Harvey Ho

Modeling the hepatic arterial buffer response in the liver

In this paper we present an electrical analog model for the hepatic arterial buffer response (HABR), an intrinsic regulation mechanism in the liver whereby the arterial flow counteracts the changes in portal venous flow. The model itself is a substantial simplification of a previously published model, with nonlinear arterial and portal resistors introduced to account for the dynamic HABR effects. We calibrate the baseline model using published hemodynamic data, and then perform a virtual portal occlusion simulation where the portal vein is half or fully occluded. The simulation results, which suggest that the increased arterial flow cannot fully compensate lost portal perfusion, are consistent with clinical reports and animal model findings. Since HABR functions in both the whole liver and liver graft after transplantation, we also simulate blood flow in a virtual right-lobe graft by adjusting the electronic component parameters in the electric circuit, and our model is able to reproduce the portal venous hyperperfusion and hepatic arterial hypoperfusion conditions due to the HABR effects.

Mechanics of the foot Part 2: A coupled solid-fluid model to investigate blood transport in the pathologic foot.

A coupled computational model of the foot consisting of a three-dimensional soft tissue continuum and a one-dimensional (1D) transient blood flow network is presented in this article. The primary aim of the model is to investigate the blood flow in major arteries of the pathologic foot where the soft tissue stiffening occurs. It has been reported in the literature that there could be up to about five-fold increase in the mechanical stiffness of the plantar soft tissues in pathologic (e.g. diabetic) feet compared with healthy ones. The increased stiffness results in higher tissue hydrostatic pressure within the plantar area of the foot when loaded. The hydrostatic pressure acts on the external surface of blood vessels and tend to reduce the flow cross-section area and hence the blood supply. The soft tissue continuum model of the foot was modelled as a tricubic Hermite finite element mesh representing all the muscles, skin and fat of the foot and treated as incompressible with transversely isotropic properties. The details of the mechanical model of soft tissue are presented in the companion paper, Part 1. The deformed state of the soft tissue continuum because of the applied ground reaction force at three foot positions (heel-strike, midstance and toe-off) was obtained by solving the Cauchy equations based on the theory of finite elasticity using the Galerkin finite element method. The geometry of the main arterial network in the foot was represented using a 1D Hermite cubic finite element mesh. The flow model consists of 1D Navier-Stokes equations and a nonlinear constitutive equation to describe vessel radius-transmural pressure relation. The latter was defined as the difference between the fluid and soft tissue hydrostatic pressure. Transient flow governing equations were numerically solved using the two-step Lax-Wendroff finite difference method. The geometry of both the soft tissue continuum and arterial network is anatomically-based and was developed using the data derived from visible human images and magnetic resonance images of a healthy male volunteer. Simulation results reveal that a two-fold increase in tissue stiffness leads to about 28% reduction in blood flow to the affected region.

Multiscale Modeling of Intracranial Aneurysms: Cell Signaling, Hemodynamics, and Remodeling

The genesis, growth, and rupture of intracranial aneurysms (IAs) involve physics at the molecular, cellular, blood vessel, and organ levels that occur over time scales ranging from seconds to years. Comprehensive mathematical modeling of IAs, therefore, requires the description and integration of events across length and time scales that span many orders of magnitude. In this letter, we outline a strategy for mulstiscale modeling of IAs that involves the construction of individual models at each relevant scale and their subsequent combination into an integrative model that captures the overall complexity of IA development. An example of the approach is provided using three models operating at different length and time scales: 1) shear stress induced nitric oxide production; 2) smooth muscle cell apoptosis; and 3) fluid-structure-growth modeling. A computational framework for combining them is presented. We conclude with a discussion of the advantages and challenges of the approach.

Hemodynamic Analysis for Transjugular Intrahepatic Portosystemic Shunt (TIPS) in the Liver Based on a CT-Image

In this paper, we apply a 3-D flow model and a 1-D circulation model to the hemodynamic analysis of transjugular intrahepatic portosystemic shunt (TIPS), the therapy for treating acute portal hypertension (PH) induced diseases. Using the 3-D model we are able to simulate the blood flow within a patient-specific TIPS system which was reconstructed from a computed tomography image, and quantify such hemodynamic data as the wall shear stress and flow velocity. The 1-D model is used for the investigation of generic TIPS-induced hepatic circulation phenomena. By incorporating physiological data into the 1-D model we can reproduce some complex flow patterns such as the increased arterial flow after TIPS implantation, the formation of retrograde flow in the portal vein, etc. In particular, our model gives a quantitative analysis of the interplay between TIPS and hepatic flows. In conclusion, the presented computational model can be used for the theoretical analysis of TIPS, in which clinical decisions are often made based on contradictory considerations to balance the procedure-induced complications and the urgency of relieving acute PH symptoms.

Blood flow simulation for the liver after a virtual right lobe hepatectomy.

In this paper we present a hybrid OD-3D modeling method to investigate the hepatic flow in a virtual right lobe hepatectomy (RLH), the surgical procedure for adult-to-adult living donor liver transplanation (LDLT). The 3D method is employed to simulate complex 3D flow in the portal vein, and the OD model is used to study the systemic hepatic circulation. In particular, we quantify the flow velocity and wall shear stress (WSS) in the left portal vein which increase dramatically post-RLH, and also simulate the essential hepatic distribution features in a healthy adult pre- and post-procedure. We further predict the arterial flow in the remnant left liver, which would decrease due to a hepatic arterial buffer response (HABR) effect. Finally we discuss the physiological significance of these phenomena, and the potential of this hybrid modeling approach.

A Hybrid 1D and 3D Approach to Hemodynamics Modelling for a Patient-Specific Cerebral Vasculature and Aneurysm

In this paper we present a hybrid 1D/3D approach to haemodynamics modelling in a patient-specific cerebral vasculature and aneurysm. The geometric model is constructed from a 3D CTA image. A reduced form of the governing equations for blood flow is coupled with an empirical wall equation and applied to the arterial tree. The equation system is solved using a MacCormack finite difference scheme and the results are used as the boundary conditions for a 3D flow solver. The computed wall shear stress (WSS) agrees with published data.

Numerical Simulation of Blood Flow in an Anatomically-Accurate Cerebral Venous Tree

Although many blood flow models have been constructed for cerebral arterial trees, few models have been reported for their venous counterparts. In this paper, we present a computational model for an anatomically accurate cerebral venous tree which was created from a computed tomography angiography (CTA) image. The topology of the tree containing 42 veins was constructed with 1-D cubic-Hermite finite element mesh. The model was formulated using the reduced Navier-Stokes equations together with an empirical constitutive equation for the vessel wall which takes both distended and compressed states of the wall into account. A robust bifurcation model was also incorporated into the model to evaluate flow across branches. Furthermore, a set of hierarchal inflow pressure boundary conditions were prescribed to close the system of equations. Some assumptions were made to simplify the numerical treatment, e.g., the external pressure was considered as uniform across the venous tree, and a vein was either distended or partially collapsed but not both. Using such a scheme we were able to evaluate the blood flow over several cardiac cycles for the large venous tree. The predicted results from the model were compared with ultrasonic measurements acquired at several sites of the venous tree and agreements have been reached either qualitatively (flow waveform shape) or quantitatively (flow velocity magnitude). We then discuss the significance of this venous model, its potential applications, and also present numerical experiments pertinent to limitations of the proposed model.

Blood Flow Simulation in a Giant Intracranial Aneurysm and Its Validation by Digital Subtraction Angiography

In this study we simulate the blood flow in a giant aneurysm using computational fluid dynamics (CFD) techniques and validate the results using the 2D X-ray image sequence generated from digital subtraction angiography (DSA). The 3D geometry of the aneurysm was retrieved from a computed tomography angiography (CTA) image. The pulsatile blood flow was numerically solved, and the hemodynamic quantities such as the wall shear stress (WSS) and flow velocity field were analyzed at four instants of a cardiac cycle. The computed intra-aneurysm flow velocity was validated using a DSA sequence over several time frames. The time-averaged flow velocity (∼ 0.2 m/s) agreed with the flow velocity estimated from the DSA. We further compared the Newtonian blood model with a non-Newtonian (Carreau) model and found that the Newtonian model overestimated the flow velocity and WSS.

Roadmap for cardiovascular circulation model.

Computational models of many aspects of the mammalian cardiovascular circulation have been developed. Indeed, along with orthopaedics, this area of physiology is one that has attracted much interest from engineers, presumably because the equations governing blood flow in the vascular system are well understood and can be solved with well‐established numerical techniques. Unfortunately, there have been only a few attempts to create a comprehensive public domain resource for cardiovascular researchers. In this paper we propose a roadmap for developing an open source cardiovascular circulation model. The model should be registered to the musculo‐skeletal system. The computational infrastructure for the cardiovascular model should provide for near real‐time computation of blood flow and pressure in all parts of the body. The model should deal with vascular beds in all tissues, and the computational infrastructure for the model should provide links into CellML models of cell function and tissue function. In this work we review the literature associated with 1D blood flow modelling in the cardiovascular system, discuss model encoding standards, software and a model repository. We then describe the coordinate systems used to define the vascular geometry, derive the equations and discuss the implementation of these coupled equations in the open source computational software OpenCMISS. Finally, some preliminary results are presented and plans outlined for the next steps in the development of the model, the computational software and the graphical user interface for accessing the model.

Non-newtonian blood flow analysis for the portal vein based on a CT image

In this paper we perform a Newtonian and a non-Newtonian blood flow analysis for a patient-specific portal vein (PV), which was digitized from a CT image. The non-linear relationship between the shear stress and shear rate was simulated using a Carreau model. We found that, under normal physiological conditions, the computed data from the non-Newtonian model was only marginally different from that of the Newtonian model. However, when the portal flow was severely reduced (e.g., 10% of its normal value), the difference between the two models was significant. Hence we suggest that the Newtonian model is a good approximation for portal flow in physiological conditions whereas a non-Newtonian model should be used in pathological conditions when the very low flow rate induces a much higher blood viscosity.