Biomechanics and Modeling in Mechanobiology

A tumour resection normally involves a large tissue resection and bone replacement. Polyether ether ketone (PEEK) has become a suitable candidate for use in various prostheses owing to its lightness in weight, modulus close to that of natural bone, and good biocompatibility, among other factors. This study proposes a new design method for a rib prosthesis using the centroid trajectory of the natural replaced rib, where the strength can be adjusted by monitoring the cross-sectional area, shape, and properties. A custom-designed rib prosthesis was manufactured using fused deposition modelling (FDM) manufacturing technology, and the mechanical behaviour was found to be close to that of a natural rib. A finite element analysis of the designed rib was carried out under similar loading conditions to those used in mechanical testing. The results indicate that the centroid trajectory derived from a natural rib diaphysis can provide reliable guidance for the design of a rib prosthesis. Such methodology not only offers considerable design freedom in terms of shape and required strength, but also benefits the quality of the surface finishing for samples manufactured using the FDM technique. FDM-printed PEEK rib prostheses have been successfully implanted, and good clinical performances have been achieved.

In tensional studies of bone fragments during limb lengthening, it is usually assumed that the stress level in the gap tissue before each distraction step (pre-traction stress) is rather modest. However, during the process of distraction osteogenesis, a large interfragmentary gap is generated and these pre-traction stresses may be important. To date, to the authors’ knowledge, no computational study has been developed to assess the effect of stress accumulation during limb lengthening. In this work, we present a macroscopic growth mixture formulation to investigate the influence of pre-traction stresses on the outcome of this clinical procedure. In particular, the model is applied to the simulation of the regeneration of tibial defects by means of distraction osteogenesis. The evolution of pre-traction forces, post-traction forces and peak forces is evaluated and compared with experimental data. The results show that the inclusion of pre-traction stresses in the model affects the evolution of the regeneration process and the corresponding reaction forces.

As a prelude to the understanding of mechanotransduction in human embryonic stem cell (hESC) differentiation, the mechanical behavior of hESCs in the form of cell pellet is studied. The pellets were tested after 3 or 5 weeks of cell culture in order to demonstrate the effect of the duration of cell culture on the mechanical properties of the pellets. A micromechanical tester was used to conduct unconfined compression on hESC pellet, and experimental, numerical, and analytical methods were combined to determine the mechanical properties of hESC pellet. It is assumed that the mechanical behavior of hESC pellets can be described by an isotropic, linear viscoelastic model consisting of a spring and two Maxwell units in parallel, and the Poisson’s ratio of the hESC pellet is constant based on pellet deformation in the direction perpendicular to the compression direction. Finite element method (FEM) simulation was adopted to determine the values of Poisson’s ratio and the five parameters contained in the viscoelastic model. The variations of Poisson’s ratio and the initial elastic modulus are found to be larger compared with those of the four other parameters. Results show that longer duration of cell culture leads to higher modulus of hESC pellet. The effect of pellet size error on the values of mechanical parameters determined is studied using FEM simulation, and it is found that the effect of size error on Poisson’s ratio and initial elastic modulus is much larger than that on the other parameters.

The adolescent idiopathic scoliosis (AIS) is a 3D deformity of the spine whose origin is unknown and clinical evolution unpredictable. In this work, a mixed theoretical and numerical approach based on energetic considerations is proposed to study the global spine deformations. The introduced mechanical model aims at overcoming the limitations of computational cost and high variability in physical parameters. The model is constituted of rigid vertebral bodies associated with 3D effective stiffness tensors. The spine equilibrium is found using minimization methods of the mechanical total energy which circumvents forces and loading calculation. The values of the model parameters exhibited in the stiffness tensor are retrieved using a combination of clinical images post-processing and inverse algorithms implementation. Energy distribution patterns can then be evaluated at the global spine scale to investigate given time patient-specific features. To verify the reliability of the numerical methods, a simplified model of spine was implemented. The methodology was then applied to a clinical case of AIS (13-year-old girl, Lenke 1A). Comparisons of the numerical spine geometry with clinical data equilibria showed numerical calculations were performed with great accuracy. The patient follow-up allowed us to highlight the energetic role of the apical and junctional zones of the deformed spine, the repercussion of sagittal bending in sacro-illiac junctions and the significant role of torsion with scoliosis aggravation. Tangible comparisons of output measures with clinical pathology knowledge provided a reliable basis for further use of those numerical developments in AIS classification, scoliosis evolution prediction and potentially surgical planning.

Computational modelling of the cardiovascular system offers much promise, but represents a truly interdisciplinary challenge, requiring knowledge of physiology, mechanics of materials, fluid dynamics and biochemistry. This paper aims to provide a summary of the recent advances in cardiovascular structural modelling, including the numerical methods, main constitutive models and modelling procedures developed to represent cardiovascular structures and pathologies across a broad range of length and timescales; serving as an accessible point of reference to newcomers to the field. The class of so-called hyperelastic materials provides the theoretical foundation for the modelling of how these materials deform under load, and so an overview of these models is provided; comparing classical to application-specific phenomenological models. The physiology is split into components and pathologies of the cardiovascular system and linked back to constitutive modelling developments, identifying current state of the art in modelling procedures from both clinical and engineering sources. Models which have originally been derived for one application and scale are shown to be used for an increasing range and for similar applications. The trend for such approaches is discussed in the context of increasing availability of high performance computing resources, where in some cases computer hardware can impact the choice of modelling approach used.

The altered biomechanical function of the knee following partial meniscectomy results in ongoing articular cartilage overload, which may lead to progressive osteoarthritis (OA). An artificial medial meniscus implant (NUsurface® Meniscus Implant, Active Implants LLC., Memphis, TN, USA) was developed to mimic the native meniscus and may provide an effective long-term solution for OA patients, alleviate pain, and restore joint function. The goal of the current study was to investigate the potential effect of an artificial medial meniscus implant on the function of the lateral compartment of the knee and on the potential alterations in load distribution between the two compartments under static axial loading, using advanced piezo-resistive sensors. We used an integrated in situ/in vivo experimental approach combining contact pressure measurements of cadaveric knees with MRI joint space measurements of 72 mild OA patients. We employed this integrated approach to evaluate the mechanical consequences in both the medial (treated) and lateral knee compartments of two levels of meniscectomy and implantation of an artificial meniscus implant. Partial and subtotal meniscectomies of the medial meniscus resulted in statistically significant decrease in contact areas (p = 0.008 and p < 0.0001, respectively) and increased contact pressures in the medial compartment; however, implantation of the artificial meniscus implant restored the average contact pressure to 93 ± 14% of its pre-meniscectomy, intact value. Additionally, we found that neither the two different grades of medial meniscectomies, nor implantation of the artificial medial meniscus implant affected the lateral compartment of the knee. The MRI data from the patient cohort facilitated the integration of real-life clinical results together with the laboratory measurements from our cadaveric study, as these two approaches complement each other. We conclude that the use of the artificial medial meniscus implant may re-establish normal load distribution across the articulating surfaces of the medial compartment and not increase loading across the lateral knee compartment.

Myocardial infarction (MI) triggers a series of maladaptive events that lead to structural and functional changes in the left ventricle. It is crucial to better understand the progression of adverse remodeling, in order to develop effective treatment. In addition, being able to assess changes in vivo would be a powerful tool in the clinic. The goal of the current study is to quantify the in vivo material properties of infarcted and remote myocardium 1 week after MI, as well as the orientation of collagen fibers in the infarct. This will be accomplished by using a combination of magnetic resonance imaging (MRI), catheterization, finite element modeling, and numerical optimization to analyze a porcine model ( $$N = 4$$ ) of posterolateral myocardial infarction. Specifically, properties will be determined by minimizing the difference between in vivo strains and volume calculated from MRI and finite element model predicted strains and volume. The results indicate that the infarct region is stiffer than the remote region and that the infarct collagen fibers become more circumferentially oriented 1 week post-MI. These findings are consistent with previous studies, which employed ex vivo techniques. The proposed methodology will ultimately provide a means of predicting remote and infarct mechanical properties in vivo at any time point post-MI.