Prediction of myocardial blood flow under stress conditions by means of a computational model.

PURPOSE: Quantification of myocardial blood flow (MBF) and functional assessment of coronary artery disease (CAD) can be achieved through stress myocardial computed tomography perfusion (stress-CTP). This requires an additional scan after the resting coronary computed tomography angiography (cCTA) and administration of an intravenous stressor. This complex protocol has limited reproducibility and non-negligible side effects for the patient. We aim to mitigate these drawbacks by proposing a computational model able to reproduce MBF maps. METHODS: A computational perfusion model was used to reproduce MBF maps. The model parameters were estimated by using information from cCTA and MBF measured from stress-CTP (MBFCTP) maps. The relative error between the computational MBF under stress conditions (MBFCOMP) and MBFCTP was evaluated to assess the accuracy of the proposed computational model. RESULTS: Applying our method to 9 patients (4 control subjects without ischemia vs 5 patients with myocardial ischemia), we found an excellent agreement between the values of MBFCOMP and MBFCTP. In all patients, the relative error was below 8% over all the myocardium, with an average-in-space value below 4%. CONCLUSION: The results of this pilot work demonstrate the accuracy and reliability of the proposed computational model in reproducing MBF under stress conditions. This consistency test is a preliminary step in the framework of a more ambitious project which is currently under investigation, i.e., the construction of a computational tool able to predict MBF avoiding the stress protocol and potential side effects while reducing radiation exposure.

Numerical simulations of the microvascular fluid balance with a non-linear model of the lymphatic system.

Fluid homeostasis is required for life. Processes involved in fluid balance are strongly related to exchanges at the microvascular level. Computational models have been presented in the literature to analyze the microvascular-interstitial interactions. As far as we know, none of those models consider a physiological description for the lymphatic drainage-interstitial pressure relation. We develop a computational model that consists of a network of straight cylindrical vessels and an isotropic porous media with a uniformly distributed sink term acting as the lymphatic system. In order to describe the lymphatic flow rate, a non-linear function of the interstitial pressure is defined, based on literature data on the lymphatic system. The proposed model of lymphatic drainage is compared to a linear one, as is typically used in computational models. To evaluate the response of the model, the two are compared with reference to both physiological and pathological conditions. Differences in the local fluid dynamic description have been observed using the non-linear model. In particular, the distribution of interstitial pressure is heterogeneous in all the cases analyzed. The resulting averaged values of the interstitial pressure are also different, and they agree with literature data when using the non-linear model. This work highlights the key role of lymphatic drainage and its modeling when studying the fluid balance in microcirculation for both to physiological and pathological conditions, e.g. uremia.

A computational model for microcirculation including Fahraeus-Lindqvist effect, plasma skimming and fluid exchange with the tissue interstitium.

We present a two-phase model for microcirculation that describes the interaction of plasma with red blood cells. The model takes into account of typical effects characterizing the microcirculation, such as the Fahraeus-Lindqvist effect and plasma skimming. Besides these features, the model describes the interaction of capillaries with the surrounding tissue. More precisely, the model accounts for the interaction of capillary transmural flow with the surrounding interstitial pressure. Furthermore, the capillaries are represented as one-dimensional channels with arbitrary, possibly curved configuration. The latter two features rely on the unique ability of the model to account for variations of flow rate and pressure along the axis of the capillary, according to a local differential formulation of mass and momentum conservation. Indeed, the model stands on a solid mathematical foundation, which is also addressed in this work. In particular, we present the model derivation, the variational formulation, and its approximation using the finite element method. Finally, we conclude the work with a comparative computational study of the importance of the Fahraeus-Lindqvist, plasma skimming, and capillary leakage effects on the distribution of flow in a microvascular network.