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Iterative optimal design of PET experiments for estimating β-adrenergic receptor concentration

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Abstract

To estimate in vivo myocardial β-adrenergic receptor concentration with sufficient precision and to reduce the experimental complexities in positron emission tomography (PET), an iterative optimal design method is applied. An initial three-injection protocol, utilising [F-18]-labelled (R)- and (S)-fluorocarazolol and unlabelled (S)-fluorocarazolol, is optimised for ligand dosages and administration times to maximise the precision of all model parameters using the D-optimal criterion. Using this experimental protocol, PET data are collected in porcine studies, and model parameters are estimated. All model parameters are identified with satisfactory precision. The in vivo myocardial β-receptor concentration is 7.5±0.6 pmol ml−1, which corresponds to the in vitro result of 10.1±1.3pmol ml−1. With more accurate parameter values, a simplified two-injection protocol is optimally designed, utilising only radiolabelled and unlabelled (S)-fluorocarazolol, based on a new criterion to maximise the precision of the β-receptor concentration. This revised optimum design predicts that the in vivo β-receptor concentration can be estimated with good precision but reduced experiment complexity.

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Abbreviations

A i(t):

radioactivity concentration in blood MBq ml−1

B i(t):

molecular concentration of receptor-bound ligand duringith tracer injection, pmol ml−1

F i(t):

molecular concentration of ligand in its free phase in tissue duringith tracer injection, pmol ml−1

α:

fraction of vascular volume per unit volume of tissue, ml ml−1

k 1 :

rate constant of transport of ligand from plasma into its free phase in tissue, min−1

k 2 :

rate constant of ligand returning from free phase in tissue to plasma, min−1

k on :

association rate constant at which ligand binds to receptor, ml pmol−1 min−1

k off :

dissociation rate constant at which ligand dissociates from receptor, min−1

L i(t):

fraction of whole blood activity due to ligand in plasma, unitless

M j(t):

model-generated average radioactivity uptake over scan intervalj, MBqml−1

P i(t):

molecular concentration of ligand in blood, pmol ml−1

γ:

partial volume loss factor that accounts for under-estimation of radioactivity in small region due to scanner resolution effects, unitless

R :

haematocrit, fraction of blood cell volume to total blood volume, unitless

S i(t):

specific activity of radioactive ligand, MBq pmol−1

ε:

scatter fraction, fraction of radioactivity contributed from whole blood, unitless

θ:

model parameter vector

D LRi :

dose of labelled (R)-fluorocarazolol in injectioni, nmol

D LSi :

dose of labelled (S)-fluorocarazolol in injectioni, nmol

D URi :

dose of unlabelled (R)-fluorocarazolol in injectioni, nmol

D USi :

dose of unlabelled (S)-fluorocarazolol in injectioni, nmol

T i :

time of injectioni, min

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Authors and Affiliations

  1. Department of Biomedical Engineering, Case Western Reserve University, Cleveland, Ohio, USA

    R. F. Muzic Jr, G. M. Saidel, N. Zhu & A. D. Nelson

  2. Department of Radiology, University Hospital of Cleveland and Case Western Reserve University School of Medicine, Cleveland, Ohio, USA

    R. F. Muzic Jr, A. D. Nelson, L. Zheng & M. S. Berridge

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  1. R. F. Muzic Jr
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  2. G. M. Saidel
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  3. N. Zhu
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  4. A. D. Nelson
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  5. L. Zheng
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  6. M. S. Berridge
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Correspondence to R. F. Muzic Jr.

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Muzic, R.F., Saidel, G.M., Zhu, N. et al. Iterative optimal design of PET experiments for estimating β-adrenergic receptor concentration. Med. Biol. Eng. Comput. 38, 593–602 (2000). https://doi.org/10.1007/BF02344863

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  • DOI: https://doi.org/10.1007/BF02344863

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