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Finite element models (FEMs) of the spine commonly use a limited number of simplified geometries. Nevertheless, the geometric features of the spine are important in determining its FEM outcomes. The link between a spinal segment’s shape and its biomechanical response has been studied, but the co-variances of the shape features have been omitted. We used a principal component (PCA)-based statistical shape modelling (SSM) approach to investigate the contribution of shape features to the intradiscal pressure (IDP) and the facets contact pressure (FCP) in a cohort of synthetic L4/L5 functional spinal units under axial compression. We quantified the uncertainty in the FEM results, and the contribution of individual shape modes to these results. This parameterisation approach is able to capture the variability in the correlated anatomical features in a real population and sample plausible synthetic geometries. The first shape mode ($$\phi _1$$ ϕ 1 ) explained 22.6% of the shape variation in the subject-specific cohort used to train the SSM, and had the largest correlation with, and contribution to IDP (17%) and FCP (11%). The largest geometric variation in ($$\phi _1$$ ϕ 1 ) was in the annulus-nucleus ratio.

How prevalent is spontaneous thrombosis (ST) in intracranial aneurysms (IAs) for an all-size pop- ulation? How can we calibrate computational models of thrombosis based on published data from size-specific aneurysms cohorts? How does ST differ in normo- and hypertensive subjects? We ad- dress the first question by a thorough analysis of published that provide ST rates across different patient demographics and aneurysm characteristics. This analysis provides data for a subgroup of the gen- eral population, viz. large and giant aneurysms (>10 mm). Based on these observed ST rates, our novel computational modelling platform enables the first in-silico observational study of ST prevalence across a broader set of IA phenotypes. We generate 109 virtual patients and use a novel approach to calibrate two trigger thresholds: residence time (RT) and shear rate (SR), thus addressing the second question. We then address the third question by utilising this calibrated thrombosis model to provide new insights on the effects of hypertension on ST. We demonstrate how a mechanistic ST model calibrated on a reduced IA cohort can help esti- mate ST prevalence in a broader IA population. This study was enabled through a comprehensive and fully automatic multi-scale modeling pipeline. We use an emerging property, viz. ST, as an indirect population-level validation of a complex computational modeling framework. Furthermore, our frame- work allows exploration of the influence of hypertension in ST. This lays the foundation for in-silico clinical trials of cerebrovascular devices in high-risk populations, e.g. assessing the performance of flow diverters in cerebral aneurysms for hypertensive patients.

Finite element models (FEMs) of the spine commonly use a limited number of simplified geometries. Nevertheless, the geometric features of the spine are important in determining its FEM outcomes. The link between a spinal segment's shape and its biomechanical response has been studied, but the co-variances of the shape features have been omitted. We used a principal component (PCA)-based statistical shape modelling (SSM) approach to investigate the contribution of shape features to the intradiscal pressure (IDP) and the facets contact pressure (FCP) in a cohort of synthetic L4/L5 functional spinal units under axial compression. We quantified the uncertainty in the FEM results, and the contribution of individual shape modes to these results. This parameterisation approach is able to capture the variability in the correlated anatomical features in a real population and sample plausible synthetic geometries. The first shape mode ([Formula: see text]) explained 22.6% of the shape variation in the subject-specific cohort used to train the SSM, and had the largest correlation with, and contribution to IDP (17%) and FCP (11%). The largest geometric variation in ([Formula: see text]) was in the annulus-nucleus ratio.

Deformable image registration (DIR) can be used to track cardiac motion. Conventional DIR algorithms aim to establish a dense and non-linear correspondence between independent pairs of images. They are, nevertheless, computationally intensive and do not consider temporal dependencies to regulate the estimated motion in a cardiac cycle. In this paper, leveraging deep learning methods, we formulate a novel hierarchical probabilistic model, termed DragNet, for fast and reliable spatio-temporal registration in cine cardiac magnetic resonance (CMR) images and for generating synthetic heart motion sequences. DragNet is a variational inference framework, which takes an image from the sequence in combination with the hidden states of a recurrent neural network (RNN) as inputs to an inference network per time step. As part of this framework, we condition the prior probability of the latent variables on the hidden states of the RNN utilised to capture temporal dependencies. We further condition the posterior of the motion field on a latent variable from hierarchy and features from the moving image. Subsequently, the RNN updates the hidden state variables based on the feature maps of the fixed image and the latent variables. Different from traditional methods, DragNet performs registration on unseen sequences in a forward pass, which significantly expedites the registration process. Besides, DragNet enables generating a large number of realistic synthetic image sequences given only one frame, where the corresponding deformations are also retrieved. The probabilistic framework allows for computing spatio-temporal uncertainties in the estimated motion fields. Our results show that DragNet performance is comparable with state-of-the-art methods in terms of registration accuracy, with the advantage of offering analytical pixel-wise motion uncertainty estimation across a cardiac cycle and being a motion generator. We will make our code publicly available.

Real-time augmented reality (AR) for minimally invasive surgery without extra tracking devices is a valuable yet challenging task, especially considering dynamic surgery environments. Multiple different motions between target organs are induced by respiration, cardiac motion or operative tools, and often must be characterized by a moving, manually positioned endoscope. Therefore, a 6DoF motion tracking method that takes advantage of the latest 2D target tracking methods and non-linear pose optimization and tracking loss retrieval in SLAM technologies is proposed and can be embedded into such an AR system. Specifically, the SiamMask deep learning-based target tracking method is incorporated to roughly exclude motion distractions and enable frame matching. This algorithm’s light computation cost makes it possible for the proposed method to run in real-time. A global map and a set of keyframes as in ORB-SLAM are maintained for pose optimization and tracking loss retrieval. The stereo matching and frame matching methods are improved and a new strategy to select reference frames is introduced to make the first-time motion estimation of every arriving frame as accurate as possible. Experiments on both a clinical laparoscopic partial nephrectomy dataset and an ex-vivo porcine kidney dataset are conducted. The results show that the proposed method gives a more robust and accurate performance compared with ORB-SLAM2 in the presence of motion distractions or motion blur; however, heavy smoke still remains a big factor that reduces the tracking accuracy.

An improved skin tissue substitute for use in photoelastic testing is required to enable investigation of the mechanics of needle insertion into soft tissue. Current tissue substitutes are mainly used in large scale testing and can neglect the small scale mechanical properties of soft tissue. A series of experiments on konjac glucomannan are performed to characterise its mechanical properties, and the results are compared to published results from similar experiments on skin tissue. The optical properties of the gel, such as its strain optic coefficient, are also assessed using a grey field polariscope (GFP2500). A concentration of 1.5% konjac to water produced a viscoelastic gel whose mechanical response closely matches published data for skin. A strain optic coefficient was recorded and found ideal for the planned testing with a GFP2500. Overall konjac glucomannan was found to be a potential soft tissue surrogate for use in small scale photoelastic testing.

This work presents a locking-free smoothed finite element method (S-FEM) for the simulation of soft matter modelled by the equations of quasi-incompressible hyperelasticity. The proposed method overcomes well-known issues of standard finite element methods (FEM) in the incompressible limit: the over-estimation of stiffness and sensitivity to severely distorted meshes. The concepts of cell-based, edge-based and node-based S-FEMs are extended in this paper to three-dimensions. Additionally, a cubic bubble function is utilized to improve accuracy and stability. For the bubble function, an additional displacement degree of freedom is added at the centroid of the element. Several numerical studies are performed demonstrating the stability and validity of the proposed approach. The obtained results are compared with standard FEM and with analytical solutions to show the effectiveness of the method.

In this paper, we propose to train deep neural networks with biomechanical simulations, to predict the prostate motion encountered during ultrasound-guided interventions. In this application, unstructured points are sampled from segmented pre-operative MR images to represent the anatomical regions of interest. The point sets are then assigned with point-specific material properties and displacement loads, forming the un-ordered input feature vectors. An adapted PointNet can be trained to predict the nodal displacements, using finite element (FE) simulations as ground-truth data. Furthermore, a versatile bootstrap aggregating mechanism is validated to accommodate the variable number of feature vectors due to different patient geometries, comprised of a training-time bootstrap sampling and a model averaging inference. This results in a fast and accurate approximation to the FE solutions without requiring subject-specific solid meshing. Based on 160,000 nonlinear FE simulations on clinical imaging data from 320 patients, we demonstrate that the trained networks generalise to unstructured point sets sampled directly from holdout patient segmentation, yielding a near real-time inference and an expected error of 0.017 mm in predicted nodal displacement.

Accurately determining the spatial relationship between the pelvis and acetabulum is challenging due to their inherently complex three-dimensional (3D) anatomy. A standardized 3D pelvic coordinate system (PCS) and the precise assessment of acetabular orientation would enable the relationship to be determined. We present a surface-based method to establish a reliable PCS and develop software for semi-automatic measurement of acetabular spatial parameters. Vertices on the acetabular rim were manually extracted as an eigenpoint set after 3D models were imported into the software. A reliable PCS consisting of the anterior pelvic plane, midsagittal pelvic plane, and transverse pelvic plane was then computed by iteration on mesh data. A spatial circle was fitted as a succinct description of the acetabular rim. Finally, a series of mutual spatial parameters between the pelvis and acetabulum were determined semi-automatically, including the center of rotation, radius, and acetabular orientation. Pelvic models were reconstructed based on high-resolution computed tomography images. Inter- and intra-rater correlations for measurements of mutual spatial parameters were almost perfect, showing our method affords very reproducible measurements. The approach will thus be useful for analyzing anatomic data and has potential applications for preoperative planning in individuals receiving total hip arthroplasty.

This paper offers a new insight into the computational modelling of crack and delamination of carbon fiber composite. Both transversal cracks (intralaminar) and delamination (interlaminar) are modelled with Extended Finite Element Method (XFEM). Constitutive and fracture laws are integrated to model the initiation of crack or delamination, and their subsequent evolution. The study includes the size effect assessment of composite due to the increment of composite thickness. The results are in close agreement between the experimental and analytical data of each specimen modelled based on the size of the carbon fiber composite volume.

Numerous problems of relevance in physiology and biomechanics, have at their core, the presence of a deformable solid matrix which experiences flow-induced strain. Often, this fluid–structure interaction (FSI) is directed the opposite way, i.e. it is solid deformation that creates flow, with the heart being the most prominent example. In many cases, this interaction of fluid and solid is genuinely bidirectional and strongly coupled, with solid deformation inducing flow and fluid pressure deforming the solid. Although an FSI problem, numerous cases in biomechanics are not tractable via the traditional FSI methodologies: in the internal flows that are of interest to use, the number and range of fluid passages is so vast that the direct approach of a deterministically defined boundary between fluid and solid is impossible to apply. In these cases, homogenisation and statistical treatment of the material-fluid system is possibly the only way forward. Such homogenisation,quite common to flow-only systems through porous media considerations, is also possible for FSI systems, where the loading is effectively internal to the material. A prominent technique of this type is that of poroelasticity. In this paper, we discuss a class of poroelastic theory techniques that allow for the co-existence of a multitude of – always statistically treated – channels and passages of widely different properties: termed multiple-network poroelasticity (or multicompartmental poroelasticity). This paradigm is particularly suitable for the study of living tissue, that is invariably permeated – perfused – by fluids, often different in nature and across a wide range of scales. Multicompartmental poroelasticity is capable of accounting for bidirectional coupling between the fluids and the solid matrix and allows us to track transport of a multitude of substances together with the deformation of the solid material that this transport gives rise to or is caused by, or both. For the purposes of demonstration, we utilise a complex and physiologically very important system, the human brain (specifically, we target the hippocampus), to exemplify the qualities and efficacy of this methodology during the course of Alzheimer’s Disease. The methodology we present has been implemented through the Finite Element Method, in a general manner, allowing for the co-existence of an arbitrary number of compartments. For the applications used in this paper to exemplify the method, a four-compartment implementation is used. A unified pipeline is used on a cohort of 35 subjects to provide statistically meaningful insight into the underlying mechanisms of the neurovascular unit (NVU) in the hippocampus, and to ascertain whether physical activity would have an influence in both swelling and drainage by taking into account both the scaled strain field and the proportion of perfused blood injected into the brain tissue. A key result garnered from his study is the statistically significant differences in right hemisphere hippocampal NVU swelling between males in the control group and females with mild cognitive impairment during high and low activity states.

For precision medicine to be implemented through the lens of in silico technology, it is imperative that biophysical research workflows offer insight into treatments that are specific to a particular illness and to a particular subject. The boundaries of precision medicine can be extended using multiscale, biophysics-centred workflows that consider the fundamental underpinnings of the constituents of cells and tissues and their dynamic environments. Utilising numerical techniques that can capture the broad spectrum of biological flows within complex, deformable and permeable organs and tissues is of paramount importance when considering the core prerequisites of any state-of-the-art precision medicine pipeline. In this work, a succinct breakdown of two precision medicine pipelines developed within two Virtual Physiological Human (VPH) projects are given. The first workflow is targeted on the trajectory of Alzheimer's Disease, and caters for novel hypothesis testing through a multicompartmental poroelastic model which is integrated with a high throughput imaging workflow and subject-specific blood flow variability model. The second workflow gives rise to the patient specific exploration of Aortic Dissections via a multi-scale and compliant model, harnessing imaging, computational fluid-dynamics (CFD) and dynamic boundary conditions. Results relating to the first workflow include some core outputs of the multiporoelastic modelling framework, and the representation of peri-arterial swelling and peri-venous drainage solution fields. The latter solution fields were statistically analysed for a cohort of thirty-five subjects (stratified with respect to disease status, gender and activity level). The second workflow allowed for a better understanding of complex aortic dissection cases utilising both a rigid-wall model informed by minimal and clinically common datasets as well as a moving-wall model informed by rich datasets. ispartof: Morphologie vol:103 issue:343 pages:148-160 ispartof: location:France status: published

A probabilistic framework for registering generalised point sets comprising multiple voxel-wise data features such as positions, orientations and scalar-valued quantities, is proposed. It is employed for the analysis of magnetic resonance diffusion tensor image (DTI)-derived quantities, such as fractional anisotropy (FA) and fibre orientation, across multiple subjects. A hybrid Student’s t-Watson-Gaussian mixture model-based non-rigid registration framework is formulated for the joint registration and clustering of voxel-wise DTI-derived data, acquired from multiple subjects. The proposed approach jointly estimates the non-rigid transformations necessary to register an unbiased mean template (represented as a 7-dimensional hybrid point set comprising spatial positions, fibre orientations and FA values) to white matter regions of interest (ROIs), and approximates the joint distribution of voxel spatial positions, their associated principal diffusion axes, and FA. Specific white matter ROIs, namely, the corpus callosum and cingulum, are analysed across healthy control (HC) subjects (K = 20 samples) and patients diagnosed with mild cognitive impairment (MCI) (K = 20 samples) or Alzheimer’s disease (AD) (K = 20 samples) using the proposed framework, facilitating inter-group comparisons of FA and fibre orientations. Group-wise analyses of the latter is not afforded by conventional approaches such as tract-based spatial statistics (TBSS) and voxel-based morphometry (VBM).

Residual stress has a great influence on the mechanical behaviour of arterial wall. Numerous research groups used the Uniform Stress Hypothesis to allow the inclusion of the effects of residual stress when computing stress distributions in the arterial wall. Nevertheless, the available methods used for this purpose are very computationally expensive, due to their iterative nature. In this paper we present a new method for including the effects of residual stress on the computed stress distribution in the arterial wall.The new method, by using the Uniform Stress Hypothesis, enables computing the effect of residual stress by averaging stresses across the thickness of the arterial wall.Being a post-processing method for the computed stress distributions, the proposed method is computationally inexpensive, and thus, better suited for clinical applications than the previously used ones.The resulting stress distributions and values obtained using the proposed method based on the Uniform Stress Hypothesis are very close to the ones returned by an existing iterative method.

Skin tribology is complex and in situ behaviour of skin varies considerably between test subjects. The main influencing factor, elasticity, varies due to structural and moisture differences. To find a more reliable test platform, for the first time, synthetic and biological (tissue engineered) substitutes were compared to ex vivo skin, epidermis and dermis. Friction initially increased with rising hydration, before decreasing beyond a threshold for all samples. Friction for Synthetic skin and dermis increased at a similar rate to the other samples, but from a different starting point, and friction dropped at lower hydration. Tissue engineered skin could provide a reliable test platform, but the synthetic skin could only be used if the offset in the data is accounted for.

Medical image analysis has grown into a matured field challenged by progress made across all medical\ud imaging technologies and more recent breakthroughs in biological imaging. The cross-fertilisation\ud between medical image analysis, biomedical imaging physics and technology, and domain knowledge\ud from medicine and biology has spurred a truly interdisciplinary effort that stretched outside the original\ud boundaries of the disciplines that gave birth to this field and created stimulating and enriching synergies.\ud Consideration on how the field has evolved and the experience of the work carried out over the last\ud 15 years in our centre, has led us to envision a future emphasis of medical imaging in Precision Imaging.\ud Precision Imaging is not a new discipline but rather a distinct emphasis in medical imaging borne\ud at the cross-roads between, and unifying the efforts behind mechanistic and phenomenological modelbased\ud imaging. It captures three main directions in the effort to deal with the information deluge in\ud imaging sciences, and thus achieve wisdom from data, information, and knowledge. Precision Imaging is\ud finally characterised by being descriptive, predictive and integrative about the imaged object. This paper\ud provides a brief and personal perspective on how the field has evolved, summarises and formalises our\ud vision of Precision Imaging for Precision Medicine, and highlights some connections with past research\ud and current trends in the field.

Purpose MR elastography (MRE) of the brain is being explored as a biomarker of neurodegenerative disease such as dementia. However, MRE measures for healthy brain have varied widely. Differing wave delivery methodologies may have influenced this, hence finite element-based simulations were performed to explore this possibility. Methods The natural frequencies of a series of cranial models were calculated, and MRE-associated vibration was simulated for different wave delivery methods at varying frequency, using simple isotropic viscoelastic material models for the brain. Displacement fields and the corresponding brain constitutive properties estimated by standard inversion techniques were compared across delivery methods and frequencies. Results The delivery methods produced widely different MRE displacement fields and inversions. Furthermore, resonances at natural frequencies influenced the displacement patterns. Consequently, some delivery methods led to lower inversion errors than others, and the error on the storage modulus varied by up to 11% between methods. Conclusion Wave delivery has a considerable impact on brain MRE reliability. Assuming small variations in brain biomechanics, as recently reported to accompany neurodegenerative disease (e.g., 7% for Alzheimer's disease), the effect of wave delivery is important. Hence, a consensus should be established on a consistent methodology to ensure diagnostic and prognostic consistency.

Low trauma fractures are amongst the most frequently encountered problems in the clinical assessment and treatment of bones, with dramatic health consequences for individuals and high financial costs for health systems. Consequently, significant research efforts have been dedicated to the development of accurate computational models of bone biomechanics and strength. However, the estimation of the fabric tensors, which describe the microarchitecture of the bone, has proven to be challenging using in vivo imaging. On the other hand, existing research has shown that isotropic models do not produce accurate predictions of stress states within the bone, as the material properties of the trabecular bone are anisotropic. In this paper, we present the first biomechanical study that uses statistically-derived fabric tensors for the estimation of bone strength in order to obtain patient-specific results. We integrate a statistical predictive model of trabecular bone microarchitecture previously constructed from a sample of ex vivo micro-CT datasets within a biomechanical simulation workflow. We assess the accuracy and flexibility of the statistical approach by estimating fracture load for two different databases and bone sites, i.e., for the femur and the T12 vertebra. The results obtained demonstrate good agreement between the statistically-driven and micro-CT-based estimates, with concordance coefficients of 98.6 and 95.5% for the femur and vertebra datasets, respectively.

There is emerging evidence suggesting that Alzheimer's disease is a vascular disorder, caused by impaired cerebral perfusion, which may be promoted by cardiovascular risk factors that are strongly influenced by lifestyle. In order to develop an understanding of the exact nature of such a hypothesis, a biomechanical understanding of the influence of lifestyle factors is pursued. An extended poroelastic model of perfused parenchymal tissue coupled with separate workflows concerning subject-specific meshes, permeability tensor maps and cerebral blood flow variability is used. The subject-specific datasets used in the modelling of this paper were collected as part of prospective data collection. Two cases were simulated involving male, non-smokers (control and mild cognitive impairment (MCI) case) during two states of activity (high and low). Results showed a marginally reduced clearance of cerebrospinal fluid (CSF)/interstitial fluid (ISF), elevated parenchymal tissue displacement and CSF/ISF accumulation and drainage in the MCI case. The peak perfusion remained at 8 mm s −1 between the two cases.

Biomechanical and biophysical models are key tools in many applications of surgical planning and optimisation, surgical guidance, and interactive simulation for training and rehearsal. The most robust and accurate models usually are those based on the relevant equations of continuum mechanics (solid, fluid, thermal, etc.), and which are generally solved with numerical methods such as FEM. Given high quality patient-specific inputs, these can enable accurate prediction of, e.g., deformations of soft tissues, flow patterns in blood vessels, energy delivery profiles around ablation devices, etc.

Purpose Magnetic resonance elastography (MRE) of the brain has demonstrated potential as a biomarker of neurodegenerative disease such as dementia but requires further evaluation. Cranial anatomical features such as the falx cerebri and tentorium cerebelli membranes may influence MRE measurements through wave reflection and interference and tissue heterogeneity at their boundaries. We sought to determine the influence of these effects via simulation. Methods MRE-associated mechanical stimulation of the brain was simulated using steady state harmonic finite element analysis. Simulations of geometrical models and anthropomorphic brain models derived from anatomical MRI data of healthy individuals were compared. Constitutive parameters were taken from MRE measurements for healthy brain. Viscoelastic moduli were reconstructed from the simulated displacement fields and compared with ground truth. Results Interference patterns from reflections and heterogeneity resulted in artifacts in the reconstructions of viscoelastic moduli. Artifacts typically occurred in the vicinity of boundaries between different tissues within the cranium, with a magnitude of 10%–20%. Conclusion Given that MRE studies for neurodegenerative disease have reported only marginal variations in brain elasticity between controls and patients (e.g., 7% for Alzheimer's disease), the predicted errors are a potential confound to the development of MRE as a biomarker of dementia and other neurodegenerative diseases. Magn Reson Med, 2015. © 2015 Wiley Periodicals, Inc.

This paper describes a constitutive model for ballistic gelatin at the low strain rates experienced, for example, by soft tissues during surgery. While this material is most commonly associated with high speed projectile penetration and impact investigations, it has also been used extensively as a soft tissue simulant in validation studies for surgical technologies (e.g. surgical simulation and guidance systems), for which loading speeds and the corresponding mechanical response of the material are quite different. We conducted mechanical compression experiments on gelatin specimens at strain rates spanning two orders of magnitude ( ~ 0.001 – 0.1 s − 1 ) and observed a nonlinear load–displacement history and strong strain rate-dependence. A compact and efficient visco-hyperelastic constitutive model was then formulated and found to fit the experimental data well. An Ogden type strain energy density function was employed for the elastic component. A single Prony exponential term was found to be adequate to capture the observed rate-dependence of the response over multiple strain rates. The model lends itself to immediate use within many commercial finite element packages.

The personalization of trabecular micro-architecture has been recently shown to be important in patient-specific biomechanical models of the femur. However, high-resolution in vivo imaging of bone micro-architecture using existing modalities is still infeasible in practice due to the associated acquisition times, costs, and X-ray radiation exposure. In this study, we describe a statistical approach for the prediction of the femur micro-architecture based on the more easily extracted subject-specific bone shape and mineral density information. To this end, a training sample of ex vivo micro-CT images is used to learn the existing statistical relationships within the low and high resolution image data. More specifically, optimal bone shape and mineral density features are selected based on their predictive power and used within a partial least square regression model to estimate the unknown trabecular micro-architecture within the anatomical models of new subjects. The experimental results demonstrate the accuracy of the proposed approach, with average errors of 0.07 for both the degree of anisotropy and tensor norms.

Realistic modelling of soft tissue biomechanics and mechanical interactions between tissues is an important part of biomechanically-informed surgical image-guidance and surgical simulation. This submission details a contact-modelling pipeline suitable for implementation in explicit matrix-free FEM solvers. While these FEM algorithms have been shown to be very suitable for simulation of soft tissue biomechanics and successfully used in a number of image-guidance systems, contact modelling specifically for these solvers is rarely addressed, partly because the typically large number of time steps required with this class of FEM solvers has led to a perception of them being a poor choice for simulations requiring complex contact modelling. The presented algorithm is capable of handling most scenarios typically encountered in image-guidance. The contact forces are computed with an evolution of the Lagrange-multiplier method first used by Taylor and Flanagan in PRONTO 3D extended with spatio-temporal smoothing heuristics for improved stability and edge–edge collision handling, and a new friction model. For contact search, a bounding-volume hierarchy (BVH) is employed, which is capable of identifying self-collisions by means of the surface-normal bounding cone of Volino and Magnenat-Thalmann, in turn computed with a novel formula. The BVH is further optimised for the small time steps by reducing the number of bounding-volume refittings between iterations through identification of regions with mostly rigid motion and negligible deformation. Further optimisation is achieved by integrating the self-collision criterion in the BVH creation and updating algorithms. The effectiveness of the algorithm is demonstrated on a number of artificial test cases and meshes derived from medical image data. It is shown that the proposed algorithm reduces the cost of BVH refitting to the point where it becomes a negligible part of the overall computation time of the simulation. It is also shown that the proposed surface-normal cone computation formula leads to about 40 % fewer BVH subtrees that must be checked for self-collisions compared with the widely used method of Provot. The proposed contact-force formulation and friction model are evaluated on artificial test cases that allow for a comparison with a ground truth. The quality of the proposed contact forces is assessed in terms of trajectories and energy conservation; a $$

In this paper we propose a probabilistic approach to group-wise registration of unstructured high-dimensional point sets. We focus on registration of generalised point sets which encapsulate both the positions of points on surface boundaries and corresponding normal vectors describing local surface geometry. Richer descriptions of shape can be especially valuable in applications involving complex and intricate variations in geometry, where spatial position alone is an unreliable descriptor for shape registration. A hybrid mixture model combining Student’s t and Von-Mises-Fisher distributions is proposed to model position and orientation components of the point sets, respectively. A group-wise rigid and non-rigid registration framework is then formulated on this basis. Two clinical data sets, comprising 27 brain ventricle and 15 heart shapes, were used to assess registration accuracy. Significant improvement in accuracy and anatomical validity of the estimated correspondences was achieved using the proposed approach, relative to state-of-the-art point set registration approaches, which consider spatial positions alone.

In this paper, we study the dissection of arterial layers by means of a stiff, planar, penetrating external body (a 'wedge'), and formulate a novel model of the process using cohesive zone formalism. The work is motivated by a need for better understanding of, and numerical tools for simulating catheter-induced dissection, which is a potentially catastrophic complication whose mechanisms remain little understood. As well as the large deformations and rupture of the tissue, models of such a process must accurately capture the interaction between the tissue and the external body driving the dissection. The latter feature, in particular, distinguishes catheter-induced dissection from, for example, straightforward peeling, which is relatively well-studied. As a step towards such models, we study a scenario involving a geometrically simpler penetrating object (the wedge), which affords more reliable comparison with experimental observations, but which retains the key feature of dissection driven by an external body, as described. Particular emphasis is placed on assessing the reliability of cohesive zone approaches in this context. A series of wedge-driven dissection experiments on porcine aorta were undertaken, from which tissue elastic and fracture parameters were estimated. Finite element models of the experimental configuration, with tissue considered to be a hyperelastic medium, and evolution of tissue rupture modelled with a consistent large-displacement cohesive formulation, were then constructed. Model-predicted and experimentally measured reaction forces on the wedge throughout the dissection process were compared and found to agree well. The performance of the cohesive formulation in modelling externally driven dissection is finally assessed, and the prospects for numerical models of catheter-induced dissection using such approaches is considered.

Image registration is an essential technique to obtain point correspondences between anatomical structures from different images. Conventional non-rigid registration methods assume a continuous and smooth deformation field throughout the image. However, the deformation field at the interface of different organs is not necessarily continuous, since the organs may slide over or separate from each other. Therefore, imposing continuity and smoothness ubiquitously would lead to artifacts and increased errors near the discontinuity interface. In computational mechanics, the eXtended Finite Element Method (XFEM) was introduced to handle discontinuities without using computational meshes that conform to the discontinuity geometry. Instead, the interpolation bases themselves were enriched with discontinuous functional terms. Borrowing this concept, we propose a multiresolution eXtented Free-Form Deformation (XFFD) framework that seamlessly integrates within and extends the standard Free-Form Deformation (FFD) approach. Discontinuities are incorporated by enriching the B-spline basis functions coupled with extra degrees of freedom, which are only introduced near the discontinuity interface. In contrast with most previous methods, restricted to sliding motion, no ad hoc penalties or constraints are introduced to reduce gaps and overlaps. This allows XFFD to describe more general discontinuous motions. In addition, we integrate XFFD into a rigorously formulated multiresolution framework by introducing an exact parameter upsampling method. The proposed method has been evaluated in two publicly available datasets: 4D pulmonary CT images from the DIR-Lab dataset and 4D CT liver datasets. The XFFD achieved a Target Registration Error (TRE) of 1.17 ± 0.85 mm in the DIR-lab dataset and 1.94 ± 1.01 mm in the liver dataset, which significantly improves on the performance of the state-of-the-art methods handling discontinuities.

A probabilistic group-wise similarity registration technique based on Student's t-mixture model (TMM) and a multi-resolution extension of the same (mr-TMM) are proposed in this study, to robustly align shapes and establish valid correspondences, for the purpose of training statistical shape models (SSMs). Shape analysis across large cohorts requires automatic generation of the requisite training sets. Automated segmentation and landmarking of medical images often result in shapes with varying proportions of outliers and consequently require a robust method of alignment and correspondence estimation. Both TMM and mrTMM are validated by comparison with state-of-the-art registration algorithms based on Gaussian mixture models (GMMs), using both synthetic and clinical data. Four clinical data sets are used for validation: (a) 2D femoral heads (K= 1000 samples generated from DXA images of healthy subjects); (b) control-hippocampi (K= 50 samples generated from T1-weighted magnetic resonance (MR) images of healthy subjects); (c) MCI-hippocampi (K= 28 samples generated from MR images of patients diagnosed with mild cognitive impairment); and (d) heart shapes comprising left and right ventricular endocardium and epicardium (K= 30 samples generated from short-axis MR images of: 10 healthy subjects, 10 patients diagnosed with pulmonary hypertension and 10 diagnosed with hypertrophic cardiomyopathy). The proposed methods significantly outperformed the state-of-the-art in terms of registration accuracy in the experiments involving synthetic data, with mrTMM offering significant improvement over TMM. With the clinical data, both methods performed comparably to the state-of-the-art for the hippocampi and heart data sets, which contained few outliers. They outperformed the state-of-the-art for the femur data set, containing large proportions of outliers, in terms of alignment accuracy, and the quality of SSMs trained, quantified in terms of generalization, compactness and specificity.

In this study, we examine the effect of collagenase, elastase and glutaraldehyde treatments on the response of porcine aorta to controlled peel testing. Specifically, the effects on the tissue׳s resistance to dissection, as quantified by critical energy release rate, are investigated. We further explore the utility of these treatments in creating model tissues whose properties emulate those of certain diseased tissues. Such model tissues would find application in, for example, development and physical testing of new endovascular devices. Controlled peel testing of fresh and treated aortic specimens was performed with a tensile testing apparatus. The resulting reaction force profiles and critical energy release rates were compared across sample classes. It was found that collagenase digestion significantly decreases resistance to peeling, elastase digestion has almost no effect, and glutaraldehyde significantly increases resistance. The implications of these findings for understanding mechanisms of disease-associated biomechanical changes, and for the creation of model tissues that emulate these changes are explored.

A probabilistic framework for robust, group-wise rigid alignment of point-sets using a mixture of Students t-distribution especially when the point sets are of varying lengths, are corrupted by an unknown degree of outliers or in the presence of missing data. Medical images (in particular magnetic resonance (MR) images), their segmentations and consequently point-sets generated from these are highly susceptible to corruption by outliers. This poses a problem for robust correspondence estimation and accurate alignment of shapes, necessary for training statistical shape models (SSMs). To address these issues, this study proposes to use a t-mixture model (TMM), to approximate the underlying joint probability density of a group of similar shapes and align them to a common reference frame. The heavy-tailed nature of t-distributions provides a more robust registration framework in comparison to state of the art algorithms. Significant reduction in alignment errors is achieved in the presence of outliers, using the proposed TMM-based group-wise rigid registration method, in comparison to its Gaussian mixture model (GMM) counterparts. The proposed TMM-framework is compared with a group-wise variant of the well-known Coherent Point Drift (CPD) algorithm and two other group-wise methods using GMMs, using both synthetic and real data sets. Rigid alignment errors for groups of shapes are quantified using the Hausdorff distance (HD) and quadratic surface distance (QSD) metrics.

MR elastography (MRE) of the brain is being explored as a biomarker of neurodegenerative disease such as dementia. However, MRE measures for healthy brain have varied widely. Differing wave delivery methodologies may have influenced this, hence finite element-based simulations were performed to explore this possibility.The natural frequencies of a series of cranial models were calculated, and MRE-associated vibration was simulated for different wave delivery methods at varying frequency, using simple isotropic viscoelastic material models for the brain. Displacement fields and the corresponding brain constitutive properties estimated by standard inversion techniques were compared across delivery methods and frequencies.The delivery methods produced widely different MRE displacement fields and inversions. Furthermore, resonances at natural frequencies influenced the displacement patterns. Consequently, some delivery methods led to lower inversion errors than others, and the error on the storage modulus varied by up to 11% between methods.Wave delivery has a considerable impact on brain MRE reliability. Assuming small variations in brain biomechanics, as recently reported to accompany neurodegenerative disease (e.g., 7% for Alzheimer's disease), the effect of wave delivery is important. Hence, a consensus should be established on a consistent methodology to ensure diagnostic and prognostic consistency. Magn Reson Med 78:341-356, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Nuclear magnetic resonance (NMR) is an invaluable tool for investigating porous media. Its use allows to study pore size distributions, fiber tortuosity, and permeability as a function of the relaxation time, diffusivity, and flow. This information was shown to be important in many applications, such as medical diagnosis and materials science. A complete NMR analysis involves the solution of the Bloch-Torrey (BT) equation. However, solving this equation analytically becomes intractable for all but the simplest geometries.We present an efficient numerical framework for solving the generalised BT equation. This method allows to obtain computational simulations of the NMR experiment in arbitrarily complex domains. In addition to the standard BT equation, the generalised BT formulation takes into account the flow and relaxation terms, allowing a better representation of the phenomena under scope. This framework is flexible enough to deal parametrically with any order of convergence in the spatial domain. Moreover, we developed a second-order implicit scheme for the temporal discretisation with similar computational demands as the existing explicit methods. This represents a huge step forward for obtaining reliable results with few iterations. Comparisons with analytical solutions and real data show the flexibility and accuracy of the proposed method.

A novel probabilistic, group-wise rigid registration framework is proposed in this study, to robustly align and establish correspondence across anatomical shapes represented as unstructured point sets. Student’s t-mixture model (TMM) is employed to exploit their inherent robustness to outliers. The primary application for such a framework is the automatic construction of statistical shape models (SSMs) of anatomical structures, from medical images. Tools used for automatic segmentation and landmarking of medical images often result in segmentations with varying proportions of outliers. The proposed approach is able to robustly align shapes and establish valid correspondences in the presence of considerable outliers and large variations in shape. A multi-resolution registration (mrTMM) framework is also formulated, to further improve the performance of the proposed TMM-based registration method. Comparisons with a state-of-the art approach using clinical data show that the mrTMM method in particular, achieves higher alignment accuracy and yields SSMs that generalise better to unseen shapes.

Three-dimensional reconstructions of coronary arteries can overcome some of the limitations of 2D X-ray angiography, namely artery overlap/foreshortening and lack of depth information. Model-based arterial reconstruction algorithms usually rely on 2D coronary artery segmentations and require good robustness to outliers. In this paper, we propose a novel probabilistic method to reconstruct coronary artery centrelines from retrospectively gated X-ray images based on a probabilistic mixture model. Specifically, 3D coronary artery centrelines are described by a mixture of Student’s t-distributions, and the reconstruction is formulated as maximum-likelihood estimation of the mixture model parameters, given the 2D segmentations of arteries from 2D X-ray images. Our method provides robustness against the erroneously segmented parts in the 2D segmentations by taking advantage of the inherent robustness of t-distributions. We validate our reconstruction results using synthetic phantom and clinical X-ray angiography data. The results show that the proposed method can cope with imperfect and noisy segmentation data.

A deformable registration method is described that enables automatic alignment of magnetic resonance (MR) and 3D transrectal ultrasound (TRUS) images of the prostate gland. The method employs a novel "model-to-image" registration approach in which a deformable model of the gland surface, derived from an MR image, is registered automatically to a TRUS volume by maximising the likelihood of a particular model shape given a voxel-intensity-based feature that represents an estimate of surface normal vectors at the boundary of the gland. The deformation of the surface model is constrained by a patient-specific statistical model of gland deformation, which is trained using data provided by biomechanical simulations. Each simulation predicts the motion of a volumetric finite element mesh due to the random placement of a TRUS probe in the rectum. The use of biomechanical modelling in this way also allows a dense displacement field to be calculated within the prostate, which is then used to non-rigidly warp the MR image to match the TRUS image. Using data acquired from eight patients, and anatomical landmarks to quantify the registration accuracy, the median final RMS target registration error after performing 100 MR-TRUS registrations for each patient was 2.40 mm.

Statistical shape models (SSM) are widely used in medical image analysis to represent variability in organ shape. However, representing subject-specific soft-tissue motion using this technique is problematic for applications where imaging organ changes in an individual is not possible or impractical. One solution is to synthesise training data by using biomechanical modelling. However, for many clinical applications, generating a biomechanical model of the organ(s) of interest is a non-trivial task that requires a significant amount of user-interaction to segment an image and create a finite element mesh. In this study, we investigate the impact of reducing the effort required to generate SSMs and the accuracy with which such models can predict tissue displacements within the prostate gland due to transrectal ultrasound probe pressure. In this approach, the finite element mesh is based on a simplified geometric representation of the organs. For example, the pelvic bone is represented by planar surfaces, or the number of distinct tissue compartments is reduced. Such representations are much easier to generate from images than a geometrically accurate mesh. The difference in the median root-mean-square displacement error between different SSMs of prostate was

Efficient and accurate techniques for simulation of soft tissue deformation are an increasingly valuable tool in many areas of medical image computing, such as biomechanically-driven image registration and interactive surgical simulation. For reasons of efficiency most analyses are based on simplified linear formulations, and previously almost all have ignored well established features of tissue mechanical response such as anisotropy and time-dependence. We address these latter issues by firstly presenting a generalised anisotropic viscoelastic constitutive framework for soft tissues, particular cases of which have previously been used to model a wide range of tissues. We then develop an efficient solution procedure for the accompanying viscoelastic hereditary integrals which allows use of such models in explicit dynamic finite element algorithms. We show that the procedure allows incorporation of both anisotropy and viscoelasticity for as little as 5.1% additional cost compared with the usual isotropic elastic models. Finally we describe the implementation of a new GPU-based finite element scheme for soft tissue simulation using the CUDA API. Even with the inclusion of more elaborate constitutive models as described the new implementation affords speed improvements compared with our recent graphics API-based implementation, and compared with CPU execution a speed up of 56.3× is achieved. The validity of the viscoelastic solution procedure and performance of the GPU implementation are demonstrated with a series of numerical examples.

The use of biomechanical modelling, especially in conjunction with finite element analysis, has become common in many areas of medical image analysis and surgical simulation. Clinical employment of such techniques is hindered by conflicting requirements for high fidelity in the modelling approach, and fast solution speeds. We report the development of techniques for high-speed nonlinear finite element analysis for surgical simulation. We use a fully nonlinear total Lagrangian explicit finite element formulation which offers significant computational advantages for soft tissue simulation. However, the key contribution of the work is the presentation of a fast graphics processing unit (GPU) solution scheme for the finite element equations. To the best of our knowledge, this represents the first GPU implementation of a nonlinear finite element solver. We show that the present explicit finite element scheme is well suited to solution via highly parallel graphics hardware, and that even a midrange GPU allows significant solution speed gains (up to 16.8 times) compared with equivalent CPU implementations. For the models tested the scheme allows real-time solution of models with up to 16 000 tetrahedral elements. The use of GPUs for such purposes offers a cost-effective high-performance alternative to expensive multi-CPU machines, and may have important applications in medical image analysis and surgical simulation.

The theoretical framework developed in a companion paper (Part I) is used to derive estimates of mechanical response of two meniscal cartilage specimens. The previously developed framework consisted of a constitutive model capable of incorporating confocal image-derived tissue microstructural data. In the present paper (Part II) fibre and matrix constitutive parameters are first estimated from mechanical testing of a batch of specimens similar to, but independent from those under consideration. Image analysis techniques which allow estimation of tissue microstructural parameters form confocal images are presented. The constitutive model and image-derived structural parameters are then used to predict the reaction force history of the two meniscal specimens subjected to partially confined compression. The predictions are made on the basis of the specimens' individual structural condition as assessed by confocal microscopy and involve no tuning of material parameters. Although the model does not reproduce all features of the experimental curves, as an unfitted estimate of mechanical response the prediction is quite accurate. In light of the obtained results it is judged that more general non-invasive estimation of tissue mechanical properties is possible using the developed framework.

Current development of a laser scanning confocal arthroscope within our school will enable 3D microscopic imaging of joint tissues in vivo. Such an instrument could be useful, for example, in assessing the microstructural condition of the living tissues without physical biopsy. It is envisaged also that linked to a suitable microstructural constitutive formulation, such imaging could allow non-invasive patient-specific estimation of tissue mechanical performance. Such a procedure could have applications in surgical planning and simulation, and assessment of engineered tissue replacements, where tissue biopsy is unacceptable. In this first of two papers the development of a suitable constitutive framework for generating such estimates is reported. A microstructure-based constitutive formulation for cartilaginous tissues is presented. The model extends existing fibre composite-type models and accounts for strain-rate sensitivity of the tissue mechanical response through incorporation of a viscoelastic fibre phase. Importantly, the model is constructed so as to allow direct incorporation of structural data from confocal images. A finite element implementation of the formulation suitable for incorporation within commercial codes is also presented.

Large quantities of diseased tissue are required in the research and development of new generations of medical devices, for example for use in physical testing. However, these are difficult to obtain. In contrast, porcine arteries are readily available as they are regarded as waste. Therefore, reliable means of creating from porcine tissue physical models of diseased human tissue that emulate well the associated mechanical changes would be valuable. To this end, we studied the effect on mechanical response of treating porcine thoracic aorta with collagenase, elastase and glutaraldehyde. The alterations in mechanical and failure properties were assessed via uniaxial tension testing. A constitutive model composed of the Gasser-Ogden-Holzapfel model, for elastic response, and a continuum damage model, for the failure, was also employed to provide a further basis for comparison (Calvo and Pena, 2006 and Gasser et al., 2006). For the concentrations used here it was found that: collagenase treated samples showed decreased fracture stress in the axial direction only; elastase treated samples showed increased fracture stress in the circumferential direction only; and glutaraldehyde samples showed no change in either direction. With respect to the proposed constitutive model, both collagenase and elastase had a strong effect on the fibre-related terms. The model more closely captured the tissue response in the circumferential direction, due to the smoother and sharper transition from damage initiation to complete failure in this direction. Finally, comparison of the results with those of tensile tests on diseased tissues suggests that these treatments indeed provide a basis for creation of physical models of diseased arteries.

Nuclear magnetic resonance (NMR) has proven of enormous value in the investigation of porous media. Its use allows to study pore size distributions, tortuosity, and permeability as a function of the relaxation time, diffusivity, and flow. This information plays an important role in plenty of applications, ranging from oil industry to medical diagnosis. A complete NMR analysis involves the solution of the Bloch-Torrey (BT) equation. However, solving this equation analytically becomes intractable for all but the simplest geometries.\ud We present an efficient numerical framework for solving the complete BT equation in arbitrarily complex domains. In addition to the standard BT equation, the generalised BT formulation takes into account the flow and relaxation terms, allowing a better representation of the phenomena under scope. The presented framework is flexible enough to deal parametrically with any order of convergence in the spatial domain. The major advantage of such approach is to allow both faster computations and sensitivity analyses over realistic geometries. Moreover, we developed a second-order implicit scheme for the temporal discretisation with similar computational demands as the existing explicit methods. This represents a huge step forward for obtaining reliable results with few iterations. Comparisons with analytical solutions and real data show the flexibility and accuracy of the proposed methodology.

This paper presents a novel method to treat discontinuities in a 3D piece-wise non-rigid registration framework, coined as EXtended Free-Form Deformation (XFFD). Existing discontinuities in the image, such as sliding motion of the lungs or the cardiac boundary adjacent to the blood pool, should be handled to obtain physically plausible deformation fields for motion analysis. However, conventional Free-form deformations (FFDs) impose continuity over the whole image, introducing inaccuracy near discontinuity boundaries. The proposed method incorporates enrichment functions into the FFD formalism, inspired by the linear interpolation method in the EXtended Finite Element Method (XFEM). Enrichment functions enable B-splines to handle discontinuities with minimal increase of computational complexity, while avoiding boundary-matching problem. It retains all properties of the framework of FFDs yet seamlessly handles general discontinuities and can also coexist with other proposed improvements of the FFD formalism. The proposed method showed high performance on synthetic and 3D lung CT images. The target registration error on the CT images is comparable to the previous methods, while being a generic method without assuming any type of motion constraint. Therefore, it does not include any penalty term. However, any of these terms could be included to achieve higher accuracy for specific applications.

Magnetic resonance elastography (MRE) of the brain has demonstrated potential as a biomarker of neurodegenerative disease such as dementia but requires further evaluation. Cranial anatomical features such as the falx cerebri and tentorium cerebelli membranes may influence MRE measurements through wave reflection and interference and tissue heterogeneity at their boundaries. We sought to determine the influence of these effects via simulation.MRE-associated mechanical stimulation of the brain was simulated using steady state harmonic finite element analysis. Simulations of geometrical models and anthropomorphic brain models derived from anatomical MRI data of healthy individuals were compared. Constitutive parameters were taken from MRE measurements for healthy brain. Viscoelastic moduli were reconstructed from the simulated displacement fields and compared with ground truth.Interference patterns from reflections and heterogeneity resulted in artifacts in the reconstructions of viscoelastic moduli. Artifacts typically occurred in the vicinity of boundaries between different tissues within the cranium, with a magnitude of 10%-20%.Given that MRE studies for neurodegenerative disease have reported only marginal variations in brain elasticity between controls and patients (e.g., 7% for Alzheimer's disease), the predicted errors are a potential confound to the development of MRE as a biomarker of dementia and other neurodegenerative diseases. Magn Reson Med 76:645-662, 2016. © 2015 Wiley Periodicals, Inc.

We present a finite element formulation of the full Bloch-Torrey equation for nuclear magnetic resonance (NMR) applications. We obtained parametrical expressions that allow us to compute the involved matrices in a simple and fast way for any spatial convergence order. The framework here proposed is valid for many problems related to MR, as diffusion and perfusion MRI.

Spine-related disorders are amongst the most frequently encountered problems in clinical medicine. For several applications such as 1) to improve the assessment of the strength of the spine, as well as 2) to optimize the personalization of spinal interventions, image-based biomechanical modeling of the vertebrae is expected to play an important predictive role. However, this requires the construction of computational models that are subject-specific and comprehensive. In particular, they need to incorporate information about the vertebral anisotropic micro-architecture, which plays a central role in the biomechanical function of the vertebrae. In practice, however, accurate personalization of the vertebral trabeculae has proven to be difficult as its imaging in vivo is currently infeasible. Consequently, this paper presents a statistical approach for accurate prediction of the vertebral fabric tensors based on a training sample of ex vivo micro-CT images. To the best of our knowledge, this is the first predictive model proposed and validated for vertebral datasets. The method combines features selection and partial least squares regression in order to derive optimal latent variables for the prediction of the fabric tensors based on the more easily extracted shape and density information. Detailed validation with 20 ex vivo T12 vertebrae demonstrates the accuracy and consistency of the approach for the personalization of trabecular anisotropy.

The insufflation of the abdomen in laparoscopic liver surgery leads to significant deformation of the liver. The estimation of the shape and position of the liver after insufflation has many important applications, such as providing surface-based registration algorithms used in image guidance with an initial guess and realistic patient-specific surgical simulation.

An important and longstanding field of research in orthopedic biomechanics is the elucidation and mathematical modeling of the mechanical response of cartilaginous tissues. Traditional approaches have treated such tissues as continua and have described their mechanical response in terms of macroscopic models borrowed from solid mechanics. The most important of such models are the biphasic and single-phase viscoelastic models, and the many variations thereof. These models have reached a high level of maturity and have been successful in describing a wide range of phenomena. An alternative approach that has received considerable recent interest, both in orthopedic biomechanics and in other fields, is the description of mechanical response based on consideration of a tissue's structure—so-called microstructural modeling. Examples of microstructurally based approaches include fibril-reinforced biphasic models and homogenization approaches. A review of both macroscopic and microstructural constitutive models is given in the present work.