Using a Human Circulation Mathematical Model to Simulate the Effects of Hemodialysis and Therapeutic Hypothermia

Recent Advances and Future Perspectives in the Use of Machine Learning and Mathematical Models in Nephrology

We reviewed some of the latest advancements in the use of mathematical models in nephrology. We looked over 2 distinct categories of mathematical models that are widely used in biological research and pointed out some of their strengths and weaknesses when applied to health care, especially in the context of nephrology. A mechanistic dynamical system allows the representation of causal relations among the system variables but with a more complex and longer development/implementation phase. Artificial intelligence/machine learning provides predictive tools that allow identifying correlative patterns in large data sets, but they are usually harder-to-interpret black boxes. Chronic kidney disease (CKD), a major worldwide health problem, generates copious quantities of data that can be leveraged by choice of the appropriate model; also, there is a large number of dialysis parameters that need to be determined at every treatment session that can benefit from predictive mechanistic models. Following important steps in the use of mathematical methods in medical science might be in the intersection of seemingly antagonistic frameworks, by leveraging the strength of each to provide better care.

Structure (Epicardial Stenosis) and Function (Microvascular Dysfunction) That Influence Coronary Fractional Flow Reserve Estimation

Background. The treatment of coronary stenosis is decided by performing high risk invasive surgery to generate the fractional flow reserve diagnostics index, a ratio of distal to proximal pressures in respect of coronary atherosclerotic plaques. Non-invasive methods are a need of the times that necessitate the use of mathematical models of coronary hemodynamic physiology. This study proposes an extensible mathematical description of the coronary vasculature that provides an estimate of coronary fractional flow reserve. Methods. By adapting an existing computational model of human coronary blood flow, the effects of large vessel stenosis and microvascular disease on fractional flow reserve were quantified. Several simulations generated flow and pressure information, which was used to compute fractional flow reserve under several conditions including focal stenosis, diffuse stenosis, and microvascular disease. Sensitivity analysis was used to uncover the influence of model parameters on fractional flow reserve. The model was simulated as coupled non-linear ordinary differential equations and numerically solved using our implicit higher order method. Results. Large vessel stenosis affected fractional flow reserve. The model predicts that the presence, rather than severity, of microvascular disease affects coronary flow deleteriously. Conclusions. The model provides a computationally inexpensive instrument for future in silico coronary blood flow investigations as well as clinical-imaging decision making. A combination of focal and diffuse stenosis appears to be essential to limit coronary flow. In addition to pressure measurements in the large epicardial vessels, diagnosis of microvascular disease is essential. The independence of the index with respect to heart rate suggests that computationally inexpensive steady state simulations may provide sufficient information to reliably compute the index.

Atrial Fibrillation and Anterior Cerebral Artery Absence Reduce Cerebral Perfusion: A De Novo Hemodynamic Model

Background: Atrial fibrillation is a prevalent cardiac arrhythmia and may reduce cerebral blood perfusion augmenting the risk of dementia. We hypothesize that geometric variations in the cerebral arterial structure called the Circle of Willis (CoW) play an important role in influencing cerebral perfusion. The objective of this work was to develop a novel cardio-cerebral lumped parameter hemodynamic model to investigate the role of CoW variants on cerebral blood flow dynamics under atrial fibrillation conditions. Methods: A computational blood flow model was developed by coupling whole-body and detailed cerebral circulation descriptions, modified to represent six common variations of the CoW. Cerebral blood flow dynamics were simulated in common CoW variants, under control and imposed atrial fibrillation conditions. Risk was assessed based on the frequency of beat-wise hypoperfusion events, and sensitivity analysis was performed with respect to this model output. Results: It was found that the geometry of the CoW influenced the frequency of hypoperfusion events at different heart rates, with the variant missing a P1 segment having the highest risk. Sensitivity analysis revealed that intrinsic heart rate is most associated with the considered outcome. Conclusions: Our results suggest that CoW geometry plays an important role in influencing cerebral hemodynamics during atrial fibrillation. The presented study may assist in guiding our future clinical-imaging research.