Estimation of tissue blood perfusion rate from diffusible indicator measurements: A sensitivity analysis

Recording the washout of indicator (for example, heat, radio-labeled dissolved gas, etc.) transiently introduced into tissue allows the estimation of tissue blood perfusion rate. Analysis of the washout data requires a material balance which appropriately accounts for all transport mechanisms and sources and sinks of the given indicator. From that balance one may perform a sensitivity analysis which specifies the susceptibility of the perfusion estimate to experimental errors in any of the pertinent parameters and variables. The sensitivity analysis is based on the normalized partial derivatives of tissue indicator concentration with respect to the experimental variables. The results indicate that the estimation of the tissue blood perfusion rate is highly sensitive to errors in the concentration of the diffusible indicator which dominate, by two orders of magnitude or more, the errors attributed to other parameters. For typical experimental conditions, the errors in the perfusion estimate due to the various parameters are shown to vary considerably, according to the sensor position and time of measurement. Based on this type of analysis, one may specify optimal temporal and spatial domains for the parameter estimation in order to minimize error propagation. The optimal time domains are shown to differ from those used in typical indicator washout analyses for estimating tissue perfusion rate.