter spherical domain using a finite element package (Comsol 4.2a, Stockholm, Sweden). Electrodes were modeled as two 1.0-mm diameter blunt tip needles with exposure lengths (Y) and edge-to-edge separation distances (X) given in Table 1. The electrode domains were subtracted from the tissue domain, effectively modeling the electrodes as boundary conditions.
The electric field distribution associated with the applied pulse is given by solving the Laplace equation:
∇·(σ(|E|)∇φ)=0 (1)
where σ is the electrical conductivity of the tissue, E is the electric field in V/cm, and φ is the electrical potential (Edd and Davalos, 2007). Boundaries along the tissue in contact with the energized electrode were defined as φ=Vo, and boundaries at the interface of the other electrode were set to ground. The applied voltages were manipulated to ensure that the voltage-to-distance ratios (W) corresponded to those in Table 1. The remaining boundaries were treated as electrically insulating, ∂φ/∂n=0.
The analyzed domain extends far enough from the area of interest (i.e. the area near the electrodes) that the electrically insulating boundaries at the edges of the domain do not significantly influence the results in the treatment zone. The physics-controlled finer mesh with ˜100,000 elements was used. The numerical models have been adapted to account for a dynamic tissue conductivity that occurs as a result of electroporation, which is described by an asymmetrical Gompertz curve for renal porcine tissue (Neal et al., 2012):
σ(|E|)=σo+(σmax−σo)exp[−A·exp[−B·E] (2)
where σo is the non-electroporated tissue conductivity and σmax is the maximum conductivity for thoroughly permeabilized cells, A and B are coefficients for the displacement and growth rate of the curve, respectively. Here, it is assumed that σo=0.1 S/m but this value can be scaled by a factor to match any other non-electroporated tissue conductivity or material as determined by a pre-treatment pulse. In this work the effect of the ratio of maximum conductivity to baseline conductivity in the resulting electric current was examined using the 50-μs pulse parameters (A=3.05271; B=0.00233) reported by Neal et al. (Neal et. al., 2012). The asymmetrical Gompertz function showing the tissue electric conductivity as a function of electric field is, for example, shown in
The current density was integrated over the surface of the ground electrode to determine the total current delivered. A regression analysis on the resulting current was performed to determine the effect of the parameters investigated and their interactions using the NonlinearModelFit function in Wolfram Mathematica 8.0. Current data from the numerical simulations were fit to a mathematical expression that accounted for all possible interactions between the parameters:
I=factor·[aW+bX+cY+dZ+e(W−
where I is the current in amps, W is the voltage-to-distance ratio [V/cm], X is the edge-to-edge distance [cm], Y is the exposure length [cm], and Z is the unitless ratio σmax/σo. The
Results.
A method to determine electric conductivity change following treatment based on current measurements and electrode configuration is provided. The best-fit statistical (numerical) model between the W, X, Y, and Z parameters resulted in Eqn. 3 with the coefficients in Table 2 (R2=0.999646). Every coefficient and their interactions had statistical significant effects on the resulting current (P<0.0001). With this equation one can predict the current for any combination of the W, Y, X, Z parameters studied within their ranges (500 V/cm≤W≤3000 V/cm, 0.5 cm≤X≤2.5 cm, 0.5 cm≤Y≤3.0 cm, and 1.0≤Z≤6.0). Additionally, by using the linear results (Z=1), the baseline tissue conductivity can be extrapolated for any blunt-tip electrode configuration by delivering and measuring the current of a non-electroporating pre-treatment pulse. The techniques described in this specification could also be used to determine the conductivity of other materials, such as non-biological materials, or phantoms.
In order to fully understand the predictive capability of the statistical (numerical) model, two cases in which the current is presented as a function of the exposure length and electrode separation are provided.
Model Assumptions:
Gompertz Conductivity: Pulse duration=50 μs, Ex-vivo kidney tissue
Baseline Conductivity: σ=0.1 S/m
Spherical Domain: diameter=10 cm
Applied Voltage: Voltage=1000 V
Parametric Study:
Total Combinations: 720 models
Maximum Conductivity: 1.0×, 1.25×, 1.5×, 2×, 3×, 4×, 5×, 6× the baseline
Edge-to-edge Distance: 5, 10, 15, 20, 25 mm
Electrode Exposure: 5, 10, 15, 20, 25, 30 mm
Electrode Radius: 0.5, 0.75, 1.0 mm
The output of statistical analysis software (JMP 9.0) used to fit model and determine the coefficients for all parameter combinations is shown in the tables of
Parameters of Best Fit for Dynamic Conductivity Changes Between 1×-6× the Baseline Conductivity (R2=0.96):
a=−1.428057; (*Intercept Estimate*)
b=−0.168944; (*Gap Estimate*)
c=2.1250608; (*Radius Estimate*)
d=0.2101464; (*Exposure Estimate*)
e=1.1114726; (*Factor Estimate*)
f=−0.115352; (*Gap-Radius Estimate*)
g=−0.010131; (*Gap-Exposure Estimate*)
h=−0.067208; (*Gap-Factor*)
i=0.0822932; (*Radius-Exposure Estimate*)
j=0.4364513; (*Radius-Factor Estimate*)
k=0.0493234; (*Exposure-Factor Estimate*)
l=−0.006104; (*Gap-Radius-Exposure Estimate*)
m=0.0165237; (*Radius-Exposure-Factor Estimate*)*)
n=−0.003861; (*Gap-Exposure-Factor Estimate*)
o=−0.041303; (*Gap-Radius-Factor Estimate*)
p=−0.002042; (*Gap-Radius-Exposure-Factor Estimate*)
Analytical Function for Dynamic Conductivity Changes Between 1×-6× the Baseline Conductivity (R2=0.96):
5 mm<gap=x<25 mm, 0.5 mm<radius=y<1.0 mm,
5 mm<exposure=z<30 mm, 1<factor=w<6
Default conductivity of 0.1 S/m and 1000 V which can be scaled for dynamic conductivities. The function is a linear combination of all iterations examined in the parametric study:
Current(w,x,y,z)=a+bx+cy+dz+ew+f(x+bb)(y+cc)+g(x+bb)(z+dd)+h(x+bb)(w+e e)+i(y+cc)(z+dd)+j(y+cc)(w+ee)+k(z+dd)(w+ee)+l(x+bb)(y+cc)+m(y+cc)(z+dd)(w+ee)+n(x+bb)(z+dd)(w+ee)+o(x+bb)(y+cc)(w+ee)+p(x+bb)(y+cc)(z+dd)(w+ee)
Determining the Relationship Between Blunt Tip Electrode Configuration and e-Field Distribution after IRE Treatment
Model Assumptions:
Gompertz Conductivity: Pulse duration=50 μs, Ex-vivo kidney tissue
Baseline Conductivity: σ=0.1 S/m
Spherical Domain: diameter=10 cm
Electrode Radius: r=0.5 mm
Parametric Study:
Total Combinations: 1440 models
Maximum Conductivity: 1.0×, 1.25×, 1.5×, 2×, 3×, 4×, 5×, 6× the baseline
Edge-to-edge Distance: 5, 10, 15, 20, 25 mm
Electrode Exposure: 5, 10, 15, 20, 25, 30 mm
Voltage-to-distance Ratio: 500, 1000, 1500, 2000, 2500, 3000 V/cm
Example 3Comparison of analytical solutions with statistical (numerical) model to calculate current and explanation of procedure that results in 3D IRE volume.
The process of backing-out the electrical conductivity using the analytical solutions and the one proposed in the “Towards a Predictive Model of Electroporation-Based Therapies using Pre-Pulse Electrical Measurements” abstract presented in the IEEE Engineering in Medicine and Biology Conference in Aug. 28, 2012 in San Diego, Calif. were compared. A method to determine the predictive power of the equations to calculate current is analyzing the residuals of the 1440 combinations of parameters examined. In the context of this specification, a residual is the difference between the predicted current and the actual current. As can be seen in
In terms of the prediction of the volume treated a representative method is to map out the electric field 5 cm in the directions along the (x,0,0), (0,y,0), and (0,0,z) axes from the origin. In addition, the electric field can be extracted along a line that starts at the origin and ends at 3 cm along each of the axes. These plots contain the information for determining the distances at which a particular IRE threshold occurs. In embodiments, 1440 different parameter combinations were simulated that resulted in data sets of 28,692 (x-direction), 20,538 (y-direction), 27,306 (z-direction), and 25,116 (xyz-direction) for homogeneous conductivity. Even though these simulations only include dynamic conductivity changes due to electroporation, it is believed that an identical analysis for simulations that also include the changes in conductivity due to temperature could also be performed. In this manner, it would be possible to determine irreversible electroporation thresholds as a function of temperature and electroporation. Manipulating these large data sets is challenging but it provides all the necessary information to study the effect of electrode separation, electrode length, dynamic conductivity factor, and voltage-to-distance ratio for any position along the described paths. In order to be able to manipulate the data and extract the distance for different IRE thresholds, the function NonlinearModelFit (Mathematica) was used in order to come up with analytical expressions that would closely match the electric field. A different function was used for each of the directions studied in the positive directions along the Cartesian coordinate system. The Micheilis Menten function was used along the x-direction (R2=0.978978), the analytical solution to the Laplace equation along the y-direction (R2=0.993262), and the Logistic equation in the z-direction (R2=0.983204). Each of those functions was scaled by a 3rd order polynomial function that enabled the fit to incorporate the electrode separation and electrode exposure as well. Even though the described functions were used to fit the data from the numerical data, there might be other functions that are also appropriate and this will be explored further in order to use the most reliable fit. In
The following functions describe the electric field [V/cm] distributions along the x-axis (Ex), y-axis (Ey), and z-axis (E7) as a function of voltage-to-distance (W), edge-to-edge separation between the electrodes (X), exposure length (Y), maximum conductivity to baseline conductivity (Z), and distance in the x-direction (xx), y-direction (yy), and z-direction (zz).
Micheilis Menten Equation (Electric Field in the x-Direction)
Ex(W,X,Y,Z,xx)=W*(a*Exp[−b·xx]+c)*(dX3+eX2fX+gY3hY2+iY+j)+k
The coefficients for the NonlinearModelFit are given below:
a=−0.447392, b=8.98279, c=−0.0156167, d=−0.0654974, e=0.468234, f=−6.17716, g=0.326307, h=−2.33953, I=5.90586, j=−4.83018, k−9.44083
Laplace Equation (Electric Field in the y-Direction)
The coefficients for the NonlinearModelFit are given below:
a=−56.6597, b=−42.9322, c=6.66389, d=−50.8391, e=141.263, f=138.934, g=0.00417123, h=0.184109
Logistic Equation (Electric Field in the z-Direction)
The coefficients for the NonlinearModelFit are given below:
a=49.0995, b=−0.00309563, c=1.39341, d=4.02546, e=1.24714, f=0.276404, g=−1.84076, h=4.93473, I=−9.13219, j=0.699588, k=−5.0242, I=12.8624, m=19.9113.
In order to visualize the predicted IRE shape the equation of an ellipsoid was used and the semi-axes were forced to intersect with the locations at which the IRE threshold wants to be examined. Therefore, the provided functions can be adjusted in real-time to display the IRE volume for any electric field threshold. This is important since different tissues have different IRE thresholds that depend on the temperature, dielectric properties of the tissue, the electrode configuration, and the pulse parameters used. Once again, even though the equation for an ellipsoid is used to represent the IRE volume, other functions may be evaluated that may also be appropriate to replicate the morphology of the zones of ablation being achieved experimentally such as the Cassini curve. A 1500 V/cm was used as the voltage-to-distance ratio, electrode exposure 2 cm, and electrode separation 1.5 cm to generate 3 different IRE zones using 1000 V/cm, 750 V/cm, and 500 V/cm as the IRE thresholds with z=1.
From the 3D plots representing the zones of ablation shown in
Specific Conductivity
Specific conductivity can be important in embodiments for treatment planning of irreversible electroporation (IRE). For many applications, especially when treating tumors in the brain, the volume (area) of IRE should be predicted to maximize the ablation of the tumorous tissue while minimizing the damage to surrounding healthy tissue. The specific electrical conductivity of tissue during an irreversible electroporation (IRE) procedure allows the physicians to: determine the current threshold; minimize the electric current dose; decrease the Joule heating; and reduce damage to surrounding healthy tissue. To measure the specific conductivity of tissue prior to an IRE procedure the physician typically performs one or more of the following: establishes the electrode geometry (shape factor); determines the physical dimensions of the tissue; applies a small excitation AC voltage signal (1 to 10 mV); measures the AC current response; calculates the specific conductivity (σ) using results from the prior steps. This procedure tends to not generate tissue damage (low amplitude AC signals) and will supply the physician (software) with the required information to optimize IRE treatment planning, especially in sensitive organs like the brain which is susceptible to high electrical currents and temperatures. Thus, the IRE procedure is well monitored and can also serve as a feedback system in between series of pulses and even after the treatment to evaluate the area of ablation.
Special Cases for electrode geometry
Nomenclature (units in brackets):
Ve=voltage on the hot electrode (the highest voltage), [V]
G=electroporation voltage gradient (required for electroporation), [V/m]
R1=radius of electrode with highest voltage (inner radius), [m]
R2=radius at which the outer electrodes are arranged (outer radius), [m]
i=total current, [A]
L=length of cylindrical electrode, [m]
A=area of plate electrode, [m2]
σ=electrical conductivity of tissue, [S/m]
ρ=density
c=heat capacity
Case 1
Electrical conduction between a two-cylinder (needle) arrangement of length L in an infinite medium (tissue). It is important to note that this formulation is most accurate when L>>R1,R2 and L>>w. The electrical conductivity can be calculated from,
where the shape factor (S) corresponding to the electrode dimensions and configuration is given by,
Case 2
Cylindrical arrangement in which the central electrode is a cylinder (needle) with radius R1 and the outer electrodes are arranged in a cylindrical shell with a shell radius of R2 (not the radius of the electrodes). The voltage on the central electrode is Ve. The voltage distribution in the tissue may be determined as a function of radius, r:
The required voltage on the central electrode to achieve IRE:
The required current on the central electrode:
The specific conductivity (a) of the tissue can be calculated since the voltage signal (Ve) and the current responses (i) are known.
Explanation of electrical concepts.
By using the bipolar electrode described previously in US Patent Application Publication No. 2010/0030211 A1, one can apply a small excitation AC voltage signal (for example from about 1 to 10 mV),
V(t)=V0 Sin(ωt)
where V(t) is the potential at time t, V0 is the amplitude of the excitation signal and w is the frequency in radians/s. The reason for using a small excitation signal is to get a response that is pseudo-linear since in this manner the value for the impedance can be determined indicating the ability of a system (tissue) to resist the flow of electrical current. The measured AC current (response) that is generated by the excitation signal is described by
I(t)=I0 Sin(ωt+θ)
where I(t) is the response signal, I0 is the amplitude of the response (I0≠V0) and θ is the phase shift of the signal. The impedance (Z) of the system (tissue) is described by,
Z=(V(t))/(I(t))=(V0 Sin(ωt))/(I0 Sin(ωt+θ))=Z0(Sin(ωt))/(Sin(ωt+θ))
It is important to note that the measurement of the response is at the same excitation frequency as the AC voltage signal to prevent interfering signals that could compromise the results. The magnitude of the impedance |Z0| is the electrical resistance of the tissue. The electrical resistivity (Ω m) can be determined from the resistance and the physical dimensions of the tissue in addition to the electrode geometry (shape factor). The reciprocal of the electrical resistivity is the electrical conductivity (S/m). Therefore, after deriving the electrical resistivity from the methods described above, the conductivity may be determined.
As described in U.S. Patent Application No. 61/694,144 the analytical solution (Table 4) assumes that the length of the electrodes is much larger than the electrode radius or separation distance between the electrodes. Additionally, the analytical solution is not capable of capturing the non-linear electrical response of the tissue during electroporation procedures. The proposed statistical algorithm (Table 3) is preferably used in order to capture the response in treatments that are being conducted clinically and show how the analytical overestimates the baseline and maximum current that uses the experimental data.
In Vivo Experiments
1) Animals.
IRE ablations were performed in canine kidneys in a procedure approved by the local animal ethics committee. Male canines weighing approximately 30 kg were premedicated with acetylpromazine (0.1 mg/kg), atropine (0.05 mg/kg), and morphine (0.2 mg/kg) prior to general anesthesia induced with propofol (6 mg/kg, then 0.5 mg/kg/min) and maintained with inhaled isofluorane (1-2%). Anesthetic depth was monitored by bispectral index monitoring (Covidien, Dublin, Ireland) of EEG brain activity. After ensuring adequate anesthesia, a midline incision was made and mesenchymal tissue was maneuvered to access the kidney. Pancuronium was delivered intravenously to mitigate electrically mediated muscle contraction, with an initial dose of 0.2 mg/kg, and adjusted if contractions increased.
2) Experimental Procedure.
Two modified 18 gauge needle electrodes (1.0 mm diameter and 1.0 cm in exposure) were inserted as pairs into the superior, middle, or inferior lobe of the kidney, with lobes being randomly selected. A BTX ECM830 pulse generator (Harvard Apparatus, Cambridge, Mass.) was used to deliver an initial 100 μs pre-pulse of 50 V/cm voltage-to-distance ratio (center-to-center) between the electrodes to get an initial current able to be used to determine baseline conductivity. Electrical current was measured with a Tektronix TCP305 electromagnetic induction current probe connected to a TCPA300 amplifier (both Tektronix, Beaverton, Oreg.). A Protek DSO-2090 USB computer-interface oscilloscope provided current measurements on a laptop using the included DSO-2090 software (both GS Instruments, Incheon, Korea). A schematic of the experimental setup can be found in
3) Kidney Segmentation and 3D Reconstruction.
Numerical models provide an advantageous platform for predicting electroporation treatment effects by simulating electric field, electrical conductivity, and temperature distributions. By understanding the electric field distribution, one can apply an effective lethal electric field threshold for IRE, EIRE, to predict ablation lesion dimensions under varying pulse protocols (electrode arrangements and applied voltages). However, in order to do so, these models should first be calibrated with experimental data. Here, the numerical simulation algorithm developed from porcine kidneys was expanded that accounts for conductivity changes using an asymmetrical sigmoid function (R. E. Neal, 2nd, et al., “Experimental characterization and numerical modeling of tissue electrical conductivity during pulsed electric fields for irreversible electroporation treatment planning,” IEEE Trans Biomed Eng., vol. 59, pp. 1076-85. Epub 2012 Jan. 6, 2012 (“R. E. Neal, 2nd, et al., 2012”)). The model is calibrated to the experimental lesions to determine an effective electric field threshold under the three experimental setups used. In addition, static and linear conductivity functions are also correlated to the lesion dimensions. The three functions are used to evaluate which numerical technique will result in better accuracy in matching lesion shapes and resulting current from actual IRE ablations in mammalian tissue, particularly for kidney.
The imaging-based computational model domains were constructed from a magnetic resonance imaging (MRI) scan of a kidney from a canine subject of similar size to those in the study. The scans were scaled by 1.21 times in all directions to better match the experimental kidney dimensions while maintaining the anatomical characteristics. Mimics 14.1 image analysis software (Materialise, Leuven, BG) was used to segment the kidney geometry from the surrounding tissues. The kidney was traced in each of the two-dimensional (2D) MRI axial slices, which were then integrated into a three-dimensional (3D) solid representation of the kidney volume which was refined and exported to 3-matic version 6.1 (Materialise, Leuven, BG) to generate a volumetric mesh compatible with Comsol Multiphysics finite element modeling software (Comsol Multiphysics, v.4.2a, Stockholm, Sweden).
Electrodes were simulated as paired cylinders, each 1 cm long and 1 mm in diameter, and separated by 1 or 1.5 cm to represent the two experimental conditions. The pairs were inserted into the 3D kidney mesh in two configurations, representing both experimental approaches that used either the superior/inferior (vertical) or middle (horizontal) lobe of the kidney, both with tips 1.5 cm deep. The finite element model simulated the electric field distribution in the kidney, which was used to determine cell death EIRE by correlating the electric field values with the average in vivo lesion height and width dimensions.
4) Electric Field Distribution and Lethal EIRE Determination.
The electric field distribution is determined according to
−∇·(σ(|E|)∇ϕ)=0 (1)
where σ is the electrical conductivity of the tissue, E is the electric field in V/cm, and ϕ is the electrical potential. Tissue-electrode boundaries for the cathode and anode were defined as ϕ=Vo and ground, respectively. The remaining boundaries were treated as electrically insulating, dϕ/dn=0, since the kidneys were isolated from the surrounding mesenchymal tissue during the experimental procedures. The current density was integrated over a mid-plane parallel to both electrodes to determine simulated electric current.
The model was solved for the vertical and horizontal electrode configurations, each considering three electrical conductivity tissue responses. These responses included a homogeneous static conductivity (σ0) as well as two that accounted for electroporation based conductivity changes in tissue that result from cell membrane permeabilization. The dynamic models are based on a relationship between a minimum baseline and a maximum conductivity. The static conductivity model was used to determine the baseline conductivity, σ0, by matching simulated electrical current with the pre-pulse experimental data, where the field strength should be below that able to permeabilize any cells in the tissue. The maximum conductivity, σmax, occurs when the number of cells electroporated in the tissue has saturated, and the cellular membranes no longer restrict the extent of interstitial electrolyte mobility. The statistical model discussed in (P. A. Garcia, et al., “Towards a predictive model of electroporation-based therapies using pre-pulse electrical measurements,” Conf Proc IEEE Eng Med Biol Soc, vol. 2012, pp. 2575-8, 2012 (“P. A. Garcia, et al., 2012”)) was used to predict σmax from previously characterized tissue response to pre-pulse σ0 and electrical data.
The σ0 and σmax values provide the required parameters to define the electric field-dependent conductivity, σ(|E|), of renal tissue in vivo. One model assumed a linear relationship that grew between the minimum and maximum conductivities over a range from 200 to 2000 V/cm, σL|E|), and the second used an asymmetrical sigmoid Gompertz curve, σS(|E|), derived from the work described in (R. E. Neal, 2nd, et al., 2012) using the equation:
σs(|E|)=σ0+(σmax−σ0)·exp[−A·exp(−B·E)] (2)
where A and B are unitless coefficients that vary with pulse length, t(s). This function was fit using curve parameters for a 100 μs long pulse, where A=3.053 and B=0.00233 (R. E. Neal, 2nd, et al., 2012)
The electric field distribution along a width and height projection based at the midpoint length of the electrodes was used to determine the electric field magnitude that matched experimental lesion dimensions. This was performed for all three conductivity scenarios in all three experimental protocol setups in order to determine which model best matched the IRE ablations, providing the optimum conductivity modeling technique for mammalian tissue.
5) Results: In Vivo Experiments.
Electrical Currents.
All animals survived the procedures without adverse event until euthanasia. Electrical pre-pulse currents were 0.258±0.036 A (mean±SD) for the 1 cm electrode separation trials and 0.343±0.050 A for the 1.5 cm separation trials. Electrical currents from the trials for pulses 1-10, 40-50, and 90-100 are reported in Table 6. Although currents are typically reported to increase with consecutive pulses, there is no statistically significant correlation between pulse number and measured current. Therefore, all numerical calibrations to match electrical current and determine σmax used the average current from all captured pulses for each experimental setup.
6) Determination of Dynamic Conductivity Function.
Pre-pulse electrical current was used to calculate the baseline conductivity, σ0, used in the static numerical simulation. In addition, the baseline and maximum, σmax, electrical conductivities required for generating the asymmetrical sigmoid and linear dynamic conductivity functions were calculated according to the procedure outlined in (P. A. Garcia, et al., 2012) and are provided in Table 7. The ratio between these conductivities was calculated and demonstrates an increase in conductivity between 2.09 and 3.15 times, consistent with values determined in the literature for other organs (N. Payselj, et al., “The course of tissue permeabilization studied on a mathematical model of a subcutaneous tumor in small animals,” IEEE Trans Biomed Eng, vol. 52, pp. 1373-81, August 2005).
How to Use the Ratio of Maximum Conductivity to Baseline Conductivity in Modifying the Electric Field Distribution and Thus the Cassini Oval Equation.
Irreversible electroporation (IRE) is a promising new method for the focal ablation of undesirable tissue and tumors. The minimally invasive procedure involves placing electrodes into the region of interest and delivering a series of low energy electric pulses to induce irrecoverable structural changes in cell membranes, thus achieving tissue death. To achieve IRE, the electric field in the region of interest needs to be above a critical threshold, which is dependent on a variety of conditions such as the physical properties of the tissue, electrode geometry and pulse parameters. Additionally, the electric conductivity of the tissue changes as a result of the pulses, redistributing the electric field and thus the treatment area. The effect of a dynamic conductivity around the electrodes where the highest electric fields are generated was investigated in order to better predict the IRE treatment for clinical use.
The electric field distribution associated with the electric pulse is given by solving the governing Laplace equation, ∇·(σ∇φ)=0, where σ is the tissue electrical conductivity (baseline 0.2 S/m) and φ the electrical potential (3000 V). The dynamic changes in electrical conductivity due to electroporation were modeled with the flc2hs Heaviside function within the finite element modeling software used in the study (Comsol Multiphysics 3.5a, Stockholm, Sweden). The dynamic conductivity factor ranged between 2.0-7.0 times the baseline value in the regions exceeding 3000 V/cm. The total electrical current, volumes, and lesion shapes from the IRE treatment were evaluated.
A method to predict IRE lesions and incorporate the dynamic changes in conductivity due to electroporation around the electrodes is presented in this example. This procedure provides additional tools to better approximate the electric field distributions in tissue and thus help to generate more reliable IRE treatment planning for clinical use using Finite Element Analysis (FEA) models.
Specifically in order to adapt the Cassini Oval to match experimental lesions or electric field distributions the following procedure should be used:
In IRE treatments, the electric field distribution is the primary factor for dictating defect formation and the resulting volume of treated tissue (J. F. Edd and R. V. Davalos, “Mathematical modeling of irreversible electroporation for treatment planning,” Technol Cancer Res Treat, vol. 6, pp. 275-286, 2007; D. Sel, et al., “Sequential finite element model of tissue electropermeabilization,” IEEE Trans Biomed Eng, vol. 52, pp. 816-27, May 2005; S. Mahnic-Kalamiza, et al., “Educational application for visualization and analysis of electric field strength in multiple electrode electroporation,” BMC Med Educ, vol. 12, p. 102, 2012 (“S. Mahnic-Kalamiza, et al., 2012”)). The electric field is influenced by both the geometry and positioning of the electrodes as well as the dielectric tissue properties. Additionally, altered membrane permeability due to electroporation influences the tissue conductivity in a non-linear manner. Therefore numerical techniques are preferably used to account for different electrode configurations and incorporate tissue-specific functions relating the electrical conductivity to the electric field distribution (i.e. extent of electroporation). The inventors are currently using imaging-based computational models for IRE treatment planning that use the physical properties of the tissue and patient-specific 3D anatomical reconstructions to generate electric field distributions (P. A. Garcia, et al., “Non-thermal irreversible electroporation (N-TIRE) and adjuvant fractionated radiotherapeutic multimodal therapy for intracranial malignant glioma in a canine patient,” Technol Cancer Res Treat, vol. 10, pp. 73-83, 2011 (“P. A. Garcia, et al, 2011”)).
Oftentimes in clinical practice, there is need to rapidly visualize the estimated zone of ablation without relying on complex and time consuming numerical simulations. As an alternative, analytical solutions are powerful techniques that provide valuable insight and offer the ability to rapidly visualize electric field distributions (S. Mahnic-Kalamiza, et al., 2012). However, these analytical solutions assume infinitely long electrodes which are not the case in clinical practice and do not incorporate the non-linear changes in tissue conductivity due to electroporation. Therefore, there is a need for simple, quick, and accurate methods to provide physicians with predicted IRE zones of ablation during surgery when one of the pulse parameters needs to be adjusted. To this end, the inventors have adapted the Cassini curve in an effort to provide researchers and physicians with a graphical representation of IRE zones of ablation, for example, in in vivo porcine liver. The goal of this work is to provide a correlation between experimentally produced zones of ablations in in vivo porcine liver tissue with the corresponding IRE pulse parameters and electrode configuration. These Cassini curves are calibrated to experimental IRE ablations, and incorporate the dynamic changes in tissue conductivity, a limitation of the analytical approach.
The Cassini oval is a plane curve that derives its set of values based on the distance of any given point, a, from the fixed location of two foci, q1 and q2, located at (x1, y1) and (x2, y2). The equation is similar to that of an ellipse, except that it is based on the product of distances from the foci, rather than the sum. This makes the equation for such an oval
└(x1−a)2+(y1−a)2┘·└(x2−a)2+(y2−a)2┘=b4 (3)
where b4 is a scaling factor to determine the value at any given point. For incorporation of this equation into shapes that mimic the electric field distribution, it is assumed that the two foci were equidistantly located on the x-axis at (±x,0). The flexibility of the Cassini curve is crucial since it allows for fitting a wide range of shapes by adjusting the ‘a’ and/or ‘b’ parameters from Equation 3 simultaneously and fitting them to the experimental lesion dimensions or the locations at which a particular electric field value results from the computational simulations. The new approach in this analysis is that it is not assumed that the parameter ‘a’ is related to the separation distance between the electrodes used in IRE treatments for example but will be a second parameter to match the width/depth of any distribution thus allowing for more flexibility between the shapes achieved with the Cassini Oval as can be seen in
The in vivo experimental data in porcine liver was provided from published studies performed at the Applied Radiology Laboratory of Hadassah Hebrew University Medical Center (P. A. Garcia, et al., 2011). All experiments were performed with Institutional Animal Care and Use Committee approval from the Hebrew University Medical Center. The treatments were performed with a two-needle electrode configuration, 1.5 cm center-to-center separation, 2.0 cm electrode exposure, and an applied voltage of 2250 V. In this paper we only evaluate the effect of pulse number and pulse duration on the resulting ‘a’ and ‘b’ parameters required to fit the IRE zones of ablation with the Cassini curve. The NonlinearModelFit function in Wolfram Mathematica 9 was used to determine the ‘a’ and ‘b’ parameters (average±standard deviation) for each pulse parameter resulting in three curves for each condition. This same technique can be used to fit the ‘a’ and ‘b’ parameters to match the electric field shape at any particular electric field value as well thus providing an avenue to capture the shape for any IRE lesion independent of the tissue or patient.
The NonlinearModelFit results for the ‘a’ and ‘b’ parameters to generate the Cassini curves are provided in
In mathematics, a Cassini oval is a set (or locus) of points in the plane such that each point p on the oval bears a special relation to two other, fixed points q1 and q2: the product of the distance from p to q1 and the distance from p to q2 is constant. That is, if the function dist(x,y) is defined to be the distance from a point x to a point y, then all points p on a Cassini oval satisfy the equation:
dist(q1,p)×dist(q2,p)=b2 (2)
where b is a constant.
Nevertheless, in embodiments the ‘b’ parameter can be modified to manipulate the shape of the Cassini curve and illustrate the desired electric field distribution. Therefore, the ‘b’ is a variable parameter that is determined based on the specific location (distance) of a particular electric field threshold to be displayed.
The points q1 and q2 are called the foci of the oval.
Suppose q1 is the point (a,0), and q2 is the point (−a,0). Then the points on the curve satisfy the equation:
((x−a)2+y2)((x+a)2+y2)=b4 (3)
The equivalent polar equation is:
r4−2a2r2 cos 2θ=b4−a4 (4)
The shape of the oval depends on the ratio b/a. When b/a is greater than 1, the locus is a single, connected loop. When b/a is less than 1, the locus comprises two disconnected loops. When b/a is equal to 1, the locus is a lemniscate of Bernoulli.
The Cassini equation provides a very efficient algorithm for plotting the boundary line of the treatment zone that was created between two probes on grid 200. By taking pairs of probes for each firing sequence, the first probe is set as qi being the point (a,0) and the second probe is set as q2 being the point (−a,0). This original Cassini oval formulation was revised by modifying the assumption of the ‘a’ parameter being related to the position of the electrodes. In the revised formulation the ‘a’ is a variable parameter that is adjusted depending on the width and length of the Cassini oval in order to intercept the zone of ablation in the x- and y-directions.
In summary, the ‘a’ and ‘b’ variable parameters should be determined in order to have the ability to generate a Cassini curve that could fit the shape of any electric field isocontour. Specifically from the electric field simulations or experimental irreversible electroporation zones of ablation the user should determine the distance along the x-axis and y-axis that the Cassini curve should intersect.
For example in the case of a Finite Element Analysis (FEA) simulation using two 1-mm in diameter electrodes, separated by a center-to-center distance of 2.0 cm, 1.5 cm in exposure, and an applied voltage of 3000 V to one electrode and ground to the other electrode the distances from the point in between the electrodes to a specific electric field contour is given below (Table 8 for the baseline (non-electroporated) and σmax/σ0=3.6 (electroporated) models.
Using the 500 V/cm electric field isocontour as an example it can be determined that the Cassini oval using the baseline model will intersect the points (1.70,0) and (0,0.49) and the model using σmax/σ0=3.6 will intersect the point (1.99,0) and (0,1.01). Using the two points that will be intersected by the Cassini oval of each specific model type (non-electroporated vs. electroporated) allows for determination of the ‘a’ and ‘b’ variable parameter and still satisfy the mathematical condition outlined above in the first paragraph of this section by way of least square fits such as the NonlinearModelFit function in Mathematica or via interpolation tables as the one presented below.
The interpolation method involves assuming values for the ‘a’ parameter from 0.00 cm to 3.00 cm in steps of 0.01 cm and calculating the ‘b’ parameter using the specific points from the previous paragraph. The distance and steps were arbitrarily chosen and can vary depending on the specific Cassini oval that is being developed. In the case of Table 9 the point p1x=(1.70 cm, 0 cm) and the point p2y=(0 cm, 0.49 cm) and the corresponding distances to either q1 (−a,0) or q2 (a,0) are calculated.
In the baseline case analyzed above when the variable parameter ‘a’ was 1.15 cm the calculated b2 were 1.568 and 1.563 for the d1*d2 and d3*d4, respectively. The last column calculates the ratio of both b2 values in order to determine the location at which they are the same (or closest) which happens when (d1*d2)/(d3*d4)=1.00.
Once it is determined that ‘a’=1.15 cm provides the closest ratio to one, the average of the d1*d2 (1.568) and d3*d4 (1.563) quantities is calculated and used to determine the corresponding ‘b’ parameter by taking the square root as shown in the equation below.
Once the ‘a’ and ‘b’ parameters are determined then any plotting software can be used to illustrate the Cassini curve in Cartesian coordinates using the modified equation
The steps outlined in the previous paragraphs just above can also be used to determine the ‘a’ and ‘b’ parameters using the same methodology and with points p3x=(1.99 cm, 0 cm) and p4y=(0 cm, 1.01 cm) and results in ‘a’=1.21 cm and ‘b’=1.578 cm as the Cassini parameters for the electroporated model when σmax/σ0=3.6.
In
The polar equation for the Cassini curve could also be used because since it provides an alternate method for computation. The current Cartesian coordinate algorithm can work equally as well by using the polar equation of the Cassini curve. By solving for r2 from eq. (4) above, the following polar equation was developed:
r2=a2 cos(2*theta)+/−sqrt(b4−a4 sin2(2*theta)) (5)
and the ‘a’ and ‘b’ parameters should be determined as previously described in this application.
Example 8: Mapping of Electric Field and Thermal Contours Using a Simplified Data Cross-Referencing ApproachThis method can be used to identify the volume of tissue which will be elevated above a specific temperature (e.g. 45° C.) for specific treatment parameters. This contour can then be correlated with electric field intensity. This data in turn can be used to fit a contour using the Cassini oval software in the NANOKNIFE® System.
Methods: A mathematical model was built with COMSOL Multiphysics (Version 4.2a, Comsol Inc., Burlington, Mass., USA) to estimate the temperature rise within tissue due to Joule heating effects. The electric field distribution within the simulation domain was solved using the Joule Heating module, as described by the Laplace Equation:
∇2ϕ=0
where ϕ is the electric potential, this equation is solved with boundary conditions:
{right arrow over (n)}·{right arrow over (J)}=0 at the boundaries
ϕ=Vin at the boundary of the first electrode
ϕ=0 at the boundary of the second electrode
wherein {right arrow over (n)} is the normal vector to the surface, {right arrow over (J)} is the electrical current and Vin is the electrical potential applied. Heat transfer in the solid domain was calculated as:
where ρ is the density, Cp is the heat capacity, k is the thermal conductivity, Qjh and are the resistive losses
where J is the induced current density
and σ is the tissue conductivity and E is the electric field
To account for the pulsed nature of the applied electric field, the Joule heating term in COMSOL was adjusted by adding in a duty cycle term equal to 100×10-6, the pulse duration (100 μs) (See P. A. Garcia, et al., “A Parametric Study Delineating Irreversible Electroporation from Thermal Damage Based on a Minimally Invasive Intracranial Procedure,” Biomed Eng Online, vol. 10, p. 34, Apr. 30 2011).
In the Joule Heating Model equation view, the equation for resistive losses was modified to:
jh.Qrh=((jh.Jix+jh.Jex)*duty_cycle*jh.Ex+(jh.Jiy+jh.Jey)*duty_cycle*jh.Ey+(jh.Jiz+jh.Jez)*duty_cycle*jh.Ez)*)t<=90)+0*(t>90)
The resulting behavior was to calculate Joule heating only for the first 90 seconds (Ninety pulses of 100 μs each) of the simulation, after which, heat was allowed to dissipate within the tissue domain without additional heating. The parameters used in the simulations are provided in Table 11 below.
Results: The COMSOL model was used to solve for temperature distributions at times between 0 and 900 seconds (10 second increment 0-100 s, 100 second increment 100-900 seconds). Electric Field and Temperature distributions were exported along lines on the x-(width) and y-axis (depth) with 100 micrometer spacing between data points. These values were imported into Excel and used as the basis for the Cassini oval calculations.
The Cassini oval spreadsheet has been programmed so that the user can plot contour lines for specified voltages (500, 1000, 1500, 2000, 2500, 3000 V), electrode separations (0.5, 1.0, 1.5, 2.0, 2.5 cm), Simulation times (0-900 seconds), Temperatures (37-Tmax ° C.), and electric field intensities (0-infinity V/cm).
The Cassini oval approximation can also be used to investigate the contours of any temperature.
The Cassini oval approximation tool provides a rapid method for determining the temperature distribution expected for a given set of treatment parameters (
Additional examples of usage of the Cassini oval approximation tool are shown in the following figures.
Model Limitations: This model was designed to give a rapid approximation for the temperature distribution within a volume of tissue without the need for complex finite element simulations. The data used to fit the Cassini oval curves uses values calculated assuming a constant conductivity of 0.2 S/m. This represents an approximate conductivity of human tissue, though conductivities of tissue vary between patients, tissue types, locations, and pathologies. Changing conductivity due to temperature increases or electroporation effects were not included.
The effects of blood flow and perfusion through the tissue, metabolic heat generation, or diffusion of heat at the tissue domain boundaries were not considered. It is anticipated that these effects will result in lower temperatures. Therefore, the visualization tool provides a conservative (worst case scenario) estimate as to the zones exposed to critical temperatures. The effects of changing conductivity and conductivities other than 0.2 S/m were not considered. Elevated conductivities are anticipated to result in higher temperatures within the tissue. Blood flow, metabolic heat generation, tissue conductivity, and ratios of changing conductivity are tissue type specific and will require the inclusion of in-vivo derived data.
Conclusions: In this Example, a real time visualization package plots the isocontour lines for an arbitrary temperature and electric field based on applied voltage, electrode spacing, and time. This data can be used to build intuition and instruct clinicians on reasonable expectations of temperature increases to prevent damage to critical structures of organs in the proximity of the treatment.
Example 9: Visualization of Electric Field Distributions Using Different Configurations of Bipolar ProbesIn this Example, as shown in the following figures, the “Goldberg” data (red-dashed line), is from pre-clinical data for a particular treatment (2700V, 90 pulses, 100 μs energized per pulse). By adjusting one or more treatment parameters, a user can determine the electric field threshold for these types of tissues (black-solid line).
An important aspect of this model is that the tissue conductivity is allowed to change as a function of electric field to simulate what happens when the tissue becomes irreversibly electroporated. This function is ‘sigmoidal’ or ‘S’ shaped and increases from a baseline (non-electroporated) to a conductivity multiplier (electroporated). This transition happens at a specific electric field intensity.
In
IRE Threshold [V/cm]: This parameter is the electric field at which the change in conductivity occurs for the sigmoidal curve. By changing this value, the sigmoidal curve shifts to the left or right. A value of 500 V/cm has been found to fit the data best.
Transition zone: This is the ‘width’ of the transition zone. By changing this value, the rate at which the conductivity increase changes. In
Sigma: This is the baseline conductivity before treatment. It has been found that a value of 0.067 (or 0.1) works well.
Conductivity Multiplier: This is how much the conductivity increases by when the tissue has been irreversibly electroporated. A 3.6× increase has been found experimentally for liver and fits the data well.
E-Field: This is the parameter that is adjusted to find the in-vivo irreversible electroporation threshold. With the values set for the other parameters above, it has been found that IRE should occur at a threshold of 580 V/cm to match the lesions found in-vivo.
The following figures show how modifying the conductivity of the tissue changes the calculated zone of ablation.
As can be seen, the calculated ablation zone increases in comparison to the Goldberg preclinical data as the conductivity multiplier increases.
Example 11: Correlating Experimental and Numerical IRE Lesions Using the Bipolar ProbePurpose: To establish a function that correlates experimentally produced zones of ablations in in vivo porcine tissue with the corresponding IRE pulse parameters (duration, number, strength) and single needle electrode configuration.
A mathematical function was developed that captures the IRE response in liver tissue as a function of applied voltage, pulse number, and pulse duration for the bipolar electrode configuration. It is important to note that the inventors used a rate equation that was fit to the 1.5 cm×2.9 cm IRE zone of ablation but this has not been validated experimentally (See Golberg, A. and B. Rubinsky, A statistical model for multidimensional irreversible electroporation cell death in tissue. Biomed Eng Online, 2010. 9(1): p. 13). The results below provide insight as to the effect of different pulse parameters and electrode/insulation dimensions in the resulting zone of IRE ablation in order to optimize the bipolar probe electrode for clinical use. In order to perform a computationally efficient study, the models were constructed in a 2-D axis-symmetric platform which generates results that are representative of the 3-D space.
Part 1: The work from Part 1 determined the electric field threshold for 0.7 cm electrodes with a 0.8 cm insulation to be 572.8 V/cm assuming a static electric conductivity (Table 12). This threshold is the average between the width (349.5 V/cm) and length (795.1 V/cm) electric field thresholds that matched the experimental lesion of 1.5 cm (width) by 2.9 cm (length). It is important to note that due to the mismatch between the electric field thresholds, the predicted width will be underestimated and the predicted length will be overestimated when using the average value of 572.8 V/cm. The model assumes an applied voltage of 2700 V, ninety 100-μs pulses, at a repetition rate of 1 pulse per second, and a viability value of 0.1% (S=0.001) as the complete cell death due to IRE exposure (
A parametric study was constructed in order to explore the effect of electrode diameter (18 G=1.27 mm, 16 G=1.65 mm, 14 G=2.11 mm), electrode spacing (0.4 cm, 0.8 cm, 1.2 cm, 1.6 cm), and electrode length (0.5 cm, 0.75 cm, 1.0 cm, 1.25 cm, and 1.5 cm). In order to provide a comprehensive analysis of all iterations we computed the volumes of tissue that would achieve a cell viability, S<0.001, and these results are reported in the table of
In an effort to better understand the effects of the electrode geometry on the ablation region an extra set of values (Table 14) was generated. The closest outputs to a 1.5 cm×2.9 cm lesion size from parameters in Table 13 were modified to better approximate the targeted lesion. Considering all 60 different runs, number 15 is closest to the targeted values with a lesion geometry of 1.301 cm×2.84 cm.
Part 2: In Part 2 the electric field distribution assuming a dynamic electric conductivity was used to determine the threshold of cell death due to IRE exposure. Specifically during this Part, a sigmoid function (
In Part 2, the effect of pulse strength (2000 V, 2250 V, 2500 V, 2750 V, 3000 V) and pulse number (20, 40, 60, 80, 100) was explicitly investigated and the results of the parametric study are provided in the table of
Table 16 and demonstrate that with increasing pulse strength and pulse number a larger volume of IRE ablation is achieved at a repetition rate of one pulse per second (
Part 3: In this Part the exposure of liver tissue to 300 (5×60) and 360 (4×90) pulses were simulated at an applied voltage of 3000 V, 100-μs pulses, at a repetition rate of one pulse per second. From the cell viability plots in
Models with exploratory geometries were developed that include multiple voltage sources and current diffusers (balloons).
The present invention has been described with reference to particular embodiments having various features. In light of the disclosure provided, it will be apparent to those skilled in the art that various modifications and variations can be made in the practice of the present invention without departing from the scope or spirit of the invention. One skilled in the art will recognize that the disclosed features may be used singularly, in any combination, or omitted based on the requirements and specifications of a given application or design. Other embodiments of the invention will be apparent to those skilled in the art from consideration of the specification and practice of the invention.
It is noted in particular that where a range of values is provided in this specification, each value between the upper and lower limits of that range is also specifically disclosed. The upper and lower limits of these smaller ranges may independently be included or excluded in the range as well. The singular forms “a,” “an,” and “the” include plural referents unless the context clearly dictates otherwise. It is intended that the specification and examples be considered as exemplary in nature and that variations that do not depart from the essence of the invention fall within the scope of the invention. In particular, for method embodiments, the order of steps is merely exemplary and variations appreciated by a skilled artisan are included in the scope of the invention. Further, all of the references cited in this disclosure are each individually incorporated by reference herein in their entireties and as such are intended to provide an efficient way of supplementing the enabling disclosure of this invention as well as provide background detailing the level of ordinary skill in the art.
Claims
1. A method of treating a tissue with a medical treatment device that applies electrical treatment energy through one or more electrodes defining a target treatment area of the tissue and comprises a display device, the method comprising:
- providing one or more parameters of a treatment protocol for delivering one or more electrical pulses to a tissue through one or more electrodes;
- modeling heat distribution and/or electric field distribution in a tissue surrounding the electrodes based on the one or more parameters;
- displaying a graphical representation of the heat and/or electric field distribution based on the modeled heat distribution in the display device;
- modifying one or more of the parameters of the treatment protocol based on the graphical representation of the heat distribution; and
- implanting the electrodes in the tissue and delivering one or more electrical pulses to the tissue through the electrodes by way of a voltage pulse generator based on the one or more modified parameters.
2. The method of claim 1, wherein the one or more parameters are chosen from one or more of voltage, electrode spacing, electrode length, treatment duration, number of pulses, pulse width, electric field intensity, electrode diameter, a baseline conductivity for the target treatment area, a change in conductivity for the target treatment area, or a conductivity for a specific tissue type.
3. A method of treatment planning for medical therapies involving administering electrical treatment energy, the method comprising:
- providing one or more parameters of a treatment protocol for delivering one or more electrical pulses to tissue through one or more electrodes;
- modeling heat and/or electric field distribution in the tissue based on the parameters; and
- displaying a graphical representation of the modeled heat and/or electric field distribution.
4. The method of claim 3, wherein the heat distribution is modeled to estimate the Joule heating in the tissue and is calculated as: ρ C p ∂ T ∂ t = ∇ · ( k ∇ T ) + Q jh [ W m 3 ] Q jh = J · E [ W m 3 ] J = σ E [ A m 2 ] E = - ∇ ϕ [ V m ]
- where ρ is the density, Cp is the heat capacity, k is the thermal conductivity,
- and Qjh are the resistive losses
- where J is the induced current density
- and σ is the tissue conductivity and E is the electric field
5. The method of claim 3, further comprising specifying a cutoff heat distribution value and providing a graphical representation of the heat and/or electric field distribution curve as an isocontour line.
6. The method of claim 3, further comprising:
- modeling an electrical damage and/or a thermal damage in the tissue based on the parameters;
- displaying a graphical representation of the modeled electrical damage and/or thermal damage.
7. The method of claim 6, wherein the electric field distribution is calculated as:
- ∇2ϕ=0
- where ϕ is the electric potential, this equation is solved with boundary conditions:
- {right arrow over (n)}·{right arrow over (J)}=0 at the boundaries
- ϕ=Vin at the boundary of the first electrode
- ϕ=0 at the boundary of the second electrode
- wherein {right arrow over (n)} is the normal vector to the surface, {right arrow over (J)} is the electrical current and Vin is the electrical potential applied.
8. The method of claim 6, further comprising specifying a cutoff electrical field distribution value and providing a graphical representation of the electrical field distribution value as an isocontour line.
9. The method of claim 3, wherein the parameters are chosen from one or more of voltage, electrode spacing, electrode diameter, electrode length, number of pulses, treatment duration, pulse width, electric field intensity, a baseline conductivity for the target treatment area, a change in conductivity for the target treatment area, or a conductivity for a specific tissue type.
10. The method of claim 8, further comprising one or more databases comprising a plurality of sets of parameters for treatment protocols stored in the database.
11. The method of claim 10, wherein the graphical representations of the modeled heat and electrical field distributions are derived from Cassini oval calculations.
12. A system for treatment planning for medical therapies involving administering electrical treatment energy, the system comprising:
- a computer comprising: a memory; a display device; a processor coupled to the memory and the display device; and a treatment planning module stored in the memory and executable by the processor, the treatment planning module adapted to: receive as input one or more parameters of a treatment protocol for delivering electrical pulses to tissue through one or more electrodes; model heat and/or electric field distribution in the tissue based on the parameters; display a graphical representation of the modeled heat and/or electric field distribution on the display device.
13. The system of claim 12, further comprising one or more databases comprising a plurality of sets of parameters for treatment protocols stored in the databases.
14. The system of claim 12, wherein the inputs are chosen from one or more of voltage, electrode spacing, treatment duration, pulse width, electric field intensity, a baseline conductivity for the target treatment area, a change in conductivity for the target treatment area, or a conductivity for a specific tissue type.
15. The system of claim 14, wherein the change in conductivity is expressed as a ratio of the baseline conductivity to the maximum conductivity of the tissue that is reached during treatment.
16. The system of claim 14, wherein the conductivity for a specific tissue type is provided in a database for a plurality of tissues.
17. The system of claim 12, wherein the one or more electrodes is provided by one or more bipolar probes.
18. The system of claim 12, wherein the one or more electrodes are provided by one or more single needle electrodes.
19. The system of claim 15, wherein the change in conductivity is calculated in real-time based on measured voltages and currents before, during, and/or after pulse delivery.
20. The method of claim 6, wherein the graphical representation of the modeled thermal damage and/or electrical damage is derived from Cassini oval calculations.
21-22. (canceled)
Type: Application
Filed: Oct 5, 2018
Publication Date: Jan 27, 2022
Patent Grant number: 11272979
Inventors: Paulo A. Garcia (Blacksburg, VA), Christopher B. Arena (Burlington, NC), Michael B. Sano (Durham, NC), Rafael V. Davalos (Blacksburg, VA)
Application Number: 16/152,743
