SYSTEM AND METHOD FOR DETERMINING AMOUNT OF RADIOACTIVE MATERIAL TO ADMINISTER TO A PATIENT
A computerized system and method are provided for determining an optimum amount of radioactivity to administer to a patient, comprising: assuming an activity retention limit; utilizing the activity retention limit to determine a dose rate for a phantom category; utilizing the dose rate for the phantom category to determine the dose rate for a second phantom category; and utilizing the dose rate for a second phantom category to find information regarding the second phantom category. In other embodiments, a computerized system and method are provided for determining an optimum amount of radioactivity to administer to a patient, comprising: obtaining at least one image relating to anatomy of a particular patient; obtaining multiple images regarding radioactivity distribution over time in the particular patient; combining the radioactivity images with the anatomy images; running a Monte Carlo simulation to obtain dose image information; and using the dose image information to obtain BED and/or EUD information.
This application is a Divisional of U.S. patent application Ser. No. 12/514,853, filed May 14, 2009, which is a National Stage of International Application No. PCT/US2007/085400 filed Nov. 21, 2007, which claims priority to U.S. Provisional Application No. 60/860,315 filed Nov. 21, 2006 and U.S. Provisional Application No. 60/860,319 filed Nov. 21, 2006. All of the foregoing are incorporated by reference in their entireties.
This invention was made with Government support under NIH/NCI grant RO1CA116477 and NIH/NCI grant RO1CA116477 and DOE grant DE-FG02-05ER63967. The authors also acknowledge the U.S. Government has certain rights in this invention.
BRIEF DESCRIPTION OF THE FIGURESIn 105, an activity retention limit is chosen or assumed. This activity retention limit can be assumed based on data sets, such as the Benua-Leeper studies or other studies that have determined the maximum tolerated dose in a patient population. The Benua-Leeper studies have proposed a dosimetry-based treatment planning approach to 131I thyroid cancer therapy. The Benua-Leeper approach was a result of the observation that repeated 131I treatment of metastatic thyroid carcinoma with sub-therapeutic doses often fails to cause tumor regression and can lead to loss of iodine-avidity in metastases. The Benua-Leeper study attempted to identify the largest administered 131I radioactivity that would be safe yet optimally therapeutic. Drawing upon patient studies, the Benua-Leeper study formulated constraints upon the administered activity. For example, the Benua-Leeper study determined that the blood absorbed dose should not exceed 200 rad. This was recognized to be a surrogate for red bone marrow absorbed dose and was intended to decrease the likelihood of severe marrow depression, the dose-limiting toxicity in radioiodine therapy of thyroid cancer. In addition, it was determined that whole-body retention at 48 h should not exceed 120 mCi. This was shown to prevent release of 131I-labeled protein into the circulation from damaged tumor. Furthermore, in the presence of diffuse lung metastases, it was determined that the 48 h whole-body retention should not exceed 80 mCi. This constraint helped avoid pneumonitis and pulmonary fibrosis. Thus, for example, referring to
In 110 of
DRP(t)−ALU(t)·SLU←LUP+ARB(t)·SLU←RBP (1)
with:
ALU(t) lung activity at time t,|
SLU←LUP lung to lung 131I S-factor for reference phantom, P,
ARB(t) remainder body activity (total-body-lung) at time, t,
SLU←RBP remainder body to hung 131I S-factor for reference phantom, P,
AT whole-body activity at time, T,
FT fraction of AT that is in the lungs at time, T,
λLU effective clearance rate from lungs (=ln(2)/TE; with TE=effective half-life),
λRB effective clearance rate from remainder body (=ln(2)/TRB, with TRB=effective half-life in remainder body),
SLU←TBP total-body to lung 131I S-factor for reference phantom. P,
MRBP total-body mass of reference phantom. P,
MLUP lung mass of reference phantom. P.
Equation (2) describes a model in which radioiodine uptake in tumor-bearing lungs is assumed instantaneous relative to the clearance kinetics. Clearance is modeled by an exponential expression with a clearance rate constant, λLU, and corresponding effective half-life, TE. At a particular time, T, after administration, the fraction of whole-body activity that is in the lungs is given by the parameter, FT. Activity that is not in the lungs (i.e., in the remainder body (RB)) is also modeled by an exponential clearance (Equation (3)), but with a different rate constant, λRB. At time, T, the fraction of whole-body activity in this compartment is 1-FT. Equation (4) can be obtained from the following reference: Loevinger et al., MIRD Primer for Absorbed Dose Calculations, Revised Edition. The Society of Nuclear Medicine, Inc. (1991).
Using equations (2) and (3) to replace ALU(t) and ARB(t) in equation 1, the dose rate to lungs at time, T, for phantom, P, is:
DRP(T)=AT·FT·SLU←LUP+AT·(1−FT)·SLU←RBP, (5)
Derived Activity Constraint
In 115, once we have the dose-rate at a certain time (e.g., 48 h) as the relative constraint for a certain phantom, then dose-rate constraints (DRCs) at this same time (e.g., 48 h) can be derived for different reference phantoms. Thus, for example, If we assume that the dose-rate to the lungs at 48 h is the relevant constraint on avoiding prohibitive lung toxicity, then, one may derive 48-hour activity constraints for different reference phantoms that give a 48 h dose rate equal to a pre-determined fixed dose rate constraint, denoted, DRC. By re-ordering expression 5 and renaming AT to ADRCP, the activity constraint for phantom P so that DRP(48 h)=DRC, we get:
In equation 6, ADRCP, depends upon the fraction of whole-body activity in lungs at 48 hours and also on the reference phantom that best matches the patient characteristics.
Corresponding Administered ActivityIn 120, once we have the dose rate constraints for different phantoms, corresponding administered activity can be found for those phantoms. Equation (6) gives the 48 hour whole-body activity constraint so that the dose rate to lungs at 48 hours does not exceed DRC. The corresponding constraint on the maximum administered activity, AAmax, can be derived by using equations 2 and 3, to give an expression for the total-body activity as a function of time:
Replacing AT with ADRCP and setting t=0, the following expression is obtained for AAmax:
The denominator in each term of this expression scales the activity up to reflect the starting value needed to obtain ATB (48 h)=ADRCP. AAmax is shown to be dependent on λDU, and λRB (or equivalently on TE and TRB).
Mean Lung Absorbed DoseIn 125, the mean absorbed dose may be obtained by integrating the dose rate from zero to infinity. Thus, the mean lung absorbed does can be obtained by integrating equation (1) from 1 to infinity:
DLU=ÃLU·SLU←LUP+ÃRB·SLU←RBP (9)
Integrating the expressions for lung and remainder body activity as a function of time, (equations (2) and (3), respectively) and replacing parameters with the 48 hour constraint values the following expressions are obtained for ÃLU and ÃRB:
In equations (10) and (11), the λ values have been replaced to explicitly show the dependence of the cumulated activities on the clearance half-lives.
If TRB is kept constant and TE is varied, the minimum absorbed dose to the lungs will occur at a TE value that gives a minimum for equation (9). This can be obtained by differentiating with respect to TE, setting the resulting expression to zero and solving for TE. This gives TE=ln(2)48 h=33 h.
Electron v. Photon Contribution to the Lung Dose
Since almost all of the activity in tumor-bearing lungs would be localized to tumor cells, it is instructive to separate the electron contribution to the estimated lung dose from the photon contribution. The electron contribution would be expected, depending upon the tumor geometry (11), to irradiate tumor cells predominantly, while the photon contribution will irradiate lung parenchyma. The dose contribution from the remainder body is already limited to photon emissions. The photon only lung to lung S-value (SLU←LUP) for a phantom, P, is obtained from the S-factor value and the delta value for electron emissions of 131I:
Δelectron131
The table in
To derive the dose-rate to lungs associated with the 80 mCi, 48 h constraint we assume that 90% of the whole-body activity is uniformly distributed in the lungs (F48=0.9). The original reports describing the 80 mCi, 48 h limit do not provide a value for this parameter; the value chosen is consistent with the expected biodistribution in patients with disease that is dominated by diffuse lung metastases. As noted above, the 80 mCi activity constraint was derived primarily from results obtained in females. Accordingly, the conversion from activity to dose-rate is performed using S-factors and masses for the adult female phantom. Using equation, (5), with F48=0.9, the dose-rate constraint (DRC) corresponding to the 48 h, 80 mCi limit is 41.1 cGy/h. This is the estimated dose-rate to the lungs when 80 mCi of 131I are uniformly distributed in the lungs of an adult female whose anatomy is consistent with the standard female adult phantom geometry. Implicit in the 80 mCi at 48 h constraint is that radiation induced pneumonitis and pulmonary fibrosis will be avoided as long as the dose-rate is not in excess of 41.1 cGy/h at 48 h after 131I administration. If we assume that this dose-rate based constraint applies to pediatric patients, then using equation 6, we may calculate the 48 h activity limitation if the patient anatomy is consistent with the 15 or 10 year-old standard phantom.
The majority of patients with diffuse 131I-avid lung metastases exhibit prolonged whole-body retention. In such cases, the whole-body kinetics are dominated by tumor-associated activity. Assuming that 90% of the whole-body activity is in the lungs and that this clears with an effective half-life of 100 h, while the remainder activity clears with an effective half-life of 20 h (corresponding to a treatment plant that includes hormone withdrawal), equation (8) may be used to calculate the administered activity that will yield the corresponding 48 h activity constraint for each phantom. The administered activity values are 6.64, 5.23, 4.37 and 3.08 GBq (180, 143, 118 and 83.2 mCi), respectively, for adult male, female, 15 year old and 10 year old standard phantom anatomies. These values depend on the assumed clearance half life of activity in the remainder of the body. If an effective half-life of 10 h (consistent with use of recombinant human TSH (rhTSH)) is assumed, the corresponding administered activity values are: 15.1, 12.0, 9.92 and 6.98 GBq (407, 323, 268 and 189 mCi).
Less is known regarding the effects of lung irradiation on pediatric patients or patients with already compromised lung function. In such cases a more conservative dose-rate limit may be appropriate. As noted earlier, the results shown in
All of the lung absorbed dose values shown on
Unlike the total dose, the photon dose is also more heavily dependent upon the phantom. At TE=100 h, the photon lung dose to the adult male ranges from 8.75 (F48=1.0) to 9.03 (F48=0.6) Gy when TRB=20 h; the corresponding values when TRB=10 h, are 8.75 (F48=1.0) and 9.56 (F48=0.6) Gy. In the 15-year-old, the corresponding values are: 7.85, 8.10, 7.85 and 8.55 Gy; corresponding values for the 10-year-old are: 7.09, 7.33, 7.09 and 7.78 Gy. 3D-RD (3D-Radiobiological Dosimetry)
In one embodiment, a method is provided that incorporates radiobiological modeling to account for the spatial distribution of absorbed dose and also the effect of dose-rate on biological response. The methodology is incorporated into a software package which is referred to herein as 3D-RD (3D-Radiobiological Dosimetry). Patient-specific, 3D-image based internal dosimetry is a dosimetry methodology in which the patient's own anatomy and spatial distribution of radioactivity over time are factored into an absorbed dose calculation that provides as output the spatial distribution of absorbed dose.
In 1408, images are obtained relating to radioactive distribution across time.
In 1410, the images related to the radioactive distribution are registered across time. At this point, one of at least two options (1415-1440 or 1450-1465) can be followed. In 1415, each radioactivity image can be combined with an anatomy image. The anatomical image voxel values can be utilized to assign density and composition (i.e., water, air and bone).
In 1420, Monte Carlo simulations are nm on each activity image. Thus, the 3-D activity image(s) and the matched anatomical image(s) can be used to perform a Monte Carlo calculation to estimate the absorbed dose at each of the activity image collection times by tallying energy deposition in each voxel.
In 1425, the dose image at each point in time is used to obtain a dose-rate image and a total dose image.
In 1430, the dose-rate and the total dose image are utilized to obtain the BED image. In 1440, the BED image is utilized to obtain the EUD of BED value for a chosen anatomical region.
In the other option, after 1410, activity images can be integrated across time voxel-wise to obtain a cumulated activity (CA) image. In 1455, the CA image is combined with an anatomy image. In 1460, a Monte Carlo (MC) calculation is run to get the total dose image. In 1465, the dose image is utilized to obtain the EUD of the dose value for a chosen anatomical region.
EUD and BED formulas (as described in more detail below and also illustrated in
The uniformity (or lack thereof) of absorbed dose distributions and their biological implications have been examined. Dose-volume histograms have been used to summarize the large amount of data present in 3-D distributions of absorbed dose in radionuclide dosimetry studies. The EUD model introduces the radiobiological parameters, α and β, the sensitivity per unit dose and per unit dose squared, respectively, in the linear-quadratic dose-response model. The EUD model converts the spatially varying absorbed dose distribution into an equivalent uniform absorbed dose value that would yield a biological response similar to that expected from the original dose distribution. This provides a single value that may be used to compare different dose distributions. The value also reflects the likelihood that the magnitude and spatial distribution of the absorbed dose is sufficient for tumor kill.
It is known that dose rate influences response. The BED formalism, sometimes called Extrapolated Response Dose, was developed to compare different fractionation protocols for external radiotherapy. BED may be thought of as the actual physical dose adjusted to reflect the expected biological effect if it were delivered at a reference dose-rate. As in the case of EUD, by relating effects to a reference value, this makes it possible to compare doses delivered under different conditions. In the case of EUD the reference value relates to spatial distribution and is chosen to be a uniform distribution. In the case of BED the reference value relates to dose rate and is chosen to approach zero (total dose delivered in an infinite number of infinitesimally small fractions).
As described above with respect to 1415, the patient-specific anatomical image(s) are combined with radioactivity images into paired 3D data sets. Thus, the anatomical image voxel values can be utilized to assign density and composition (i.e., water, air and bone). This information, coupled with assignment of the radiobiological parameters, α, β, μ, the radiosensitivity per unit dose, radiosensitivity per unit dose squared and the repair rate assuming an exponential repair process, respectively, is used to generate a BED value for each voxel, and subsequently an EUD value for a particular user-defined volume.
In external radiotherapy, the expression for BED is:
This equation applies for N fractions of an absorbed dose, d, delivered over a time interval that is negligible relative to the repair time for radiation damage (i.e., at high dose rate) where the interval between fractions is long enough to allow for complete repair of repairable damage induced by the dose d; repopulation of cells is not considered in this formulation but there are formulations that include this and this could easily be incorporated in embodiments of the present invention. The parameters, .alpha. and .beta. are the coefficients for radiation damage proportional to dose (single event is lethal) and dose squared (two events required for lethal damage), respectively.
A more general formulation of equation (1) is:
BED(T)=(DT(T)·RE(T) (2),
where BED(T) is the biologically effective dose delivered over a time T, DT(T) is the total dose delivered over this time and RE(T) is the relative effectiveness per unit dose at time, T. The general expression for RE(T) assuming a time-dependent dose rate described by D(t) is given by:
The second integration over the time-parameter, w, represents the repair of potentially lethal damage occurring while the dose is delivered, i.e., assuming an incomplete repair model. If we assume that the dose rate for radionuclide therapy, D(t), at a given time, t, can be expressed as an exponential expression:
{dot over (D)}(t)={dot over (D)}0e−A1 (4),
Where D0 is the initial dose rate and λ is the effective clearance rate (=ln(2)/te; te=effective clearance half-life of the radiopharmaceutical), then, in the limit, as T approaches infinity, the integral in equation (3) reduces to:
Substituting this expression and replacing DT(T) with D, the total dose delivered, and using D0=λD, which may be derived from equation (4), we get:
In this expression, the effective clearance rate, λ, is represented by ln(2)/te. The derivation can be completed as discussed in the following references: Dale et al., The Radiobiology of Conventional Radiotherapy and its Application to Radionuclide Therapy, Cancer Biother Radiopharm (2005), Volume 20, Chapter 1, pages 47-51; Dale, Use of the Linear-Quadratic Radiobiological Model for Quantifying Kidney Response in Targeted Tadiotherapy, Cancer Biother Radiopharm, Volume 19, Issue 3, pages 363-370 (2004).
In cases where the kinetics in a particular voxel are not well fitted by a single decreasing exponential alternative, formalisms have been developed that account for an increase in the radioactivity concentration followed by exponential clearance. Since the number of imaging time-points typically collected in dosimetry studies would not resolve a dual parameter model (i.e., uptake and clearance rate), in one embodiment, the methodology assumes that the total dose contributed by the rising portion of a tissue or tumor time-activity curve is a small fraction of the total absorbed dose delivered.
Equation (6) depends upon the tissue-specific intrinsic parameters, α, β and μ. These three parameters are set constant throughout a user-defined organ or tumor volume. The voxel specific parameters are the total dose in a given voxel and the effective clearance half-life assigned to the voxel. Given a voxel at coordinates (i,j,k), Dijk and teijk are the dose and effective clearance half-life for the voxel. The imaging-based formulation of expression (6) that is incorporated into 3D-RD is then:
The user inputs values of α, β and μ for a particular volume and Dijk and teijk are obtained directly from the 3-D dose calculation and rate image, respectively. This approach requires organ or tumor segmentation that corresponds to the different α, β and μ values. The dose values are obtained by Monte Carlo calculation as described previously, and the effective clearance half-lives are obtained by fitting the data to a single exponential function. Once a spatial distribution of BED values has been obtained a dose-volume histogram of these values can be generated. Normalizing so that the total area under the BED (differential) DVH curve is one, converts the BED DVH to a probability distribution of BED values denoted, P(.PSI.), where .PSI. takes on all possible values of BED. Then, following the derivation for EUD as described in O'Donoghue's Implications of Nonuniform Tumor Doses for Radioimmunotherapy, J Nucl Med., Volume 40, Issue 8, pages 1337-1341 (1999), the EUD (1440) is obtained as:
The EUD of the absorbed dose distribution (1465), as opposed to the BED distribution (1440), can also be obtained using equation (8), but using a normalized DVH of absorbed dose values rather than BED values. Expression (8) may be derived by determining the absorbed dose required to yield a surviving fraction equal to that arising from the probability distribution of dose values (absorbed dose or BED) given by the normalized DVH.
A rigorous application of equation (7) would require estimation of the absorbed dose at each time point (as in 1420); the resulting set of absorbed dose values for each voxel would then be used to estimate tcijk (1425). In using activity-based rate images to obtain the teijk , instead of the absorbed dose at each time point, the implicit assumption is being made that the local, voxel self-absorbed dose contribution is substantially greater than the cross-voxel contribution. This assumption avoids the need to estimate absorbed dose at multiple time-points, thereby substantially reducing the time required to perform the calculation. In another embodiment of the invention absorbed dose images at each time-point are generated and used for the BED calculation (1430), thereby avoiding the assumption regarding voxel self-dose vs cross-dose contribution.
Radiobiological Parameters for Clearance Rate Effect Example
The illustrative simplified examples and also the clinical implementation involve dose estimation to lungs and to a thyroid tumor. Values of α and β for lung, and the constant of repair, μ, for each tissue was taken from various sources. The parameter values are listed in the table in
As explained above, a sphere can be generated in a 563 matrix such that each voxel represents a volume of (0.15 cm)3. All elements with a centroid greater than 1 cm and less than or equal to (2.0 cm)⅓ from the matrix center (at 28,28,28) were given a clearance rate value (λ) corresponding to a half life of 2 hours. Those elements with a center position less than or equal to 1.0 cm from the center voxel were assigned a λ value equivalent to a 4 hour half life. In this way an outer shell (with 2 hour half life) was separated from an inner sphere (with 4 hour half life) (
Absorbed Dose Distribution Effects. To demonstrate the impact of dose distribution on EUD, the following model was evaluated (
Density Effects. To illustrate the effect of density differences, a sphere with radius 1.26 cm was created that had unit cumulated activity throughout, but a density of 2 g/cc in a central spherical region with radius 1 cm and 1 g/cc in the surrounding spherical shell (
The 3D-RD dosimetry methodology was applied to an 11 year old female thyroid cancer patient who has been previously described in a publication on MCNP-based 3D-ID dosimetry.
Imaging. SPECT/CT images were obtained at 27, 74, and 147 hours post injection of a 37 MBq (1.0mCi) tracer 131I dose. All three SPECT/CT images focused on the chest of the patient and close attention was directed at aligning the patient identically for each image. The images were acquired with a GE Millennium VG Hawkeye system with a 1.59 cm thick crystal.
An OS-EM based reconstruction scheme was used to improve quantization of the activity map. A total of 10 iterations with 24 subsets per iteration was used. This reconstruction accounts for effects including attenuation, patient scatter, and collimator response. Collimator response includes septal penetration and scatter. The SPECT image counts were converted to units of activity by accounting for the detector efficiency and acquisition time. This quantification procedure, combined with image alignment, made it possible to follow the kinetics of each voxel. Using the CTs, which were acquired with each SPECT, each subsequent SPECT and CT image was aligned to the 27 hour 3-D image set. A voxel by voxel fit to an exponential expression was then applied to the aligned data set to obtain the clearance half-time for each voxel.
To obtain mean absorbed dose, mean BED and EUD, as well as absorbed dose and BED-volume-histograms, voxels were assigned to either tumor or normal lung parenchyma using an activity threshold of 21% of highest activity value.
Spherical Model ExampleA spherical model was used to validate and illustrate the concepts of BED and EUD.
Clearance Rate Effects. Assuming that the sphere was lung tissue and applying the radiobiological parameters listed in the table of
Absorbed Dose Distribution Effects. The EUD value over the whole sphere when a uniform activity distribution was assumed recovered the mean absorbed dose of 10 Gy. A non-uniform absorbed dose distribution was applied such that the inner sphere was assigned an absorbed dose of zero, and an outer shell of equal volume, an absorbed dose of 20 Gy. In this case, the mean absorbed dose is 10 Gy, but the EUD was 1.83 Gy. The substantially lower EUD value is no longer a quantity that may be obtained strictly on physics principles, but rather is dependent on the applied biological model. The true absorbed dose has been adjusted to reflect the negligible probability of sterilizing all cells in a tumor volume when half of the tumor volume receives an absorbed dose of zero.
Density Effects. In the sphere with non-uniform density (inner sphere density of 2 g/cc, outer shell of equal volume (1 g/cc)) and an average absorbed dose of 10 Gy, the EUD over the whole sphere was 6.83 Gy. The EUD value is lower than the absorbed dose value to reflect the dose non-uniformity in spatial absorbed dose (inner sphere=5 Gy, outer shell=15 Gy) arising from the density differences.
Application to a Patient Study. A 3D-RD calculation was performed for the clinical case described in the methods. A dosimetric analysis for this patient, without the radiobiological modeling described in this work has been previously published using the Monte Carlo code MCNP as opposed to EGSnrc which was used in this work. The clinical example illustrates all of the elements investigated using the simple spherical geometry. As shown on the CT scan (
A comparison between the EGS-based 3D-RD calculation and the previously published MCNP-based calculation was performed.
While various embodiments have been described above, it should be understood that they have been presented by way of example, and not limitation. It will be apparent to persons skilled in the relevant art(s) that various changes in form and detail can be made therein without departing from the spirit and scope. In fact, after reading the above description, it will be apparent to one skilled in the relevant art(s) how to implement alternative embodiments. Thus, the present embodiments should not be limited by any of the above described exemplary embodiments.
In addition, it should be understood that any figures which highlight the functionality and advantages, are presented for example purposes only. The disclosed architecture is sufficiently flexible and configurable, such that it may be utilized in ways other than that shown. For example, the steps listed in any flowchart may be re-ordered or only optionally used in some embodiments.
Further, the purpose of the Abstract of the Disclosure is to enable the U.S. Patent and Trademark Office and the public generally, and especially the scientists, engineers and practitioners in the art who are not familiar with patent or legal terms or phraseology, to determine quickly from a cursory inspection the nature and essence of the technical disclosure of the application. The Abstract of the Disclosure is not intended to be limiting as to the scope in any way.
Finally, it is the applicant's intent that only claims that include the express language “means for” or “step for” be interpreted under 35 U.S.C. 112, paragraph 6. Claims that do not expressly include the phrase “means for” or “step for” are not to be interpreted under 35 U.S.C. 112, paragraph 6.
Claims
1. A computerized method for determining an optimum amount of radioactivity to administer to a patient, comprising:
- assuming an activity retention limit; utilizing the activity retention limit to determine a dose rate for a phantom category;
- utilizing the dose rate for the phantom category to determine the dose rate for a second phantom category; and
- utilizing the dose rate for a second phantom category to find information regarding the second phantom category.
2. The method of claim 1, wherein the information is the activity retention limit for the second phantom category.
3. The method of claim 1, further comprising:
- obtaining the mean absorbed dose by integrating the dose rate over time;
- using the mean absorbed dose to determine an optimum amount of radioactivity to administer to the patient.
4. The method of claim 1, wherein a dose rate resulting from short range particulate emissions is distinguished from a dose rate resulting from longer range emissions.
5. The method of claim 4, wherein the short range particulate emissions are electrons.
6. The method of claim 4, wherein the longer range emissions are photons.
7. The method of claim 1, wherein utilizing the activity retention limit to determine the dose rate for the phantom category further comprises calculating how the dose rate is related to the activity retention limit in a particular point in time.
8. The method of claim 1, wherein utilizing the activity retention limit to determine the dose rate for the phantom category further comprises using the following formula: with: A LU ( t ) = A T · F T - π LU · T - λ LU · T, ( 2 ) A RB ( t ) = A T · ( 1 - F T ) - λ RB · T - λ RB · T, ( 3 ) S LU ← RB P = S LU ← TB P · M TB P M TB P - M LU P - S LU ← LU P · M LU P M TB P - M LU P, ( 4 )
- DRP(t)=ALU(t)·SLU←LUP+ARB(t)·SLU←RBP (1),
- ALU(t) lung activity at time t,|
- SLU←LUP lung to lung 131I S-factor for reference phantom, P,
- ARB(t) remainder body activity (total-body-lung) at time, t,
- SLU←RBP remainder body to hung 131I S-factor for reference phantom, P,
- AT whole-body activity at time, T,
- FT fraction of AT that is in the lungs at time, T,
- λLU effective clearance rate from lungs (=ln(2)/TE; with TE=effective half-life),
- λRB effective clearance rate from remainder body (=ln(2)/TRB, with TRB=effective half-life in remainder body),
- SLU←TBP total-body to lung 131I S-factor for reference phantom. P,
- MRBP total-body mass of reference phantom. P,
- MLUP lung mass of reference phantom. P.
9. The method of claim 3, wherein obtaining the mean absorbed dose by integrating the dose rate over time further comprises utilizing the following formula: with A ~ LU = A DRC P · F 48 · l n ( 2 ) T E T ln ( 2 ) · T E, ( 10 ) A ~ RB = A DRC P · ( 1 - F 48 ) · l n ( 2 ) T RB · T ln ( 2 ) · T RB. ( 11 )
- DLU=ÃLU·SLU←LUP+ÃRB·SLU←RBP (9)
10. A computerized system for determining an optimum amount of radioactivity to administer to a patient, comprising:
- a server coupled to a network;
- a user terminal coupled to the network;
- an application coupled to the server and/or the user terminal, wherein the application is configured for: assuming an activity retention limit; utilizing the activity retention limit to determine a dose rate for a phantom category; utilizing the dose rate for the phantom category to determine the dose rate for a second phantom category; and utilizing the dose rate for a second phantom category to find information regarding the second phantom category.
11. The system of claim 10, wherein the information is the activity retention limit for the second phantom category.
12. The system of claim 10, wherein the application is further configured for: obtaining the mean absorbed dose by integrating the dose rate over time; using the mean absorbed dose to determine an optimum amount of radioactivity to administer to the patient.
13. The system of claim 10, wherein a dose rate resulting from short range particulate emissions is distinguished from a dose rate resulting from longer range emissions.
14. The system of claim 13, wherein the short range particulate emissions are electrons.
15. The system of claim 13, wherein the longer range emissions are photons.
16. The system of claim 10, wherein utilizing the activity retention limit to determine the dose rate for the phantom category further comprises calculating how the dose rate is related to the activity retention limit in a particular point in time.
17. The system of claim 10, wherein utilizing the activity retention limit to determine the dose rate for the phantom category further comprises using the following formula: with: A LU ( t ) = A T · F T - π RB · T - λ LU · T, ( 2 ) A RB ( t ) = A T · ( 1 - F T ) - λ RB · T - λ RB · T, ( 3 ) S LU ← RB P = S LU ← TB P · M TB P M TB P - M LU P - S LU ← LU P · M LU P M TB P - M LU P, ( 4 )
- DRP(t)=ALU(t)·SLU←LUP+ARB(t)·SLU←RBP (1),
- ALU(t) lung activity at time t,|
- SLU←LUP lung to lung 131I S-factor for reference phantom, P,
- ARB(t) remainder body activity (total-body-lung) at time, t,
- SLU←RBP remainder body to hung 131I S-factor for reference phantom, P,
- AT whole-body activity at time, T,
- FT fraction of AT that is in the lungs at time, T,
- λLU effective clearance rate from lungs (=ln(2)/TE; with TE=effective half-life),
- λRB effective clearance rate from remainder body (=ln(2)/TRB, with TRB=effective half-life in remainder body),
- SLU←RBP total-body to lung 131I S-factor for reference phantom. P,
- MRBP total-body mass of reference phantom. P,
- MLUP lung mass of reference phantom. P.
18. The method of claim 12, wherein obtaining the mean absorbed dose by integrating the dose rate over time further comprises utilizing the following formula: with A ~ LU = A DRC P · F 48 · l n ( 2 ) T E T ln ( 2 ) · T E, ( 10 ) A ~ RB = A DRC P · ( 1 - F 48 ) · l n ( 2 ) T RB · T ln ( 2 ) · T RB. ( 11 )
- DLU=ÃLU·SLU←LUP+ÃRB·SLU←RBP (9)
Type: Application
Filed: Apr 19, 2016
Publication Date: Oct 6, 2016
Inventors: George SGOUROS (Ellicott City, MD), Hong SONG (Towson, MD), Andrew PRIDEAUX (Baltimore, MD), Robert HOBBS (Baltimore, MD)
Application Number: 15/132,590