Modeling Reactive Hyperemia to Better Understand and Assess Microvascular Function: A Review of Techniques

Reactive hyperemia is a well-established technique for the non-invasive evaluation of the peripheral microcirculatory function, measured as the magnitude of limb re-perfusion after a brief period of ischemia. Despite widespread adoption by researchers and clinicians alike, many uncertainties remain surrounding interpretation, compounded by patient-specific confounding factors (such as blood pressure or the metabolic rate of the ischemic limb). Mathematical modeling can accelerate our understanding of the physiology underlying the reactive hyperemia response and guide in the estimation of quantities which are difficult to measure experimentally. In this work, we aim to provide a comprehensive guide for mathematical modeling techniques that can be used for describing the key phenomena involved in the reactive hyperemia response, alongside their limitations and advantages. The reported methodologies can be used for investigating specific reactive hyperemia aspects alone, or can be combined into a computational framework to be used in (pre-)clinical settings

On the poro-elastic models for microvascular blood flow resistance: An in vitro validation

Nowadays, adequate and accurate representation of the microvascular flow resistance constitutes one of the major challenges in computational haemodynamic studies. In this work, a theoretical, porous media framework, ultimately designed for representing downstream resistance, is presented and compared against an in vitro experimental results. The resistor consists of a poro-elastic tube, with either a constant or variable porosity profile in space. The underlying physics, characterizing the fluid flow through the porous media, is analysed by considering flow variables at different network locations. Backward reflections, originated in the reservoir of the in vitro model, are accounted for through a reflection coefficient imposed as an outflow network condition. The simulation results are in good agreement with the measurements for both the homogenous and heterogeneous porosity conditions. In addition, the comparison allows identification of the range of values representing experimental reservoir reflection coefficients. The pressure drops across the heterogeneous porous media increases with respect to the simpler configuration, whilst flow remains almost unchanged. The effect of some fluid network features, such as tube Young’s modulus and fluid viscosity, on the theoretical results is also elucidated, providing a reference for the and simulation of different microvascular conditions

A Robust Finite Element Modeling Approach to Conjugate Heat Transfer in Flexible Elastic Tubes and Tube Networks

In this work, heat transfer between fluid flow in elastic tubes and external environment is modeled using a robust finite element approach. The transport of energy is coupled to fluid flow that is linked to the pressure and cross-sectional area variations of the tube. The novel model developed is applied to flow and heat transfer in elastic tubes with different geometric and material properties. The effects of reflections due to discontinuities and bifurcations in the tubes are also investigated. To determine the heat transport by conduction in the elastic walls, a radial heat conduction model is also incorporated. The coupled flow equations are solved using the locally conservative Galerkin finite element method, which provides an explicit element-wise conservation of fluxes. Several simulations are performed for different parametric variations to understand the relevant aspects of heat transfer in flexible elastic tubes. The results show that small temperature fluctuations are possible, inline with the pulsatile flow boundary conditions. It is also observed that increased flexibility of tubes leads to better heat transfer between the fluid and the wall. The results clearly indicate that any flow reflections also increase the heat transfer between the fluid and the wall

Understanding aspects of cardiovascular physiology and disease via a multi-physics modelling methodology

The overall aim of this study is to develop and analyse the performance of a multiscale framework involving arterial wall dynamics and blood flow in realistic vascular architectures that can facilitate the understanding of the onset and progression of vascular disease. This comprehensive modelling framework will also allow the virtual testing and ultimately inform the design of novel pharmacological probes. To achieve this aim, we need to deliver an arterial model able to account for i) the wall contractility triggered by biochemical processes at the cellular level ii) the interaction between the flow and vessel deformation, and iii) the transport phenomena along the arterial systemic circulation. For each problem component, a solution procedure has been proposed and validated against benchmark theoretical results and experimental measurements. First we characterised the structural behaviour of the arterial media layer and its response to the active contractile activity modulated by the smooth muscle Ca2+ dynamics. In this study, we modelled the activation, modulation and inhibition of the smooth muscle contraction by pharmacological interventions. Subsequently we have focused on the fluid structure interaction between wall mechanics and hemodynamics. This work required coupling a traditional incompressible arterial fluid model to a solid boundary, which represents the elastic arterial wall. The methodology proposed has been validated against a set of classical benchmark cases and exhibits improved numerical efficiency and significant memory savings. The third component of the work focuses on modelling transport and diffusion phenomena along the arterial branching network and within surrounding tissues. For the purpose of this study, a network of vessels was embedded within a solid tissue model of the human body. This model was able to predict how a property (in this application energy,but equivalently drug concentrations) is transported and diffused from the blood vessels to the tissues

A framework for incorporating 3D hyperelastic vascular wall models in 1D blood flow simulations

We present a novel framework for investigating the role of vascular structure on arterial haemodynamics in large vessels, with a special focus on the human common carotid artery (CCA). The analysis is carried out by adopting a three-dimensional (3D) derived, fibre-reinforced, hyperelastic structural model, which is coupled with an axisymmetric, reduced order model describing blood flow. The vessel transmural pressure and lumen area are related via a Holzapfel–Ogden type of law, and the residual stresses along the thickness and length of the vessel are also accounted for. After a structural characterization of the adopted hyperelastic model, we investigate the link underlying the vascular wall response and blood-flow dynamics by comparing the proposed framework results against a popular tube law. The comparison shows that the behaviour of the model can be captured by the simpler linear surrogate only if a representative value of compliance is applied. Sobol’s multi-variable sensitivity analysis is then carried out in order to identify the extent to which the structural parameters have an impact on the CCA haemodynamics. In this case, the local pulse wave velocity (PWV) is used as index for representing the arterial transmission capacity of blood pressure waveforms. The sensitivity analysis suggests that some geometrical factors, such as the stress-free inner radius and opening angle, play a major role on the system’s haemodynamics. Subsequently, we quantified the differences in haemodynamic variables obtained from different virtual CCAs, tube laws and flow conditions. Although each artery presents a distinct vascular response, the differences obtained across different flow regimes are not significant. As expected, the linear tube law is unable to accurately capture all the haemodynamic features characterizing the current model. The findings from the sensitivity analysis are further confirmed by investigating the axial stretching effect on the CCA fluid dynamics. This factor does not seem to alter the pressure and flow waveforms. On the contrary, it is shown that, for an axially stretched vessel, the vascular wall exhibits an attenuation in absolute distension and an increase in circumferential stress, corroborating the findings of previous studies. This analysis shows that the new model offers a good balance between computational complexity and physics captured, making it an ideal framework for studies aiming to investigate the profound link between vascular mechanobiology and blood flow

Novel semi-implicit, locally conservative Galerkin (SILCG) methods: Application to blood flow in a systemic circulation

Three novel, locally conservative Galerkin (LCG) methods in their semi-implicit form are proposed for 1D blood flow modelling in arterial networks. These semi-implicit discretizations are: the second order Taylor expansion (SILCG-TE) method, the streamline upwind Petrov–Galerkin (SILCG-SUPG) procedure and the forward in time and central in space (SILCG-FTCS) method. In the LCG method, enforcement of the flux continuity condition at the element interfaces allows to solve the discretized system of equations at element level. For problems with a large number of degrees of freedoms, this offers a significant advantage over the standard continuous Galerkin (CG) procedure. The well established fully explicit LCG method is used for assessing the accuracy of the proposed new methods. Results presented in this work demonstrate that the proposed SILCG methods are stable and as accurate as the explicit LCG method. Among the three methods proposed, the SILCG-FTCS method requires considerably lower number of iterations per element, and thus requires lowest amount of CPU time. On the other hand, the SILCG-TE and SILCG-SUPG methods are stable and accurate for larger time step sizes. Although the standard Newton method requires evaluation of both the Jacobian matrix and the residual for every single iteration, which may be expensive for standard implicit solvers, the computed results show that the maximum number of iterations per element for SILCG-TE and SILCG-SUPG is less than unity (less than 0.3 and 0.7 respectively). Also, numerical experiments show that the Jacobian matrix can be calculated only once per time step, allowing to save a significant amount of computational time

Modelling accidental hypothermia effects on a human body under different pathophysiological conditions

Accidental exposure to cold water environment is one of the most challenging situations in which hypothermia occurs. In the present work, we aim to characterise the energy balance of a human body subjected to such extreme environmental conditions. This study is carried out using a recently developed computational model and by setting boundary conditions needed to simulate the effect of cold surrounding environment. A major finding is the capacity of the body core regions to maintain their temperature high for a substantial amount of time, even under the most extreme environmental conditions. We also considered two disease states that highlight the spectrum of possible pathologies implicated in thermal regulation of the human body. These states are (i) cardiomyopathy, which affects the operating capacity of the heart, and (ii) malnutrition, which directly impairs the body’s ability to regulate heat exchange with the environment. We have found that cardiomyopathy has little influence on the thermal balance of the human body, whereas malnutrition has a profound negative effect on the thermal balance and leads to dramatic reduction in core temperature

An advanced computational bioheat transfer model for a human body with an embedded systemic circulation

In the present work, an elaborate one-dimensional thermofluid model for a human body is presented. By contrast to the existing pure conduction-/perfusion-based models, the proposed methodology couples the arterial fluid dynamics of a human body with a multi-segmental bioheat model of surrounding solid tissues. In the present configuration, arterial flow is included through a network of elastic vessels. More than a dozen solid segments are employed to represent the heat conduction in the surrounding tissues, and each segment is constituted by a multilayered circular cylinder. Such multi-layers allow flexible delineation of the geometry and incorporation of properties of different tissue types. The coupling of solid tissue and fluid models requires subdivision of the arterial circulation into large and small arteries. The heat exchange between tissues and arterial wall occurs by convection in large vessels and by perfusion in small arteries. The core region, including the heart, provides the inlet conditions for the fluid equations. In the proposed model, shivering, sweating, and perfusion changes constitute the basis of the thermoregulatory system. The equations governing flow and heat transfer in the circulatory system are solved using a locally conservative Galerkin approach, and the heat conduction in the surrounding tissues is solved using a standard implicit backward Euler method. To investigate the effectiveness of the proposed model, temperature field evolutions are monitored at different points of the arterial tree and in the surrounding tissue layers. To study the differences due to flow-induced convection effects on thermal balance, the results of the current model are compared against those of the widely used modelling methodologies. The results show that the convection significantly influences the temperature distribution of the solid tissues in the vicinity of the arteries. Thus, the inner convection has a more predominant role in the human body heat balance than previously thought. To demonstrate its capabilities, the proposed new model is used to study different scenarios, including thermoregulation inactivity and variation in surrounding atmospheric conditions

Modelling ozone disinfection process for creating COVID-19 secure spaces

PurposeA novel modelling approach is proposed to study ozone distribution and destruction in indoor spaces. The level of ozone gas concentration in the air, confined within an indoor space during an ozone-based disinfection process, is analysed. The purpose of this work is to investigate how ozone is distributed in time within an enclosed space.Design/methodology/approachA computational methodology for predicting the space- and time-dependent ozone concentration within the room across the consecutive steps of the disinfection process (generation, dwelling and destruction modes) is proposed. The emission and removal of ozone from the air volume are possible by means of a generator located in the middle of the room. This model also accounts for ozone reactions and decay kinetics, and gravity effect on the air.FindingThis work is validated against experimental measurements at different locations in the room during the disinfection cycle. The numerical results are in good agreement with the experimental data. This comparison proves that the presented methodology is able to provide accurate predictions of the time evolution of ozone concentration at different locations of the enclosed space.Originality/valueThis study introduces a novel computational methodology describing solute transport by turbulent flow for predicting the level of ozone concentration within a closed room during a COVID-19 disinfection process. A parametric study is carried out to evaluate the impact of system settings on the time variation of ozone concentration within the space considered