This review is devoted to recent developments in blood flow modelling. It begins with the discussion of blood rheology and its non-Newtonian properties. After that we will present some modelling methods where blood is considered as a heterogeneous fluid composed of plasma and blood cells. Namely, we will describe the method of Dissipative Particle Dynamics and will present some results of blood flow modelling. The last part of this paper deals with one-dimensional global models of blood circulation. We will explain the main ideas of this approach and will present some examples of its application.

/pdf/methods-of-blood-flow-modelling-4mengux450.pdf

Methods of blood flow modelling

The calf muscle pump is a mechanism which increases venous return and thereby compensates for the fluid shift towards the lower body during standing. During a muscle contraction, the embedded deep veins collapse and venous return increases. In the subsequent relaxation phase, muscle perfusion increases due to increased perfusion pressure, as the proximal venous valves temporarily reduce the distal venous pressure (shielding). The superficial and deep veins are connected via perforators, which contain valves allowing flow in the superficial-to-deep direction. The aim of this study is to investigate and quantify the physiological mechanisms of the calf muscle pump, including the effect of venous valves, hydrostatic pressure, and the superficial venous system. Using a one-dimensional pulse wave propagation model, a muscle contraction is simulated by increasing the extravascular pressure in the deep venous segments. The hemodynamics are studied in three different configurations: a single artery-vein configuration with and without valves and a more detailed configuration including a superficial vein. Proximal venous valves increase effective venous return by 53% by preventing reflux. Furthermore, the proximal valves shielding function increases perfusion following contraction. Finally, the superficial system aids in maintaining the perfusion during the contraction phase and reduces the refilling time by 37%.

/pdf/a-1d-pulse-wave-propagation-model-of-the-hemodynamics-of-3l2jafhcc9.pdf

A 1D pulse wave propagation model of the hemodynamics of calf muscle pump function

Abstract Atherosclerotic diseases of coronary vessels are the main reasons of myocardial ischemia. The value of the fractional flow reserve (FFR) factor is the golden standard for making decision on coronary network surgical treatment. The FFR measurements require expensive endovascular diagnostics. We propose a noninvasive method of the virtual FFR assessment in patient-specific coronary network based on angiography and computer tomography data. Also we analyze sensitivity of the model to the heart stroke volume.

Virtual fractional flow reserve assessment in patient-specific coronary networks by 1D hemodynamic model

Abstract Patient-specific simulations of human physiological processes remain the challenge for many years. Detailed 3D reconstruction of body anatomical parts on the basis of medical images is an important stage of individualized simulations in physiology. In this paper we present and develop the methods and algorithms for construction of patient-specific discrete geometric models. These models are represented by anatomically correct computational meshes. Practical use of these methods is demonstrated for two important medical applications: numerical evaluation of fractional flow reserve in coronary arteries and electrocardiography simulation

Patient-specific anatomical models in human physiology

The review presents the state of the art in the atherosclerosis modelling. It begins with the biological introduction describing the mechanisms of chronic inflammation of artery walls characterizing the development of atherosclerosis. In particular, we present in more detail models describing this chronic inflammation as a reaction-diffusion wave with regimes of propagation depending on the level of cholesterol (LDL) and models of rolling monocytes initializing the inflammation. Further development of this disease results in the formation of atherosclerotic plaque, vessel remodelling and possible plaque rupture due its interaction with blood flow. We review plaque-flow interaction models as well as reduced models (0D and 1D) of blood flow in atherosclerotic vasculature.

https://www.mmnp-journal.org/articles/mmnp/pdf/2019/06/mmnp190135.pdf

Mathematical Modelling of Atherosclerosis

Abstract This work is aimed at computational study of the blood flow in lower extremities under intense physical load. We present a modified 1D cardiovascular system model describing skeletal-muscle pumping and autoregulation effects on the blood flow in lower extremities. Skeletal-muscle pump effect is introduced as an external time-periodical pressure function applied to a group of veins. The period of this function is associated with the two-stride period during running. The computational study reveals the explicit optimal stride frequency providing the maximum blood flow through the lower extremities. It is shown that the optimal stride frequency depends on personal parameters. The model is validated by a comparison to the stride frequencies of a number of top-level athletes, therefore, providing a method to assess the level of physical conditioning.

Computational study of blood flow in lower extremities under intense physical load

/pdf/effects-of-vipassana-insight-meditation-on-quality-of-life-3aoht7ke.pdf

Effects of Vipassana Insight Meditation on Quality of Life and Plasma Endogenous Beta-endorphin Level in Registered Meditators Practicing Meditation at the Well-established Meditation Centres in Selangor

The scientific study of blood flow through human circulatory system has been the subject of scientific re-search for a couple of centuries. It is a complex problem due to the complicated structure of blood vessels and the blood itself. The experimental studies are very useful for the diagnosis of cardiovascular diseases and other practical applications. Unfortunately, experiments are usually expensive and have technical limitations. That’s why mathematical models are so important in studying human circulatory system. They help to predict the consequences of different impacts on human body and calculate various blood parameters. We use 1D network dynamical model of systemic circulation [1, 2] et. al. in this work that is briefly presented in the beginning. It provides adequate and detailed enough description for the blood flow in the heart, major large arteries and veins of hands and legs. We introduce new method of model validation and identification by comparing calculated and experimental values of the pulse wave velocity (PWV) [3, 4]. We use PWV index in this work to specify model parameters more adequate for specific cases of trained athletes [5, 6]. The work is focused on extending this model with mathematical model of skeletal-muscle pumping that is described in the second part. The skeletal-muscle pump is an effect of the group of skeletal muscles during exercise providing additional pressure to the blood flowing to the heart from extremities. Such pumping is especially important in the veins of the legs during walking and running. Numerical simulations are presented showing blood flow redistribution during intensive exercise. Basing on the purely mechanical approach we conclude that effective blood flow through lower extremities during intensive running can be optimized by the stride frequency that depends on the cardiovascular network morphological properties.

Computational Model of Blood Flow Optimization in Lower Extremities during Intensive Exercise

Item analysis of type “A” multiple choice questions of biochemistry in GIM module, year 1 MBBS program

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Papers

Computational study of blood flow in lower extremities under intense physical load

Effects of Vipassana Insight Meditation on Quality of Life and Plasma Endogenous Beta-endorphin Level in Registered Meditators Practicing Meditation at the Well-established Meditation Centres in Selangor

Computational Model of Blood Flow Optimization in Lower Extremities during Intensive Exercise

Item analysis of type “A” multiple choice questions of biochemistry in GIM module, year 1 MBBS program