Distributed models

Distributed models describe spatial and temporal variations and are generally accepted to correspond more closely to physiological reality than simpler compartmental models (Zierler, 1981; Kuikka et al 1991). Compartmental models are inadequate when the data have high temporal resolution (Zierler, 1981; Munk et al 2003).

However, in PET imaging, compartmental models have been shown to provide estimates of receptor concentration that are as good as those of a distributed model, and are assumed to be adequate for analysis of PET imaging data in general, when there is limited temporal resolution (Muzic & Saidel, 2003). More complex distributed-parameter models may not even be adequate at all for PET data in some cases (Quarles et al., 1993).

See also:

• Compartmental model
• Spectral analysis
• Reaction-diffusion model
• Tissue heterogeneity
• Input function

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References:

Knudsen GM, Pettigrew KD, Paulson OB, Hertz MM, Patlak CS. Kinetic analysis of blood-brain barrier transport of D-glucose in man: quantitative evaluation in the presence of tracer backflux and capillary heterogeneity. Microvasc Res. 1990; 39: 28-49. doi: 10.1016/0026-2862(90)90057-X.

Kuikka JT, Bassingthwaighte JB, Henrich MM, Feinendegen LE. Mathematical modelling in nuclear medicine. Eur J Nucl Med. 1991; 18: 351-362. PMID: 1936044.

Liu D, Chalkidou A, Landau DB, Marsden PK, Fenwick JD. Interstitial diffusion and the relationship between compartment modelling and multi-scale spatial-temporal modelling of ¹⁸F-FLT tumour uptake dynamics. Phys Med Biol. 2014; 59(17): 5175-5202. doi: 10.1088/0031-9155/59/17/5175.

Munk OL, Bass L, Feng H, Keiding S. Determination of regional flow by use of intravascular PET tracers: microvascular theory and experimental validation for pig livers. J Nucl Med. 2003; 44: 1862-1870. PMID: 14602871.

Muzic RF Jr, Saidel GM. Distributed versus compartmental models for PET receptor studies. IEEE Trans Med Imaging 2003; 22:11-21. doi: 10.1109/TMI.2002.806576.

Quarles RP, Mintun MA, Larson KB, Markham J, MacLeod AM, Raichle ME. Measurement of regional cerebral blood flow with positron emission tomography: a comparison of [¹⁵O]water to [¹¹C]butanol with distributed-parameter and compartmental models. J Cereb Blood Flow Metab. 1993; 13: 733-747. doi: 10.1038/jcbfm.1993.94.

Wilks MQ, Knowles SM, Wu AM, Huang S-C. Improved modeling of in vivo kinetics of slowly diffusing radiotracers for tumor imaging. J Nucl Med. 2014; 55(9): 1539-1544. doi: 10.2967/jnumed.114.140038.

Zierler K. A critique of compartmental analysis. Annu Rev Biophys Bioeng. 1981; 10:531-562. doi: 10.1146/annurev.bb.10.060181.002531.

Tags: Modeling, Compartmental model, Distributed model

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Updated at: 2019-03-07
Created at: 2005-06-12
Written by: Vesa Oikonen