A numerical implementation of the maximum-likelihood method of parameter estimation for tracer-kinetic data

Joanne Markham; Donald L. Snyder; Jerome R. Cox

doi:10.1016/0025-5564(76)90128-0

A numerical implementation of the maximum-likelihood method of parameter estimation for tracer-kinetic data

Joanne Markham
, Donald L. Snyder
, Jerome R. Cox

Division of Radiological Sciences

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

The performance is compared of several nonlinear optimization techniques applied to the maximum-likelihood function for Poisson-distributed radiotracer data having a multiexponential intensity function. A new method is described in which the Fisher information matrix associated with the data is employed in place of the Hessian matrix to insure non-negative-definiteness. This method reaches a solution in a few iterations for a wide spread in initial parameter estimates. Moreover, it is more accurate and simple computationally than least-squares techniques currently in use.

Original language	English
Pages (from-to)	275-300
Number of pages	26
Journal	Mathematical Biosciences
Volume	28
Issue number	3-4
DOIs	https://doi.org/10.1016/0025-5564(76)90128-0
State	Published - 1976

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10.1016/0025-5564(76)90128-0

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@article{215d5ae2eddf4205806c8a5aed1e1d47,

title = "A numerical implementation of the maximum-likelihood method of parameter estimation for tracer-kinetic data",

abstract = "The performance is compared of several nonlinear optimization techniques applied to the maximum-likelihood function for Poisson-distributed radiotracer data having a multiexponential intensity function. A new method is described in which the Fisher information matrix associated with the data is employed in place of the Hessian matrix to insure non-negative-definiteness. This method reaches a solution in a few iterations for a wide spread in initial parameter estimates. Moreover, it is more accurate and simple computationally than least-squares techniques currently in use.",

author = "Joanne Markham and Snyder, \{Donald L.\} and Cox, \{Jerome R.\}",

note = "Funding Information: Radioactive tracers are frequently used in clinical and physiological studies. These studies have the advantage of being relatively noninvasive because radiation emanating from the tracer can be monitored using an external detector. The entire time course of radioactivity is monitored in dynamic or kinetic studies. In common practice, the total interval of observation of radioactivity is divided into several subintervals, typically about 100, in each of which the number of gamma or annihilation photons is observed. Thus, the data usually obtained in tracer-kinetic studies consist *This work was supported by the National Institutes of Health Research Grants RR-00396 and HL-13851, the National Institutes of Health Training Grant T01-GM-1747, and the National Science Foundation Grant ENG-74-07800.",

year = "1976",

doi = "10.1016/0025-5564(76)90128-0",

language = "English",

volume = "28",

pages = "275--300",

journal = "Mathematical Biosciences",

issn = "0025-5564",

number = "3-4",

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TY - JOUR

T1 - A numerical implementation of the maximum-likelihood method of parameter estimation for tracer-kinetic data

AU - Markham, Joanne

AU - Snyder, Donald L.

AU - Cox, Jerome R.

N1 - Funding Information: Radioactive tracers are frequently used in clinical and physiological studies. These studies have the advantage of being relatively noninvasive because radiation emanating from the tracer can be monitored using an external detector. The entire time course of radioactivity is monitored in dynamic or kinetic studies. In common practice, the total interval of observation of radioactivity is divided into several subintervals, typically about 100, in each of which the number of gamma or annihilation photons is observed. Thus, the data usually obtained in tracer-kinetic studies consist *This work was supported by the National Institutes of Health Research Grants RR-00396 and HL-13851, the National Institutes of Health Training Grant T01-GM-1747, and the National Science Foundation Grant ENG-74-07800.

PY - 1976

Y1 - 1976

N2 - The performance is compared of several nonlinear optimization techniques applied to the maximum-likelihood function for Poisson-distributed radiotracer data having a multiexponential intensity function. A new method is described in which the Fisher information matrix associated with the data is employed in place of the Hessian matrix to insure non-negative-definiteness. This method reaches a solution in a few iterations for a wide spread in initial parameter estimates. Moreover, it is more accurate and simple computationally than least-squares techniques currently in use.

AB - The performance is compared of several nonlinear optimization techniques applied to the maximum-likelihood function for Poisson-distributed radiotracer data having a multiexponential intensity function. A new method is described in which the Fisher information matrix associated with the data is employed in place of the Hessian matrix to insure non-negative-definiteness. This method reaches a solution in a few iterations for a wide spread in initial parameter estimates. Moreover, it is more accurate and simple computationally than least-squares techniques currently in use.

UR - https://www.scopus.com/pages/publications/0017228273

U2 - 10.1016/0025-5564(76)90128-0

DO - 10.1016/0025-5564(76)90128-0

M3 - Article

AN - SCOPUS:0017228273

SN - 0025-5564

VL - 28

SP - 275

EP - 300

JO - Mathematical Biosciences

JF - Mathematical Biosciences

IS - 3-4

ER -

A numerical implementation of the maximum-likelihood method of parameter estimation for tracer-kinetic data

Abstract

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