Abstract: A spectrometric technique is described for quantitatively determining the change in concentration of a substance which is contained in a medium which both absorbs and scatters spectroscopically interrogated radiation, and in particular to the specific case in which the change in concentration of the substance occurs in one spatially distinct region of the medium. The medium includes a plurality of such regions displaying potentially different absorption and scattering properties to the radiation. Specific applications are disclosed involving the noninvasive determination of changes in concentration of the substances oxyhemoglobin and deoxyhemoglobin and/or changes in the redox state of the substance cytochrome oxidase within the brain or skeletal muscle, and in cases where the brain or skeletal muscle is interrogated by radiation in the near-infrared part of the electromagnetic spectrum through intervening surface tissues, i.e.