Computational Biomechanics for Medicine

Blood cells are subjected to turbulent flow in some disease states and in cardiovascular devices. In general, the details of the microscale flow and stress on cells are unknown for these flows. This chapter is a discussion and review of efforts to identify simple parameters that can quantify the effects of turbulence on cells. It is shown that Reynolds stress and Kolmogorov scale alone are not adequate descriptors of the turbulent flow. The energy spectrum of turbulence must be considered also, so that cell loading at all length scales is properly represented. A deeper quantitative model will require understanding of two-phase flow effects.

We model and simulate avascular tumor growth in three dimensions using lattice gas cellular automata (LGCA). Our 3D models are an advance over current state-of-the-art where most three dimensional (3D) models are in fact only a series of two dimensional models simulated to give an appearance of a 3D model. In our 3D model, we use binary description of cells and their states for computational speed and efficiency. The fate and distribution of cells in our model are determined by the Lattice–Boltzmann energy. We simulate our model in a comparable size of lattice and show that the findings are in good agreement with biological tumor behavior.

In this paper we present a tumourous cell growth model based on cellular automata (CA), where a colony composed of competing normal and cancer cells was placed in an array intertwined with blood vessels. The CA models are able to incorporate both cell growth and complex vascular geometry at the microcirculation level, whereby CA rules are implemented to govern cell development, evolution and death. The vasculature, which is the constant source of oxygen, was generated using a diffusion-limited aggregation-based CA model, whilst the diffusion of oxygen molecules across the domain was implemented, first, using a “random walk” approach and then employing classic diffusion law. With appropriate rules of CA implemented the cancer cells were able to grow at a faster rate and spread a greater distance compared to the normal cells. Once the cancer cells were allowed to proliferate over the vasculature, they would dominate the model lattice and, in one case, overwhelm the normal cells. However, normal cells also own the ability to defend themselves from the invasion of cancerous cells. It was clear from this model that with metastasis tumours exhibit far more dangerous characteristics as they suffocate, control and direct the growth of normal cells. The proposed growth model can be further extended to incorporate more growth patterns and control mechanisms.

Atherosclerotic plaques are found to occur in arterial segments exposed to low wall shear stress (WSS). In order for WSS to be precisely calculated, an accurate representation of the coronary anatomy is critical. Several side-branches originate along the length of the coronary arteries, which should be included in simulations. The aim of this work is to investigate the influence of excluding the coronary side-branches on WSS and on predicting coronary artery disease progression with WSS. Three patient-specific coronary arteries were imaged using virtual histology intravascular ultrasound (VH-IVUS) at baseline and 12 months follow-up. Using the baseline images, 3D reconstructions were created and side-branches as visible in IVUS images were added to each patient. WSS was calculated for models with and without side-branches. There were large differences in absolute WSS between the models with side-branches and those without. WSS was found to be low opposite the flow divider in models with side-branches while this was not always the case in models without side-branches. There was little difference between both models in predicting plaque progression.

Computational hemodynamic studies of abdominal aortic aneurysm (AAA) can help elucidate the mechanisms responsible for growth and development. The aim of this work is to determine if AAAs expand and develop intraluminal thrombus (ILT) in regions of low wall shear stress (WSS) predicted with computational fluid dynamics (CFD). Computed tomography (CT) data of an AAA was acquired at four time-points over 2.5 years, from the time of detection to immediately prior to rupture. We used 3D unsteady, laminar, CFD models to investigate the hemodynamics at each time-point. Our three-dimensional reconstructions showed that the primary region of expansion was in the proximal lobe, which not only coincided with the main region of low time-averaged WSS (TAWSS) in our CFD simulations, but also with the development of ILT in vivo. Interestingly, this region was also the rupture location. This is the first serial computational study of an AAA and the work has shown the potential of CFD to model the changing hemodynamics and the relation with ILT development and AAA growth.

Clinical management of abdominal aortic aneurysms (AAA) can benefit from patient-specific computational biomechanics-based assessment of the disease. Individual variations in shape and aortic material properties are expected to influence the assessment of AAA wall mechanics. While patient-specific geometry can be reproduced using medical images, the accurate individual and regionally varying tissue material property estimation is currently not feasible. This work addresses the relative uncertainties arising from variations in AAA material properties and its effect on the ensuing wall mechanics. Computational simulations were performed with five different isotropic material models based on an ex-vivo AAA wall material characterization and a subject population sample of 28 individuals. Care was taken to exclude the compounding effects of variations in all other geometric and biomechanical factors. To this end, the spatial maxima of the principal stress (σ _max), principal strain (ε _max), strain-energy density (ψ _max), and displacement (δ _max) were calculated for the diameter-matched cohort of 28 geometries for each of the five different constitutive materials. This led to 140 quasi-static simulations, the results of which were assessed on the basis of intra-patient (effect of material constants) and inter-patient (effect of individual AAA shape) differences using statistical averages, standard deviations, and Box and Whisker plots. Mean percentage variations for σ _max, ε _max, ψ _max, and δ _max for the intra-patient analysis were 1.5, 7.1, 8.0, and 6.1, respectively, whereas for the inter-patient analysis these were 11.1, 4.5, 15.3, and 12.9, respectively. Changes in the material constants of an isotropic constitutive model for the AAA wall have a negligible influence on peak wall stress. Hence, this study endorses the use of population-averaged material properties for the purpose of estimating peak wall stress, strain-energy density, and wall displacement. Conversely, strain is more dependent on the material constant variation than on the differences in AAA shape in a diameter-matched population cohort.

Extramedullary devices are being extensively employed to treat fractures in normal and diseased bone. Studies conducted in hospitals have shown that there is a wide variability in the manner different surgeons employ these devices for similar fracture types. Clinically, fixation devices are required to be able to: sustain loads; minimise patient discomfort and possible implant loosening; and promote healing. Computer simulation of the mechanical behaviour of these devices can help clinicians in selecting a device and optimising its configuration. Numerical modelling of the mechanical behaviour of bone-fixator constructs has been used in the past to evaluate the performance of these devices with respect to some of the clinical requirements. This Chapter considers the mechanics of some of the most commonly used extramedullary devices, their peculiarities and modelling implications while appraising existing numerical modelling literature that has attempted to address the above clinical demands. It finds that while many of the clinical questions have been answered satisfactorily using simple models, answers to some others require complex and sophisticated modelling approaches.

Worldwide in 2008, more than 1.4 billion adults, age 20 and older, were overweight. Overweight and obesity are defined as abnormal or excessive fat accumulation that may impair health. The World Health Organization defines overweight as having a body mass index (BMI) greater than or equal to 25 kg/m² and obese as a BMI greater than or equal to 30 kg/m². The aim of this study was to compare peak hip, knee, and ankle joint compressive loads during gait at self-selected speed between overweight and healthy weight individuals and to examine the functional relationship between body mass and peak joint forces. Twelve subjects, six high BMI subjects and six normal BMI control subjects, participated in this investigation. Absolute peak hip, knee, and ankle joint forces were 40 %, 43 %, and 48 % greater, respectively, for the high-BMI versus normal group. Joint loads were found to increase approximately linearly with body mass. Body mass accounted for 70–80 % of the variation in the peak compressive load at the hip, knee, and ankle during gait. These findings support the link that increased body mass leads to increased biomechanical loading of the joints and could be a factor linking obesity to osteoarthritis.

Registration of whole-body radiographic images is an important task in analysis of the disease progression and assessment of responses to therapies. Numerous registration algorithms have been successfully used in applications where differences between source and target images are relatively small. However, registration of whole-body CT scans remains extremely challenging for such algorithms as it requires taking large deformations of body organs and articulated skeletal motions into account. For registration problems involving large differences between source and target images, registration using biomechanical models has been recommended in the literature. Therefore, in this study, we propose a patient-specific nonlinear finite element model to predict the movements and deformations of body organs for the whole-body CT image registration. We conducted a verification example in which a patient-specific torso model was implemented using a suite of nonlinear finite element algorithms we previously developed, verified and successfully used in neuroimaging registration. When defining the patient-specific geometry for the generation of computational grid for our model, we abandoned the time-consuming hard segmentation of radiographic images typically used in patient-specific biomechanical modelling to divide the body into non-overlapping constituents with different material properties. Instead, an automated Fuzzy C-Means (FCM) algorithm for tissue classification was applied to assign the constitutive properties at finite element mesh integration points. The loading was defined as a prescribed displacement of the vertebrae (treated as articulated rigid bodies) between the two CT images. Contours of the abdominal organs obtained by warping the source image using the deformation field within the body predicted using our patient-specific finite element model differed by only up to only two voxels from the actual organs’ contours in the target image. These results can be regarded as encouraging step in confirming feasibility of conducting accurate registration of whole-body CT images using nonlinear finite element models without the necessity for time-consuming image segmentation when building patient-specific finite element meshes.