Computational Biomechanics for Medicine

Although internal organ injury in car crashes occurs at a relatively lower frequency compared to bone fracture, it tends to be ranked higher in terms of injury severity. A generalized injury risk can be assessed in car crash tests by evaluating abdominal force and viscous criterion (VC) using a crash test dummy, but the injury risk to each organ cannot be estimated with current dummies due to a lack of parts representing the internal organs. Recently, human body modeling research has been conducted introducing organ parts. It is still a challenge to simulate the impact behavior of organ parts and their injury, based on an understanding of the differences in structure and material properties among the organs.

This chapter aimed to study the biomechanical response and injury mechanisms of brain in passenger car-to-pedestrian collision event. The kinematics of head impact to a passenger car was reconstructed using multibody dynamics (MBD) models. The brain injury biomechanics was investigated by using an FE model of human body head (HBM-head). The HBM-head model was developed in accordance with human head anatomy. The model consists of scalp, skull, dura mater, cerebrospinal fluid, pia mater, cerebrum, cerebellum, ventricle, brain stem, falx, tentorium, etc. The existing data from cadaveric head impact tests were used to validate the head FE model. The kinematic and kinetic responses of the head were determined by using MBD model. The brain injury-related physical parameters and the distribution of the intracranial pressure were calculated from simulations of head impact to the windscreen and A-pillar by using the HBM-head model. It is proved that the head FE model has good biofidelity and can be used to study head–brain trauma and injury mechanisms in vehicle collisions.

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.

Both 4D flow-sensitive MRI and computational fluid dynamics (CFD) have successfully been applied to analyze complex 3D flow patterns in the cardiovascular system. However, both modalities suffer from limitations related to spatiotemporal resolution, measurement errors, and noise (MRI) or incomplete model assumptions and boundary conditions (CFD). The aim of this study was to directly compare the results of 4D flow-sensitive MRI and CFD in a simple model system in vitro and in complex models of the thoracic aorta in vivo. By comparing both modalities within a single framework, discrepancies were observed but the overall patterns were coherent. If adequate methods are used (e.g., patient-specific boundary conditions, fine boundary layer mesh), CFD can compute very accurate flow and vessel wall parameters, such as wall shear stress (WSS). The combination of 4D flow-sensitive MRI and CFD can be used to refine both methodologies, which may help to enhance the assessment and understanding of blood flow in vivo.

Accuracy of image-guided prostate interventions can be improved by warping (i.e., nonrigid registration) of high-quality multimodal preoperative magnetic resonance images to the intraoperative prostate geometry. Patient-specific biomechanical models have been applied in several studies when predicting the prostate intraoperative deformations for such warping. Obtaining exact patient-specific information about the stress parameter (e.g., Young’s modulus) of the prostate peripheral zone (PZ) and central gland (CG) for such models remains an unsolved problem. In this study, we investigated the effects of ratio of Young’s modulus of the central gland E _CG to the peripheral zone E _PZ when predicting the prostate intraoperative deformation for ten cases of prostate brachytherapy. The patient-specific prostate models were implemented by means of the specialized nonlinear finite element procedures that utilize total Lagrangian formulation and explicit integration in time domain. The loading was defined by prescribing deformations on the prostate outer surface. The neo-Hookean hyperelastic constitutive model was applied to simulate the PZ and CG mechanical responses. The PZ to CG Young’s modulus ratio E _CG:E _PZ was varied between 1:1 (upper bound of the literature data) and 1:40 (lower bound of the literature data). The study indicates that the predicted prostate intraoperative deformations and results of the prostate MRIs nonrigid registration obtained using the predicted deformations depend very weakly on the E _CG:E _PZ ratio.

Intra-operative images acquired during brain surgery do not provide sufficient detail to confidently locate brain internal structures that have been identified in high-resolution pre-operative images. However, the pre-operative images can be warped to the intra-operative position of brain using predicted deformation field. While craniotomy-induced brain shift deformation can be accurately computed using patient-specific finite element models in real-time, accurate segmentation and meshing of brain internal structures remains a time-consuming task. In this chapter, we conduct a parametric study to evaluate the sensitivity of the predicted brain shift deformation to model complexity, which includes the effects of disregarding the differences in properties between the parenchyma, tumour and ventricles and applying different approaches for representing the ventricles (as a very soft solid or cavity) to minimise segmentation and meshing effort for model generation. The results suggest that the difference in brain shift deformation predicted by models due to such variation is not significant. Segmentation of brain parenchyma and skull seems sufficient to build models that can accurately predict craniotomy-induced brain shift deformation.

This study presents an approach to modeling the tearing of tissue in two dimensions taking into account both material and geometrical nonlinearities. The approach is based on the total Lagrangian explicit dynamics (TLED) algorithm and realigns edges in the mesh along the path of the tear by node relocation. As such, no new elements are created during the propagation of the tear. The material is assumed to be isotropic, and the tearing criterion is based on the maximum node-averaged principal stress. Preliminary results show that the approach is capable of handling both isotropic and anisotropic tears.

Application of biomechanical modeling techniques in the area of medical image analysis and surgical simulation implies two conflicting requirements: accurate results and high solution speeds. Accurate results can be obtained only by using appropriate models and solution algorithms. In our previous papers, we have presented algorithms and solution methods for performing accurate nonlinear finite element analysis of brain shift (which includes mixed mesh, different nonlinear material models, finite deformations and brain–skull contacts) in less than 5 s on a personal computer using a Graphics Processing Unit (GPU) for models having up to 50,000 degrees of freedom. In this chapter, we compare several approaches for implementing different element types on the GPU using the NVIDIA Compute Unified Device Architecture. Our results can be used as a guideline for selecting the best GPU implementation approach for finite element algorithms which require mixed meshes or even for meshless methods.

Characterizing a breast lesion can involve comparing X-ray and magnetic resonance (MR) images of a patient’s breast. Tracking a lesion between these imaging modalities is nontrivial because of the different types of deformation the breast undergoes during these imaging procedures. We present a retrospective clinical validation study to assess the performance of a biomechanical modeling framework for mapping lesion locations between clinical MR images and cranio-caudal X-ray mammograms. MR images from four patients were used to create customized finite element models. The unloaded configuration of each breast was then determined, and mammographic compression was simulated using finite deformation elasticity coupled with contact mechanics. The predicted location of each patient’s tumor(s) in the simulated compressed breast was compared with the true tumor locations on the mammogram as identified by clinicians. The degree of overlap between the true lesion area and the predicted lesion area, estimated using the Jaccard coefficient, ranged between 14 and 75%. The results indicate that biomechanical modeling can provide reliable co-location of lesions between MR images and mammograms.

Tagging MRI enables analysis of the local contractility of the cardiac left ventricle. It permits reliable assessment of local contractile dysfunction related to various cardiomyopathies. We present a multi-scale optical flow method, with Gabor filtering, for the extraction of dense motion fields from cardiac MR tagging. It is based on a multi-scale first-order extension of the classical optical flow constraint equation enabling the extraction first-order parameters such as rotation and strain. A quantitative validation study based on the phantom proposed by Young et al. showed excellent performance. Furthermore, strain patterns are presented for one ischemic patient case with known wall motion abnormalities and two volunteers. Patient circumferential strain abnormalities co-localize with enhanced areas in late-enhancement MRI. Rotation patterns are presented for the same patient and four volunteers. The rotation pattern described in the patient is strikingly different from that describing the volunteers.

Understanding complex human musculoskeletal systems requires an enormous amount of experimental and computational studies. The computational modeling combining anatomic, physiologic and engineering analyses can create a virtual human body to study various activities in a normal and pathological condition. Combining the virtual human body with some kinds of mechanical analyses showed strong potentials in understanding of musculoskeletal biomechanics. Modeling of human joints, such as foot–ankle–knee are most challenging, due to very complex structures. Information on the internal structures as well as foot-support interfacial load transfer during various activities is useful in enhancing our biomechanical knowledge for foot support design and surgical planning. We develop computational models as a digital foot-ankle, which can be used to understand joint biomechanics and design proper foot supports and implant. Three-dimensional geometrically accurate finite element (FE) models of the human foot–ankle–knee structures were developed from 3D reconstruction of MR images of subjects. The foot FE model consists of 28 separate bones, 72 ligaments and the plantar fascia, embedded in a volume of encapsulated soft tissue. The main bone interactions were simulated as contact deformable bodies. The analyses took into consideration the nonlinearities from material properties, large deformations, and interfacial slip/friction conditions. A series of experiments on human subjects and cadavers were conducted to validate the model measurements on in terms of plantar pressure distribution, foot arch and joint motion, plantar fascia strain under different simulated weight-bearing, and orthotic conditions of the foot. The validated models can be used for parametrical studies to investigate the biomechanical effects of tissue stiffness, muscular reaction, surgical and orthotic performances on the foot–ankle complex.

We present a semi-automatic method to segment single muscle fibres from skeletal muscle cross-section images. As a pre-processing step we apply different filters depending on the type of the manually selected image region to obtain an edge image. Then we detect circles within the image by a circular Hough transform as initial rough approximation to the muscle fibre slices. This approximation is improved by active contours, where the circles are deformed to fit to the specific shape of the muscle fibres. The implementation of the segmentation method was done in Matlab. We show qualitative and quantitative results for different image regions and also outline a straight-forward method to combine several slices to obtain a 3D piece of a muscle fibre, which forms the input to an electro-mechanical skeletal muscle model.

The levator ani (LA) muscles play an important role in pelvic floor function. With the aid of computer models and mechanics simulations, the injury mechanism of LA muscles can be better understood to prevent pelvic floor dysfunction. However, the lack of quantitative description of pelvic floor muscle organisation may compromise the accuracy of the models and simulations. The aim of this work was to establish a quantitative model of the pelvic floor muscle fibre organisation utilising the Visible Human Project^®; dataset. An anatomical finite element model of the pelvic floor muscles (levator ani and external sphincter) was constructed from the Visible Woman (VW) dataset. Fibre orientations were detected from the VW images using a structure tensor method and principal component analysis. Fibre orientation data were embedded within the geometric model using nonlinear finite element fitting. The fitted fibre field was qualitatively compared with the literature. Future work will include cadaver dissections for clearer classification of different muscles, and the creation of a generic pelvic floor fibre organisation model using DT-MRI data from living subjects and cadavers. The models will be used for pelvic floor mechanics studies such as modelling the second stage of labour during vaginal delivery.

In this chapter, we assess the impact of mesh generation on nonrigid registration of brain MR images. The solution accuracy and the speed of finite element solvers depend on how well the underlying mesh approximates the surface of the biological object (fidelity), and how well the elements of this mesh are shaped (quality). Fidelity and quality, however, are two contradicting requirements, as increased fidelity usually implies poor quality and vice versa. In this chapter, we evaluate three public mesh generators and examine how this quality-fidelity trade-off affects the accuracy and the speed of nonrigid registration solvers for brain images.

Most automated methods for cardiac segmentation are not directly applicable to tagged MRI (tMRI) because they do not handle all of the analysis challenges: tags obscure heart boundaries, low contrast, image artifacts, and radial image planes. Other methods do not process all acquired tMRI data or do not ensure tissue incompressibility. In this chapter, we present a cardiac segmentation method for tMRI which requires no user input, suppresses image artifacts, extracts heart features using 3D grayscale morphology, and constructs a biventricular model from the data that ensures the near incompressibility of heart tissue. We project landmarks of 3D features along curves in the solution to a PDE, and embed biomechanical constraints using the finite element method. Testing on normal and diseased subjects yields an RMS segmentation accuracy of ∼ 2 mm, comparing favorably with manual segmentation, interexpert variability and segmentation methods for nontagged cine MRI.