Validity of model approximations for receptor-ligand kinetics in nuclear medicine
An appropriate mathematical model is required for quantitative analysis of high affinity radioligands as direct or surrogate probes to measure receptor distribution, affinity, concentration, binding potential, and endogenous or exogenous ligand occupancy levels. For studies with positron emission to...
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description | An appropriate mathematical model is required for quantitative analysis of high affinity radioligands as direct or surrogate probes to measure receptor distribution, affinity, concentration, binding potential, and endogenous or exogenous ligand occupancy levels. For studies with positron emission tomography (PET) or single photon emission computed tomography (SPECT), the receptor-ligand compartment model has been well established and widely used. This pharmacokinetic model is represented mathematically by a set of nonlinear ordinary differential equations. Variations of models for PET and SPECT account for radioactive decay differently. These are not equivalent and entail assumptions or approximations that may be not appreciated. In this study, a general form of the model is presented and compared with others with various approximations, which are valid only under specific conditions. The various approximate formulations were analytically compared to the exact model to identify the terms that were neglected in the approximate formulations. The extent to which the approximations impact the model solutions was assessed by computer simulations based on numerical solutions to each set of equations. Specifically, each model formulation was tested using three simulated injection protocols representing a typical PET experiment, a typical SPECT experiment, and an extreme experiment where both the injected activity and the specific activity were very high. No significant differences were found among the output of the three model formulations when the PET and SPECT injection protocols were tested. The only conditions that produced significant differences occurred when the specific activity and the administered activity were simultaneously very high. These conditions, however, have little practical relevance to experimentally achievable conditions due to radiation dose and specific activity of radiopharmaceuticals. |
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For studies with positron emission tomography (PET) or single photon emission computed tomography (SPECT), the receptor-ligand compartment model has been well established and widely used. This pharmacokinetic model is represented mathematically by a set of nonlinear ordinary differential equations. Variations of models for PET and SPECT account for radioactive decay differently. These are not equivalent and entail assumptions or approximations that may be not appreciated. In this study, a general form of the model is presented and compared with others with various approximations, which are valid only under specific conditions. The various approximate formulations were analytically compared to the exact model to identify the terms that were neglected in the approximate formulations. The extent to which the approximations impact the model solutions was assessed by computer simulations based on numerical solutions to each set of equations. Specifically, each model formulation was tested using three simulated injection protocols representing a typical PET experiment, a typical SPECT experiment, and an extreme experiment where both the injected activity and the specific activity were very high. No significant differences were found among the output of the three model formulations when the PET and SPECT injection protocols were tested. The only conditions that produced significant differences occurred when the specific activity and the administered activity were simultaneously very high. 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For studies with positron emission tomography (PET) or single photon emission computed tomography (SPECT), the receptor-ligand compartment model has been well established and widely used. This pharmacokinetic model is represented mathematically by a set of nonlinear ordinary differential equations. Variations of models for PET and SPECT account for radioactive decay differently. These are not equivalent and entail assumptions or approximations that may be not appreciated. In this study, a general form of the model is presented and compared with others with various approximations, which are valid only under specific conditions. The various approximate formulations were analytically compared to the exact model to identify the terms that were neglected in the approximate formulations. The extent to which the approximations impact the model solutions was assessed by computer simulations based on numerical solutions to each set of equations. Specifically, each model formulation was tested using three simulated injection protocols representing a typical PET experiment, a typical SPECT experiment, and an extreme experiment where both the injected activity and the specific activity were very high. No significant differences were found among the output of the three model formulations when the PET and SPECT injection protocols were tested. The only conditions that produced significant differences occurred when the specific activity and the administered activity were simultaneously very high. These conditions, however, have little practical relevance to experimentally achievable conditions due to radiation dose and specific activity of radiopharmaceuticals.</description><subject>APPROXIMATIONS</subject><subject>Biomedical modeling</subject><subject>Computer simulation</subject><subject>COMPUTERIZED SIMULATION</subject><subject>DIFFERENTIAL EQUATIONS</subject><subject>Equations of state</subject><subject>Experiment design</subject><subject>LIGANDS</subject><subject>Membrane Proteins - metabolism</subject><subject>Models, Theoretical</subject><subject>nonlinear differential equations</subject><subject>NUCLEAR MEDICINE</subject><subject>Numerical modeling</subject><subject>NUMERICAL SOLUTION</subject><subject>Ordinary differential equations</subject><subject>POSITRON COMPUTED TOMOGRAPHY</subject><subject>positron emission tomography</subject><subject>Positron emission tomography (PET)</subject><subject>Positron-Emission Tomography - methods</subject><subject>RADIATION DOSES</subject><subject>Radioactive decay</subject><subject>Radioactivity</subject><subject>RADIOLOGY AND NUCLEAR MEDICINE</subject><subject>RADIOPHARMACEUTICALS</subject><subject>Radiopharmaceuticals - metabolism</subject><subject>RECEPTORS</subject><subject>SINGLE PHOTON EMISSION COMPUTED TOMOGRAPHY</subject><subject>Single photon emission computed tomography (SPECT)</subject><subject>Tomography, Emission-Computed, Single-Photon - methods</subject><issn>0094-2405</issn><issn>2473-4209</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2007</creationdate><recordtype>article</recordtype><sourceid>EIF</sourceid><recordid>eNp9kF1LHDEYRoMo7vpx4R8oAUFoYTRvZpJsLkWsFRQr2N6GTJJp085OxmRW3X_frDNgb_QqEA4neQ5CR0BOAWBxBqdUgGRcbqE5rURZVJTIbTQnRFYFrQibob2U_hBCeMnILpqBYIxRBnN0_1O33vphjUODl8G6Fuu-j-HFL_XgQ5dwEyKOzrh-CLFo_S_dWfzXd27wJmHf4W5lWqcjXjrrTb4_QDuNbpM7nM599OPr5cPFt-Lm7ur64vymMBVIWVDBYUFB1o3TkP_MJOdcE8GEWFgwleDSQK1rLisrmLGG6kZSsK7WpCZQlvvoePSGNHiVjB-c-W1C1zkzqLyfQUlIpk5GKm96XLk0qKVPxrWt7lxYJSUIk0wueAY_j6CJIaXoGtXH3CCuFRC1qaxATZUz-2mSruo8-42csmagGIFn37r1-yZ1-30Sfhn5zYzX7h--_i78FOJ_8t425T9uUaAe</recordid><startdate>200705</startdate><enddate>200705</enddate><creator>Salinas, Cristian A.</creator><creator>Muzic, Raymond F.</creator><creator>Saidel, Gerald M.</creator><general>American Association of Physicists in Medicine</general><scope>CGR</scope><scope>CUY</scope><scope>CVF</scope><scope>ECM</scope><scope>EIF</scope><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7X8</scope><scope>OTOTI</scope></search><sort><creationdate>200705</creationdate><title>Validity of model approximations for receptor-ligand kinetics in nuclear medicine</title><author>Salinas, Cristian A. ; Muzic, Raymond F. ; Saidel, Gerald M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c4199-27618219bfea147359666a075778d1c4769c1bab694d75cdc2af921deba0b0133</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2007</creationdate><topic>APPROXIMATIONS</topic><topic>Biomedical modeling</topic><topic>Computer simulation</topic><topic>COMPUTERIZED SIMULATION</topic><topic>DIFFERENTIAL EQUATIONS</topic><topic>Equations of state</topic><topic>Experiment design</topic><topic>LIGANDS</topic><topic>Membrane Proteins - metabolism</topic><topic>Models, Theoretical</topic><topic>nonlinear differential equations</topic><topic>NUCLEAR MEDICINE</topic><topic>Numerical modeling</topic><topic>NUMERICAL SOLUTION</topic><topic>Ordinary differential equations</topic><topic>POSITRON COMPUTED TOMOGRAPHY</topic><topic>positron emission tomography</topic><topic>Positron emission tomography (PET)</topic><topic>Positron-Emission Tomography - methods</topic><topic>RADIATION DOSES</topic><topic>Radioactive decay</topic><topic>Radioactivity</topic><topic>RADIOLOGY AND NUCLEAR MEDICINE</topic><topic>RADIOPHARMACEUTICALS</topic><topic>Radiopharmaceuticals - metabolism</topic><topic>RECEPTORS</topic><topic>SINGLE PHOTON EMISSION COMPUTED TOMOGRAPHY</topic><topic>Single photon emission computed tomography (SPECT)</topic><topic>Tomography, Emission-Computed, Single-Photon - methods</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Salinas, Cristian A.</creatorcontrib><creatorcontrib>Muzic, Raymond F.</creatorcontrib><creatorcontrib>Saidel, Gerald M.</creatorcontrib><collection>Medline</collection><collection>MEDLINE</collection><collection>MEDLINE (Ovid)</collection><collection>MEDLINE</collection><collection>MEDLINE</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>MEDLINE - Academic</collection><collection>OSTI.GOV</collection><jtitle>Medical physics (Lancaster)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Salinas, Cristian A.</au><au>Muzic, Raymond F.</au><au>Saidel, Gerald M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Validity of model approximations for receptor-ligand kinetics in nuclear medicine</atitle><jtitle>Medical physics (Lancaster)</jtitle><addtitle>Med Phys</addtitle><date>2007-05</date><risdate>2007</risdate><volume>34</volume><issue>5</issue><spage>1693</spage><epage>1703</epage><pages>1693-1703</pages><issn>0094-2405</issn><eissn>2473-4209</eissn><coden>MPHYA6</coden><abstract>An appropriate mathematical model is required for quantitative analysis of high affinity radioligands as direct or surrogate probes to measure receptor distribution, affinity, concentration, binding potential, and endogenous or exogenous ligand occupancy levels. For studies with positron emission tomography (PET) or single photon emission computed tomography (SPECT), the receptor-ligand compartment model has been well established and widely used. This pharmacokinetic model is represented mathematically by a set of nonlinear ordinary differential equations. Variations of models for PET and SPECT account for radioactive decay differently. These are not equivalent and entail assumptions or approximations that may be not appreciated. In this study, a general form of the model is presented and compared with others with various approximations, which are valid only under specific conditions. The various approximate formulations were analytically compared to the exact model to identify the terms that were neglected in the approximate formulations. The extent to which the approximations impact the model solutions was assessed by computer simulations based on numerical solutions to each set of equations. Specifically, each model formulation was tested using three simulated injection protocols representing a typical PET experiment, a typical SPECT experiment, and an extreme experiment where both the injected activity and the specific activity were very high. No significant differences were found among the output of the three model formulations when the PET and SPECT injection protocols were tested. The only conditions that produced significant differences occurred when the specific activity and the administered activity were simultaneously very high. These conditions, however, have little practical relevance to experimentally achievable conditions due to radiation dose and specific activity of radiopharmaceuticals.</abstract><cop>United States</cop><pub>American Association of Physicists in Medicine</pub><pmid>17555251</pmid><doi>10.1118/1.2719569</doi><tpages>11</tpages></addata></record> |
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subjects | APPROXIMATIONS Biomedical modeling Computer simulation COMPUTERIZED SIMULATION DIFFERENTIAL EQUATIONS Equations of state Experiment design LIGANDS Membrane Proteins - metabolism Models, Theoretical nonlinear differential equations NUCLEAR MEDICINE Numerical modeling NUMERICAL SOLUTION Ordinary differential equations POSITRON COMPUTED TOMOGRAPHY positron emission tomography Positron emission tomography (PET) Positron-Emission Tomography - methods RADIATION DOSES Radioactive decay Radioactivity RADIOLOGY AND NUCLEAR MEDICINE RADIOPHARMACEUTICALS Radiopharmaceuticals - metabolism RECEPTORS SINGLE PHOTON EMISSION COMPUTED TOMOGRAPHY Single photon emission computed tomography (SPECT) Tomography, Emission-Computed, Single-Photon - methods |
title | Validity of model approximations for receptor-ligand kinetics in nuclear medicine |
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