Biological variability in biomechanical engineering research: Significance and meta-analysis of current modeling practices

Computationally derived endosteal strain and strain gradients correlate with increased bone formation in an axially loaded murine tibia model

Osteoporosis is a common metabolic bone disorder characterized by low bone mass and microstructural degradation of bone tissue due to a derailed bone remodeling process. A deeper understanding of the mechanobiological phenomena that modulate the bone remodeling response to mechanical loading in a healthy bone is crucial to develop treatments. Rodent models have provided invaluable insight into the mechanobiological mechanisms regulating bone adaptation in response to dynamic mechanic stimuli. This study sheds light on these aspects by means of assessing the mechanical environment of the cortical and cancellous tissue to in vivo dynamic compressive loading within the mouse tibia using microCT-based finite element model in combination with diaphyseal strain gauge measures. Additionally, this work describes the relation between the mid-diaphyseal strains and strain gradients from the finite element analysis and bone formation measures from time-lapse in vivo tibial loading with a fluorochrome-derived histomorphometry analysis. The mouse tibial loading model demonstrated that cancellous strains were lower than those in the midshaft cortical bone. Sensitivity analyses demonstrated that the material property of cortical bone was the most significant model parameter. The computationally-modeled strains and strain gradients correlated significantly to the histologically-measured bone formation thickness at the mid-diaphyseal cross-section of the mouse tibia.

Regional differences in the biological variability of plantar pressure as a basis for refining diagnostic gait analysis

The variability of movement plays a crucial role in shaping individual's gait pattern and could, therefore, potentially serve diagnostic purposes. Nevertheless, existing concepts for the use of variability in diagnosing gait present a challenge due to the lack of adequate benchmarks and methods for comparison. We assessed the individuality of contribution of foot parts that directly mediate the transmission of forces between the foot and the ground in body weight shifting during walking based on 200 pedobarometric measurements corresponding to the analysed foot parts for each of 19 individuals in a homogeneous study group. Our results show a degree of individualisation of the contribution of particular foot parts in the weight-shift high enough to justify the need to consider it in the diagnostic analysis. Furthermore they reveal noticeable, functionally driven differences between plantar areas most apparent between the lowest individuality for the first foot ray and the highest for second one and metatarsus. The diagnostic reference standard in pedobarometry should describe the contribution in the shift of body weight during walking for each area of the foot separately and include information on the intra-individual variation and individualisation of descriptors of the contribution. Such a comprehensive standard has the potential to increase the diagnostic value of pedobarometry through enrichment of the assessment description.

Multi-frequency shear modulus measurements discriminate tumorous from healthy tissues

As far as their mechanical properties are concerned, cancerous lesions can be confused with healthy surrounding tissues in elastography protocols if only the magnitude of moduli is considered. We show that the frequency dependence of the tissue's mechanical properties allows for discriminating the tumor from other tissues, obtaining a good contrast even when healthy and tumor tissues have shear moduli of comparable magnitude. We measured the shear modulus G^*(ω) of xenograft subcutaneous tumors developed in mice using breast human cancer cells, compared with that of fat, skin and muscle harvested from the same mice. As the absolute shear modulus |G^*(ω)| of tumors increases by 42% (from 5.2 to 7.4 kPa) between 0.25 and 63 Hz, it varies over the same frequency range by 77% (from 0.53 to 0.94 kPa) for the fat, by 103% (from 3.4 to 6.9 kPa) for the skin and by 120% (from 4.4 to 9.7 kPa) for the muscle. These measurements fit well to the fractional model G^*(ω)=K(iω)ⁿ, yielding a coefficient K and a power-law exponent n for each sample. Tumor, skin and muscle have comparable K parameter values, that of fat being significantly lower; the p-values given by a Mann-Whitney test are above 0.14 when comparing tumor, skin and muscle between themselves, but below 0.001 when comparing fat with tumor, skin or muscle. With regards the n parameter, tumor and fat are comparable, with p-values above 0.43, whereas tumor differs from both skin and muscle, with p-values below 0.001. Tumor tissues thus significantly differs from fat, skin and muscle on account of either the K or the n parameter, i.e. of either the magnitude or the frequency-dependence of the shear modulus.

Multibody Models of the Thoracolumbar Spine: A Review on Applications, Limitations, and Challenges

Numerical models of the musculoskeletal system as investigative tools are an integral part of biomechanical and clinical research. While finite element modeling is primarily suitable for the examination of deformation states and internal stresses in flexible bodies, multibody modeling is based on the assumption of rigid bodies, that are connected via joints and flexible elements. This simplification allows the consideration of biomechanical systems from a holistic perspective and thus takes into account multiple influencing factors of mechanical loads. Being the source of major health issues worldwide, the human spine is subject to a variety of studies using these models to investigate and understand healthy and pathological biomechanics of the upper body. In this review, we summarize the current state-of-the-art literature on multibody models of the thoracolumbar spine and identify limitations and challenges related to current modeling approaches.

Validation of a Patient-Specific Musculoskeletal Model for Lumbar Load Estimation Generated by an Automated Pipeline From Whole Body CT

Background: Chronic back pain is a major health problem worldwide. Although its causes can be diverse, biomechanical factors leading to spinal degeneration are considered a central issue. Numerical biomechanical models can identify critical factors and, thus, help predict impending spinal degeneration. However, spinal biomechanics are subject to significant interindividual variations. Therefore, in order to achieve meaningful findings on potential pathologies, predictive models have to take into account individual characteristics. To make these highly individualized models suitable for systematic studies on spinal biomechanics and clinical practice, the automation of data processing and modeling itself is inevitable. The purpose of this study was to validate an automatically generated patient-specific musculoskeletal model of the spine simulating static loading tasks.

Methods: CT imaging data from two patients with non-degenerative spines were processed using an automated deep learning-based segmentation pipeline. In a semi-automated process with minimal user interaction, we generated patient-specific musculoskeletal models and simulated various static loading tasks. To validate the model, calculated vertebral loadings of the lumbar spine and muscle forces were compared with in vivo data from the literature. Finally, results from both models were compared to assess the potential of our process for interindividual analysis.

Results: Calculated vertebral loads and muscle activation overall stood in close correlation with data from the literature. Compression forces normalized to upright standing deviated by a maximum of 16% for flexion and 33% for lifting tasks. Interindividual comparison of compression, as well as lateral and anterior–posterior shear forces, could be linked plausibly to individual spinal alignment and bodyweight.

Conclusion: We developed a method to generate patient-specific musculoskeletal models of the lumbar spine. The models were able to calculate loads of the lumbar spine for static activities with respect to individual biomechanical properties, such as spinal alignment, bodyweight distribution, and ligament and muscle insertion points. The process is automated to a large extent, which makes it suitable for systematic investigation of spinal biomechanics in large datasets.

An EMG-Based Constitutive Law for Force Generation in Skeletal Muscle - Part I: Model Development

PURPOSE

This paper proposes a new method for estimating skeletal muscle forces using a model derived from dimensional analysis. It incorporates electromyography signals and muscle force-length, force-velocity, and force frequency relationships as inputs. The purpose of this model is to provide more accurate estimates of individualized muscle forces to better predict surrounding musculoskeletal tissue and joint contact loading.

THEORY

The derivation begins with dimensional analysis and a selection of critical parameters that define muscle force generation. The resulting constitutive equation gives way to a unique application of inverse-dynamics, one which avoids the issue of indeterminacy when reaction moments and ligament loading are minimized in a joint. The ankle joint is used as an example for developing the equations that culminate into a system of linear equations.

DISCUSSION

A muscle force model capable of being calibrated and then used to predict joint contact and surrounding tissue loading is critical in advancing biomechanics research areas like injury prevention, performance optimization, and tissue engineering, among others. This model's foundation in dimensional analysis, along with its inclusion of electromyography signals, gives promise that it will be physiologically relevant and suitable for application-based studies.

A novel in vivo approach to assess strains of the human abdominal wall under known intraabdominal pressure

The study concerns mechanical behaviour of a living human abdominal wall. A better mechanical understanding of a human abdominal wall and recognition of its material properties is required to find mechanically compatible surgical meshes to significantly improve the treatment of ventral hernias. A non-invasive methodology, based on in vivo optical measurements is proposed to determine strains of abdominal wall corresponding to a known intraabdominal pressure. The measurement is performed in the course of a standard procedure of peritoneal dialysis. A dedicated experimental stand is designed for the experiment. The photogrammetric technique is employed to recover the three-dimensional surface geometry of the anterior abdominal wall at the initial and terminal instants of the dialysis. This corresponds to two deformation states, before and after filling the abdominal cavity with dialysis fluid. The study provides information on strain fields of living human abdominal wall. The inquiry is aimed at principal strains and their directions, observed at the level from -10% to 17%. The intraabdominal pressure related to the amount of introduced dialysis fluid measured within the medical procedure covers the range 11-18.5 cmH₂O. The methodology leads to the deformation state of the abdominal wall according to the corresponding loading conditions. Therefore, the study is a step towards an identification of mechanical properties of living human abdominal wall.

The impact of anatomical uncertainties on the predictions of a musculoskeletal hand model - a sensitivity study

Outputs of musculoskeletal models should be considered probabilistic rather than deterministic as they are affected by inaccuracies and estimations associated with the development of the model. One of these uncertainties being critical for modeling arises from the determination of the muscles' line of action and the physiological cross-sectional area. Therefore, the aim of this study was to evaluate the outcome sensitivity of model predictions from a musculoskeletal hand model in comparison to the uncertainty of these input parameters. For this purpose, the kinematics and muscle activities of different hand movements (abduction of the fingers, abduction of the thumb, and flexion of the thumb) were recorded. One thousand simulations were calculated for each movement using the Latin hypercube sampling method with a corresponding variation of the muscle origin/insertion points and the cross-sectional area. Comparing the standard hand to simulations incorporating uncertainties of input parameters shows no major deviations in on- and off-set time point of muscle activities. About 60% of simulations are located within a ± 30% interval around the standard model concerning joint reaction forces. The comparison with the variation of the input data leads to the conclusion that the standard hand model is able to provide not over-scattered outcomes and, therefore, can be considered relatively stable. These results are of practical importance to the personalization of a musculoskeletal model with subject-specific bone geometries and hence changed muscle line of action.

Analyzing Uncertainty of an Ankle Joint Model with Genetic Algorithm

Recent studies in biomechanical modeling suggest a paradigm shift, in which the parameters of biomechanical models would no longer treated as fixed values but as random variables with, often unknown, distributions. In turn, novel and efficient numerical methods will be required to handle such complicated modeling problems. The main aim of this study was to introduce and verify genetic algorithm for analyzing uncertainty in biomechanical modeling. The idea of the method was to encode two adversarial models within one decision variable vector. These structures would then be concurrently optimized with the objective being the maximization of the difference between their outputs. The approach, albeit expensive numerically, offered a general formulation of the uncertainty analysis, which did not constrain the search space. The second aim of the study was to apply the proposed procedure to analyze the uncertainty of an ankle joint model with 43 parameters and flexible links. The bounds on geometrical and material parameters of the model were set to 0.50 mm and 5.00% respectively. The results obtained from the analysis were unexpected. The two obtained adversarial structures were almost visually indistinguishable and differed up to 38.52% in their angular displacements.

Finite element models of the human shoulder complex: a review of their clinical implications and modelling techniques

The human shoulder is a complicated musculoskeletal structure and is a perfect compromise between mobility and stability. The objective of this paper is to provide a thorough review of previous finite element (FE) studies in biomechanics of the human shoulder complex. Those FE studies to investigate shoulder biomechanics have been reviewed according to the physiological and clinical problems addressed: glenohumeral joint stability, rotator cuff tears, joint capsular and labral defects and shoulder arthroplasty. The major findings, limitations, potential clinical applications and modelling techniques of those FE studies are critically discussed. The main challenges faced in order to accurately represent the realistic physiological functions of the shoulder mechanism in FE simulations involve (1) subject-specific representation of the anisotropic nonhomogeneous material properties of the shoulder tissues in both healthy and pathological conditions; (2) definition of boundary and loading conditions based on individualised physiological data; (3) more comprehensive modelling describing the whole shoulder complex including appropriate three-dimensional (3D) representation of all major shoulder hard tissues and soft tissues and their delicate interactions; (4) rigorous in vivo experimental validation of FE simulation results. Fully validated shoulder FE models would greatly enhance our understanding of the aetiology of shoulder disorders, and hence facilitate the development of more efficient clinical diagnoses, non-surgical and surgical treatments, as well as shoulder orthotics and prosthetics. © 2016 The Authors. International Journal for Numerical Methods in Biomedical Engineering published by John Wiley & Sons Ltd.

A Computational Efficient Method to Assess the Sensitivity of Finite-Element Models: An Illustration With the Hemipelvis

Assessing the sensitivity of a finite-element (FE) model to uncertainties in geometric parameters and material properties is a fundamental step in understanding the reliability of model predictions. However, the computational cost of individual simulations and the large number of required models limits comprehensive quantification of model sensitivity. To quickly assess the sensitivity of an FE model, we built linear and Kriging surrogate models of an FE model of the intact hemipelvis. The percentage of the total sum of squares (%TSS) was used to determine the most influential input parameters and their possible interactions on the median, 95th percentile and maximum equivalent strains. We assessed the surrogate models by comparing their predictions to those of a full factorial design of FE simulations. The Kriging surrogate model accurately predicted all output metrics based on a training set of 30 analyses (R2 = 0.99). There was good agreement between the Kriging surrogate model and the full factorial design in determining the most influential input parameters and interactions. For the median, 95th percentile and maximum equivalent strain, the bone geometry (60%, 52%, and 76%, respectively) was the most influential input parameter. The interactions between bone geometry and cancellous bone modulus (13%) and bone geometry and cortical bone thickness (7%) were also influential terms on the output metrics. This study demonstrates a method with a low time and computational cost to quantify the sensitivity of an FE model. It can be applied to FE models in computational orthopaedic biomechanics in order to understand the reliability of predictions.

The generic modeling fallacy: Average biomechanical models often produce non-average results!

Computational biomechanics models constructed using nominal or average input parameters are often assumed to produce average results that are representative of a target population of interest. To investigate this assumption a stochastic Monte Carlo analysis of two common biomechanical models was conducted. Consistent discrepancies were found between the behavior of average models and the average behavior of the population from which the average models׳ input parameters were derived. More interestingly, broadly distributed sets of non-average input parameters were found to produce average or near average model behaviors. In other words, average models did not produce average results, and models that did produce average results possessed non-average input parameters. These findings have implications on the prevalent practice of employing average input parameters in computational models. To facilitate further discussion on the topic, the authors have termed this phenomenon the "Generic Modeling Fallacy". The mathematical explanation of the Generic Modeling Fallacy is presented and suggestions for avoiding it are provided. Analytical and empirical examples of the Generic Modeling Fallacy are also given.

Structural and material properties of human foot tendons

BACKGROUNDS

The aim of this study was to assess the mechanical properties of the main balance tendons of the human foot in vitro reporting mechanical structural properties and mechanical material properties separately. Tendon structural properties are relevant for clinical applications, for example in orthopedic surgery to elect suitable replacements. Tendon material properties are important for engineering applications such as the development of refined constitutive models for computational simulation or in the design of synthetic materials.

METHODS

One hundred uniaxial tensile tests were performed to obtain the mechanical response of the main intrinsic and extrinsic human foot tendons. The specimens were harvested from five frozen cadaver feet including: Extensor and Flexor tendons of all toes, Tibialis Anterior and Posterior tendons and Peroneus Brevis and Longus tendons.

FINDINGS

Cross-sectional area, load and strain failure, Young's modulus and ultimate tensile stress are reported as a reference of foot tendon mechanical properties. Two different behaviors could be differentiated. Tibialis and Peroneus tendons exhibited higher values of strain failure compared to Flexor and Extensor tendons which had higher Young's modulus and ultimate tensile stress. Stress-strain tendon curves exhibited proportionality between regions. The initial strain, the toe region and the yield point corresponded to the 15, 30 and 70% of the strain failure respectively.

INTERPRETATION

Mechanical properties of the lesser-studied human foot tendons are presented under the same test protocol for different engineering and clinical applications. The tendons that work at the inversion/eversion plane are more deformable at the same stress and strain rate than those that work at the flexion/extension plane.

Comprehensive, Population-Based Sensitivity Analysis of a Two-Mass Vocal Fold Model

Previous vocal fold modeling studies have generally focused on generating detailed data regarding a narrow subset of possible model configurations. These studies can be interpreted to be the investigation of a single subject under one or more vocal conditions. In this study, a broad population-based sensitivity analysis is employed to examine the behavior of a virtual population of subjects and to identify trends between virtual individuals as opposed to investigating a single subject or model instance. Four different sensitivity analysis techniques were used in accomplishing this task. Influential relationships between model input parameters and model outputs were identified, and an exploration of the model’s parameter space was conducted. Results indicate that the behavior of the selected two-mass model is largely dominated by complex interactions, and that few input-output pairs have a consistent effect on the model. Results from the analysis can be used to increase the efficiency of optimization routines of reduced-order models used to investigate voice abnormalities. Results also demonstrate the types of challenges and difficulties to be expected when applying sensitivity analyses to more complex vocal fold models. Such challenges are discussed and recommendations are made for future studies.

The in situ mechanics of trabecular bone marrow: the potential for mechanobiological response

Bone adapts to habitual loading through mechanobiological signaling. Osteocytes are the primary mechanical sensors in bone, upregulating osteogenic factors and downregulating osteoinhibitors, and recruiting osteoclasts to resorb bone in response to microdamage accumulation. However, most of the cell populations of the bone marrow niche,which are intimately involved with bone remodeling as the source of bone osteoblast and osteoclast progenitors, are also mechanosensitive. We hypothesized that the deformation of trabecular bone would impart mechanical stress within the entrapped bone marrow consistent with mechanostimulation of the constituent cells. Detailed fluid-structure interaction models of porcine femoral trabecular bone and bone marrow were created using tetrahedral finite element meshes. The marrow was allowed to flow freely within the bone pores, while the bone was compressed to 2000 or 3000 microstrain at the apparent level.Marrow properties were parametrically varied from a constant 400 mPas to a power law rule exceeding 85 Pas. Deformation generated almost no shear stress or pressure in the marrow for the low viscosity fluid, but exceeded 5 Pa when the higher viscosity models were used. The shear stress was higher when the strain rate increased and in higher volume fraction bone. The results demonstrate that cells within the trabecular bone marrow could be mechanically stimulated by bone deformation, depending on deformation rate, bone porosity, and bone marrow properties. Since the marrow contains many mechanosensitive cells, changes in the stimulatory levels may explain the alterations in bone marrow morphology with aging and disease, which may in turn affect the trabecular bone mechanobiology and adaptation.

A meta-analysis of efficacy in pre-clinical human stem cell therapies for traumatic brain injury

OBJECTIVES

Evaluate the preclinical evidence for human cell therapies for the treatment of traumatic brain injury (TBI), determine behavioral effect sizes for modified and non-modified cells, and identify variables that correlate with greater effect sizes.

METHODS

A literature search identified 58 animal studies of TBI using human stem cells. Each study received a Quality Index (QI) score based on existing guidelines. Effect sizes for cell therapies were determined for the most common behavioral endpoints: Morris Water Maze (MWM) latency/correct quadrant, and modified Neurological Severity Score (mNSS).

RESULTS

50 studies reported significant behavioral and/or histological improvement. The mean effect size for MWM latency was -1.08 for non-modified cells and -3.35 for modified cells. The mean effect size for MWM percent time in the correct quadrant was 1.66 for non-modified cells and 4.36 for modified cells. The mean effect size on the mNSS was -1.56 for non-modified cells and -4.46 for modified cells. No significant associations were found between methodological variables and effect sizes other than route of administration, where intra-lesional delivery resulted in larger effect sizes than i.v. or ventricular delivery. Studies with higher QI had smaller effect sizes; studies with larger effect sizes had greater standard errors. QI was not associated with journal impact factor.

CONCLUSIONS

Although human cell therapy studies report improved behavioral outcomes in the majority of preclinical literature, the methods are too heterogeneous to facilitate direct comparisons and bias was detected. Replication and standardization are needed to identify procedural variables to yield the best results. We encourage the use of quality criteria and rigor for future studies of human cell therapy in animal models of TBI.

Preventing lodging in bioenergy crops: a biomechanical analysis of maize stalks suggests a new approach

The hypothetical ideal for maize (Zea mays) bioenergy production would be a no-waste plant: high-yielding, with silage that is easily digestible for conversion to biofuel. However, increased digestibility is typically associated with low structural strength and a propensity for lodging. The solution to this dilemma may lie in our ability to optimize maize morphology using tools from structural engineering. To investigate how material (tissue) and geometric (morphological) factors influence stalk strength, detailed structural models of the maize stalk were created using finite-element software. Model geometry was obtained from high-resolution x-ray computed tomography (CT) scans, and scan intensity information was integrated into the models to infer inhomogeneous material properties. A sensitivity analysis was performed by systematically varying material properties over broad ranges, and by modifying stalk geometry. Computational models exhibited realistic stress and deformation patterns. In agreement with natural failure patterns, maximum stresses were predicted near the node. Maximum stresses were observed to be much more sensitive to changes in dimensions of the stalk cross section than they were to changes in material properties of stalk components. The average sensitivity to geometry was found to be more than 10-fold higher than the average sensitivity to material properties. These results suggest a new strategy for the breeding and development of bioenergy maize varieties in which tissue weaknesses are counterbalanced by relatively small increases (e.g. 5%) in stalk diameter that reduce structural stresses.

Unrealistic statistics: how average constitutive coefficients can produce non-physical results

The coefficients of constitutive models are frequently averaged in order to concisely summarize the complex, nonlinear, material properties of biomedical materials. However, when dealing with nonlinear systems, average inputs (e.g. average constitutive coefficients) often fail to generate average behavior. This raises an important issue because average nonlinear constitutive coefficients of biomedical materials are commonly reported in the literature. This paper provides examples which demonstrate that average constitutive coefficients applied to nonlinear constitutive laws in the field of biomedical material characterization can fail to produce average stress-strain responses and in some cases produce non-physical responses. Results are presented from a literature survey which indicates that approximately 90% of tissue measurement studies that employ a nonlinear constitutive model report average nonlinear constitutive coefficients. We suggest that reviewers and editors of future measurement studies discourage the reporting of average nonlinear constitutive coefficients. Reporting of individual coefficient sets for each test sample should be considered and discussed as designation for a "best practice" in the field of biomedical material characterization.

Inter-individual variation in vertebral kinematics affects predictions of neck musculoskeletal models

Experimental studies have found significant variation in cervical intervertebral kinematics (IVK) among healthy subjects, but the effect of this variation on biomechanical properties, such as neck strength, has not been explored. The goal of this study was to quantify variation in model predictions of extension strength, flexion strength and gravitational demand (the ratio of gravitational load from the weight of the head to neck muscle extension strength), due to inter-subject variation in IVK. IVK were measured from sagittal radiographs of 24 subjects (14F, 10M) in five postures: maximal extension, mid-extension, neutral, mid-flexion, and maximal flexion. IVK were defined by the position (anterior-posterior and superior-inferior) of each cervical vertebra with respect to T1 and its angle with respect to horizontal, and fit with a cubic polynomial over the range of motion. The IVK of each subject were scaled and incorporated into musculoskeletal models to create models that were identical in muscle force- and moment-generating properties but had subject-specific kinematics. The effect of inter-subject variation in IVK was quantified using the coefficient of variation (COV), the ratio of the standard deviation to the mean. COV of extension strength ranged from 8% to 15% over the range of motion, but COV of flexion strength was 20-80%. Moreover, the COV of gravitational demand was 80-90%, because the gravitational demand is affected by head position as well as neck strength. These results indicate that including inter-individual variation in models is important for evaluating neck musculoskeletal biomechanical properties.