Controlling the error on target motion through real-time mesh adaptation: Applications to deep brain stimulation

Enhancing Biomechanical Simulations Based on a Posteriori Error Estimates: The Potential of Dual-Weighted Residual-Driven Adaptive Mesh Refinement

The finite-element method (FEM) is a well-established procedure for computing approximate solutions to deterministic engineering problems described by partial differential equations. FEM produces discrete approximations of the solution with a discretisation error that can be quantified with a posteriori error estimates. The practical relevance of error estimates for biomechanics problems, especially for soft tissue where the response is governed by large strains, is rarely addressed. In this contribution, we propose an implementation of a posteriori error estimates targeting a user-defined quantity of interest, using the dual-weighted residual (DWR) technique tailored to biomechanics. The proposed method considers a general setting that encompasses three-dimensional geometries and model nonlinearities, which appear in hyperelastic soft tissues. We take advantage of the automatic differentiation capabilities embedded in modern finite-element software, which allows the error estimates to be computed generically for a large class of models and constitutive laws. First, we validate our methodology using experimental measurements from silicone samples and then illustrate its applicability for patient-specific computations of pressure ulcers on a human heel.

Modelling Keloids Dynamics: A Brief Review and New Mathematical Perspectives

Keloids are fibroproliferative disorders described by excessive growth of fibrotic tissue, which also invades adjacent areas (beyond the original wound borders). Since these disorders are specific to humans (no other animal species naturally develop keloid-like tissue), experimental in vivo/in vitro research has not led to significant advances in this field. One possible approach could be to combine in vitro human models with calibrated in silico mathematical approaches (i.e., models and simulations) to generate new testable biological hypotheses related to biological mechanisms and improved treatments. Because these combined approaches do not really exist for keloid disorders, in this brief review we start by summarising the biology of these disorders, then present various types of mathematical and computational approaches used for related disorders (i.e., wound healing and solid tumours), followed by a discussion of the very few mathematical and computational models published so far to study various inflammatory and mechanical aspects of keloids. We conclude this review by discussing some open problems and mathematical opportunities offered in the context of keloid disorders by such combined in vitro/in silico approaches, and the need for multi-disciplinary research to enable clinical progress.

Mechanistic multiscale modelling of energy metabolism in human astrocytes reveals the impact of morphology changes in Alzheimer's Disease

Astrocytes with their specialised morphology are essential for brain homeostasis as metabolic mediators between blood vessels and neurons. In neurodegenerative diseases such as Alzheimer's disease (AD), astrocytes adopt reactive profiles with molecular and morphological changes that could lead to the impairment of their metabolic support and impact disease progression. However, the underlying mechanisms of how the metabolic function of human astrocytes is impaired by their morphological changes in AD are still elusive. To address this challenge, we developed and applied a metabolic multiscale modelling approach integrating the dynamics of metabolic energy pathways and physiological astrocyte morphologies acquired in human AD and age-matched control brain samples. The results demonstrate that the complex cell shape and intracellular organisation of energetic pathways determine the metabolic profile and support capacity of astrocytes in health and AD conditions. Thus, our mechanistic approach indicates the importance of spatial orchestration in metabolism and allows for the identification of protective mechanisms against disease-associated metabolic impairments.

Soft-tissue simulation of the breast for intraoperative navigation and fusion of preoperative planning

Computational preoperative planning offers the opportunity to reduce surgery time and patient risk. However, on soft tissues such as the breast, deviations between the preoperative and intraoperative settings largely limit the applicability of preoperative planning. In this work, we propose a high-performance accurate simulation model of the breast, to fuse preoperative information with the intraoperative deformation setting. Our simulation method encompasses three major elements: high-quality finite-element modeling (FEM), efficient handling of anatomical couplings for high-performance computation, and personalized parameter estimation from surface scans. We show the applicability of our method on two problems: 1) transforming high-quality preoperative scans to the intraoperative setting for fusion of preoperative planning data, and 2) real-time tracking of breast tumors for navigation during intraoperative radiotherapy. We have validated our methodology on a test cohort of nine patients who underwent tumor resection surgery and intraoperative radiotherapy, and we have quantitatively compared simulation results to intraoperative scans. The accuracy of our simulation results suggest clinical viability of the proposed methodology.

Cortex tissue relaxation and slow to medium load rates dependency can be captured by a two-phase flow poroelastic model

This paper investigates the complex time-dependent behavior of cortex tissue, under adiabatic condition, using a two-phase flow poroelastic model. Motivated by experiments and Biot's consolidation theory, we tackle time-dependent uniaxial loading, confined and unconfined, with various geometries and loading rates from 1μm/s to 100μm/s. The cortex tissue is modeled as the porous solid saturated by two immiscible fluids, with dynamic viscosities separated by four orders, resulting in two different characteristic times. These are respectively associated to interstitial fluid and glial cells. The partial differential equations system is discretized in space by the finite element method and in time by Euler-implicit scheme. The solution is computed using a monolithic scheme within the open-source computational framework FEniCS. The parameters calibration is based on Sobol sensitivity analysis, which divides them into two groups: the tissue specific group, whose parameters represent general properties, and sample specific group, whose parameters have greater variations. Our results show that the experimental curves can be reproduced without the need to resort to viscous solid effects, by adding an additional fluid phase. Through this process, we aim to present multiphase poromechanics as a promising way to a unified brain tissue modeling framework in a variety of settings.

Mathematical modeling and computer simulation of needle insertion into soft tissue

In this study we present a kinematic approach for modeling needle insertion into soft tissues. The kinematic approach allows the presentation of the problem as Dirichlet-type (i.e. driven by enforced motion of boundaries) and therefore weakly sensitive to unknown properties of the tissues and needle-tissue interaction. The parameters used in the kinematic approach are straightforward to determine from images. Our method uses Meshless Total Lagrangian Explicit Dynamics (MTLED) method to compute soft tissue deformations. The proposed scheme was validated against experiments of needle insertion into silicone gel samples. We also present a simulation of needle insertion into the brain demonstrating the method's insensitivity to assumed mechanical properties of tissue.

Biomechanical evaluation of the stability of extra-articular distal radius fractures fixed with volar locking plates according to the length of the distal locking screw

Surgeons usually used short screws to avoid extensor tendon problems during volar locking plate fixation in distal radius fracture. However, the stability according to the length of distal locking screws have not been fully understood. We investigated this issue through finite element analysis and compression test using synthetic radius. Our results demonstrated that the bi-cortical full-length fixation does not contribute to the stiffness increase in the axial compression direction, and a reduction in length of up to more than 50% length can still provide similar stability to full-length screws. Our data can support that surgeon should undersize the distal screw.

Robotically Steered Needles: A Survey of Neurosurgical Applications and Technical Innovations

This paper surveys both the clinical applications and main technical innovations related to steered needles, with an emphasis on neurosurgery. Technical innovations generally center on curvilinear robots that can adopt a complex path that circumvents critical structures and eloquent brain tissue. These advances include several needle-steering approaches, which consist of tip-based, lengthwise, base motion-driven, and tissue-centered steering strategies. This paper also describes foundational mathematical models for steering, where potential fields, nonholonomic bicycle-like models, spring models, and stochastic approaches are cited. In addition, practical path planning systems are also addressed, where we cite uncertainty modeling in path planning, intraoperative soft tissue shift estimation through imaging scans acquired during the procedure, and simulation-based prediction. Neurosurgical scenarios tend to emphasize straight needles so far, and span deep-brain stimulation (DBS), stereoelectroencephalography (SEEG), intracerebral drug delivery (IDD), stereotactic brain biopsy (SBB), stereotactic needle aspiration for hematoma, cysts and abscesses, and brachytherapy as well as thermal ablation of brain tumors and seizure-generating regions. We emphasize therapeutic considerations and complications that have been documented in conjunction with these applications.

An adaptive finite element model for steerable needles

Penetration of a flexible and steerable needle into a soft target material is a complex problem to be modelled, involving several mechanical challenges. In the present paper, an adaptive finite element algorithm is developed to simulate the penetration of a steerable needle in brain-like gelatine material, where the penetration path is not predetermined. The geometry of the needle tip induces asymmetric tractions along the tool–substrate frictional interfaces, generating a bending action on the needle in addition to combined normal and shear loading in the region where fracture takes place during penetration. The fracture process is described by a cohesive zone model, and the direction of crack propagation is determined by the distribution of strain energy density in the tissue surrounding the tip. Simulation results of deep needle penetration for a programmable bevel-tip needle design, where steering can be controlled by changing the offset between interlocked needle segments, are mainly discussed in terms of penetration force versus displacement along with a detailed description of the needle tip trajectories. It is shown that such results are strongly dependent on the relative stiffness of needle and tissue and on the tip offset. The simulated relationship between programmable bevel offset and needle curvature is found to be approximately linear, confirming empirical results derived experimentally in a previous work. The proposed model enables a detailed analysis of the tool–tissue interactions during needle penetration, providing a reliable means to optimise the design of surgical catheters and aid pre-operative planning.

Role of mechanical cues and hypoxia on the growth of tumor cells in strong and weak confinement: A dual in vitro-in silico approach

Characterization of tumor growth dynamics is of major importance for cancer understanding. By contrast with phenomenological approaches, mechanistic modeling can facilitate disclosing underlying tumor mechanisms and lead to identification of physical factors affecting proliferation and invasive behavior. Current mathematical models are often formulated at the tissue or organ scale with the scope of a direct clinical usefulness. Consequently, these approaches remain empirical and do not allow gaining insight into the tumor properties at the scale of small cell aggregates. Here, experimental and numerical studies of the dynamics of tumor aggregates are performed to propose a physics-based mathematical model as a general framework to investigate tumor microenvironment. The quantitative data extracted from the cellular capsule technology microfluidic experiments allow a thorough quantitative comparison with in silico experiments. This dual approach demonstrates the relative impact of oxygen and external mechanical forces during the time course of tumor model progression.