Global compartmental pharmacokinetic models for spatiotemporal SPECT and PET imaging

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

A new mathematical framework is introduced for combining the linear compartmental models used in pharmacokinetics with the spatiotemporal distributions of activity that are measured in single photon emission computed tomography (SPECT) and PET imaging. This approach is global in the sense that the compartmental differential equations involve only the overall spatially integrated activity in each compartment. The kinetics for the local compartmental activities are not specified by the model and would be determined from data. It is shown that an increase in information about the spatial distribution of the local compartmental activities leads to an increase in the number of identifiable quantities associated with the compartmental matrix. These identifiable quantities, which are important kinetic parameters in applications, are determined by computing the invariants of a symmetry group. This group generates the space of compartmental matrices that are compatible with a given activity distribution, input function, and set of support constraints. An example is provided where all of the compartmental spatial supports have been separated, except that of the vascular compartment. The question of estimating the identifiable parameters from SPECT and PET data is also discussed.

Original languageEnglish (US)
Pages (from-to)203-225
Number of pages23
JournalSIAM Journal on Imaging Sciences
Volume2
Issue number1
DOIs
StatePublished - 2009

Fingerprint

Single photon emission computed tomography
Pharmacokinetics
Computed Tomography
Photon
Imaging
Imaging techniques
Kinetic parameters
Spatial distribution
Differential equations
Kinetics
Compartmental Model
Model
Symmetry Group
Spatial Distribution
Linear Model
Differential equation
Invariant
Computing

Keywords

  • Biomedical imaging
  • Compartmental modeling
  • Pharmacokinetics
  • Positron emission tomography
  • Single photon emission computed tomography

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

@article{4ea7deb92de54b43b6008b1621aa0e8a,
title = "Global compartmental pharmacokinetic models for spatiotemporal SPECT and PET imaging",
abstract = "A new mathematical framework is introduced for combining the linear compartmental models used in pharmacokinetics with the spatiotemporal distributions of activity that are measured in single photon emission computed tomography (SPECT) and PET imaging. This approach is global in the sense that the compartmental differential equations involve only the overall spatially integrated activity in each compartment. The kinetics for the local compartmental activities are not specified by the model and would be determined from data. It is shown that an increase in information about the spatial distribution of the local compartmental activities leads to an increase in the number of identifiable quantities associated with the compartmental matrix. These identifiable quantities, which are important kinetic parameters in applications, are determined by computing the invariants of a symmetry group. This group generates the space of compartmental matrices that are compatible with a given activity distribution, input function, and set of support constraints. An example is provided where all of the compartmental spatial supports have been separated, except that of the vascular compartment. The question of estimating the identifiable parameters from SPECT and PET data is also discussed.",
keywords = "Biomedical imaging, Compartmental modeling, Pharmacokinetics, Positron emission tomography, Single photon emission computed tomography",
author = "Clarkson, {Eric W} and Kupinski, {Matthew A}",
year = "2009",
doi = "10.1137/080715226",
language = "English (US)",
volume = "2",
pages = "203--225",
journal = "SIAM Journal on Imaging Sciences",
issn = "1936-4954",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "1",

}

TY - JOUR

T1 - Global compartmental pharmacokinetic models for spatiotemporal SPECT and PET imaging

AU - Clarkson, Eric W

AU - Kupinski, Matthew A

PY - 2009

Y1 - 2009

N2 - A new mathematical framework is introduced for combining the linear compartmental models used in pharmacokinetics with the spatiotemporal distributions of activity that are measured in single photon emission computed tomography (SPECT) and PET imaging. This approach is global in the sense that the compartmental differential equations involve only the overall spatially integrated activity in each compartment. The kinetics for the local compartmental activities are not specified by the model and would be determined from data. It is shown that an increase in information about the spatial distribution of the local compartmental activities leads to an increase in the number of identifiable quantities associated with the compartmental matrix. These identifiable quantities, which are important kinetic parameters in applications, are determined by computing the invariants of a symmetry group. This group generates the space of compartmental matrices that are compatible with a given activity distribution, input function, and set of support constraints. An example is provided where all of the compartmental spatial supports have been separated, except that of the vascular compartment. The question of estimating the identifiable parameters from SPECT and PET data is also discussed.

AB - A new mathematical framework is introduced for combining the linear compartmental models used in pharmacokinetics with the spatiotemporal distributions of activity that are measured in single photon emission computed tomography (SPECT) and PET imaging. This approach is global in the sense that the compartmental differential equations involve only the overall spatially integrated activity in each compartment. The kinetics for the local compartmental activities are not specified by the model and would be determined from data. It is shown that an increase in information about the spatial distribution of the local compartmental activities leads to an increase in the number of identifiable quantities associated with the compartmental matrix. These identifiable quantities, which are important kinetic parameters in applications, are determined by computing the invariants of a symmetry group. This group generates the space of compartmental matrices that are compatible with a given activity distribution, input function, and set of support constraints. An example is provided where all of the compartmental spatial supports have been separated, except that of the vascular compartment. The question of estimating the identifiable parameters from SPECT and PET data is also discussed.

KW - Biomedical imaging

KW - Compartmental modeling

KW - Pharmacokinetics

KW - Positron emission tomography

KW - Single photon emission computed tomography

UR - http://www.scopus.com/inward/record.url?scp=84939891072&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84939891072&partnerID=8YFLogxK

U2 - 10.1137/080715226

DO - 10.1137/080715226

M3 - Article

AN - SCOPUS:84939891072

VL - 2

SP - 203

EP - 225

JO - SIAM Journal on Imaging Sciences

JF - SIAM Journal on Imaging Sciences

SN - 1936-4954

IS - 1

ER -