Nested compartment models describing the transport of an extracellular contrast agent through microvessels and its bidirectional diffusion between blood plasma (average concentration ; volume ) and the interstitial space (average concentration, ; volume, ). is the plasma concentration in a tissue-feeding artery, is the apparent plasma flow, and is the permeability-surface area product. The reduced models 2 and 3 are derived under the additional assumption of high plasma flow or fast bidirectional diffusion , respectively. The quantities plotted in bold are the free model parameters to be fitted.
Representative selection of concentration-time curves (data points, 126; temporal resolution, 2.88 s). (a) Arterial input function used for the simulation and analysis of the tissue curves. The vertical lines indicate the period of CA administration. (b) Concentration-time curve of the reference tissue (, , , ). The concentration curves plotted in the lower four rows were simulated for tissues that differ from the reference tissue in one microcirculatory quantity: [(c) and (d)] , 0.09, [(e) and (f)] , 0.30, [(g) and (h)] , 0.9 ml/ml/min, and [(i) and (j)] , 0.8 ml/ml/min. The curves give the results of the pharmacokinetic analysis using the three nested models CM1 (solid line), CM2 (dotted line), and CM3 (dashed line). Please note that the fit curves for CM1 and CM2 widely overlap.
Akaike weights giving the relative strength of evidence for the three nested models CM1, CM2, and CM3 defined in Fig. 1. Data are grouped for tissue curves simulated for varying values of (a) plasma volume , (b) interstitial volume , (c) plasma flow, , and (d) permeability-surface area product, . The values of the physiological variables used for the simulations are presented in the same order in Table I.
Tissue parameters estimated by the multimodel approach for 40 tissue curves simulated with MMID4 for different values of (a) plasma volume , (b) interstitial volume , (c) plasma flow, , and (d) permeability-surface area product, . The solid lines represent the theoretically expected model parameters, whereas the different symbols indicate the model that contributes most to the estimated parameter values (CM1: ●, CM2: ▼, CM3: ▲). The open and full symbols in the flow plots (fourth row) give the apparent and the corrected plasma flow , respectively.
Values of the physiological variables used for the simulation of 40 tissue concentration-time curves. One of the specified quantities was always varied over the ten values given in the respective column while the three other variables were fixed at the reference values printed in bold.
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