Multiscale modeling methods in biomechanics

Cortical signals analysis to recognize intralimb mobility using modified RNN and various EEG quantities

Electroencephalogram (EEG) signals are critical in interpreting sensorimotor activities for predicting body movements. However, their efficacy in identifying intralimb movements, such as the dorsiflexion and plantar flexion of the foot, remains suboptimal. This study aims to explore whether various EEG signal quantities can effectively recognize intralimb movements to facilitate the development of Brain-Computer Interface (BCI) devices for foot rehabilitation. This research involved twenty-two healthy, right-handed participants. EEG data were collected using 21 electrodes positioned over the motor cortex, while two electromyography (EMG) electrodes recorded the onset of ankle joint movements. The study focused on analyzing slow cortical potential (SCP) and sensorimotor rhythms (SMR) in alpha and beta bands from the EEG. Five key features-fourth-order Autoregressive feature, variance, waveform length, standard deviation, and permutation entropy-were extracted. A modified Recurrent Neural Network (RNN) including Long Short-term Memory (LSTM) and Gated Recurrent Unit (GRU) algorithms was developed for movement recognition. These were compared against conventional machine learning algorithms, including nonlinear Support Vector Machine (SVM) and k Nearest Neighbourhood (kNN) classifiers. The performance of the proposed models was assessed using two data schemes: within-subject and across-subjects. The findings demonstrated that the GRU and LSTM models significantly outperformed traditional machine learning algorithms in recognizing different EEG signal quantities for intralimb movement. The study indicates that deep learning models, particularly GRU and LSTM, hold superior potential over standard machine learning techniques in identifying intralimb movements using EEG signals. Where the accuracies of LSTM for within and across subjects were 98.87 ± 1.80 % and 87.38 ± 0.86 % respectively. Whereas the accuracy of GRU within and across subjects were 99.18 ± 1.28 % and 86.44 ± 0.69 % respectively. This advancement could significantly benefit the development of BCI devices aimed at foot rehabilitation, suggesting a new avenue for enhancing physical therapy outcomes.

Multiscale modeling of skin mechanical Behavior: Effect of dehydrating agent on Collagen's mechanical properties

The dermis, second layer of human skin, is mainly responsible for mechanical response of the skin. The unique viscoelastic nature of this layer arises from the characteristic hierarchical structure of collagen at various length scales. The effect of topical formulation on skin's mechanical properties of great importance for several personal-care applications. Understanding the transport of an active ingredient across skin layer and its effects on the structure of collagen assembly is crucial for successful design of these applications. In this study, we report a multiscale modelling framework mimicking the skin's mechanical behavior. The framework captures the details from the nanoscale (tropocollagen) to microscale (fibers). At first, atomistic molecular dynamics simulations (MDS) of tropocollagen (TC) molecules of various lengths (∼100 nm) were performed to obtain the molecular modulus of TC. The stress-strain response data obtained from these simulations, were utilized in macroscopic models of fibrils and fibers. The modulus obtained from the mentioned framework was in good agreement with earlier reported experimental data. Further, we have utilized this framework to show the effect of dehydrating agent on skin's mechanical response. The hydration effect is utilized in many anti-ageing strategies to improve the overall mechanical property of skin. We showed that on incorporation of hydrating agent, the collagen structure changes significantly at molecular scale which effects the overall response of the skin at macroscopic scale. The reported multiscale framework can further be explored to gain insights into interlinked properties of collagen at much larger scales without extensive molecular simulations and detailed experiments.

Integration of Heterogeneous Biological Data in Multiscale Mechanistic Model Calibration: Application to Lung Adenocarcinoma

Mechanistic models are built using knowledge as the primary information source, with well-established biological and physical laws determining the causal relationships within the model. Once the causal structure of the model is determined, parameters must be defined in order to accurately reproduce relevant data. Determining parameters and their values is particularly challenging in the case of models of pathophysiology, for which data for calibration is sparse. Multiple data sources might be required, and data may not be in a uniform or desirable format. We describe a calibration strategy to address the challenges of scarcity and heterogeneity of calibration data. Our strategy focuses on parameters whose initial values cannot be easily derived from the literature, and our goal is to determine the values of these parameters via calibration with constraints set by relevant data. When combined with a covariance matrix adaptation evolution strategy (CMA-ES), this step-by-step approach can be applied to a wide range of biological models. We describe a stepwise, integrative and iterative approach to multiscale mechanistic model calibration, and provide an example of calibrating a pathophysiological lung adenocarcinoma model. Using the approach described here we illustrate the successful calibration of a complex knowledge-based mechanistic model using only the limited heterogeneous datasets publicly available in the literature.

Scientific and regulatory evaluation of mechanistic in silico drug and disease models in drug development: Building model credibility

The value of in silico methods in drug development and evaluation has been demonstrated repeatedly and convincingly. While their benefits are now unanimously recognized, international standards for their evaluation, accepted by all stakeholders involved, are still to be established. In this white paper, we propose a risk‐informed evaluation framework for mechanistic model credibility evaluation. To properly frame the proposed verification and validation activities, concepts such as context of use, regulatory impact and risk‐based analysis are discussed. To ensure common understanding between all stakeholders, an overview is provided of relevant in silico terminology used throughout this paper. To illustrate the feasibility of the proposed approach, we have applied it to three real case examples in the context of drug development, using a credibility matrix currently being tested as a quick‐start tool by regulators. Altogether, this white paper provides a practical approach to model evaluation, applicable in both scientific and regulatory evaluation contexts.

A systematic approach to the scale separation problem in the development of multiscale models

Throughout engineering there are problems where it is required to predict a quantity based on the measurement of another, but where the two quantities possess characteristic variations over vastly different ranges of time and space. Among the many challenges posed by such 'multiscale' problems, that of defining a 'scale' remains poorly addressed. This fundamental problem has led to much confusion in the field of biomedical engineering in particular. The present study proposes a definition of scale based on measurement limitations of existing instruments, available computational power, and on the ranges of time and space over which quantities of interest vary characteristically. The definition is used to construct a multiscale modelling methodology from start to finish, beginning with a description of the system (portion of reality of interest) and ending with an algorithmic orchestration of mathematical models at different scales within the system. The methodology is illustrated for a specific but well-researched problem. The concept of scale and the multiscale modelling approach introduced are shown to be easily adaptable to other closely related problems. Although out of the scope of this paper, we believe that the proposed methodology can be applied widely throughout engineering.

Credibility of In Silico Trial Technologies-A Theoretical Framing

Different research communities have developed various approaches to assess the credibility of predictive models. Each approach usually works well for a specific type of model, and under some epistemic conditions that are normally satisfied within that specific research domain. Some regulatory agencies recently started to consider evidences of safety and efficacy on new medical products obtained using computer modelling and simulation (which is referred to as In Silico Trials); this has raised the attention in the computational medicine research community on the regulatory science aspects of this emerging discipline. But this poses a foundational problem: in the domain of biomedical research the use of computer modelling is relatively recent, without a widely accepted epistemic framing for model credibility. Also, because of the inherent complexity of living organisms, biomedical modellers tend to use a variety of modelling methods, sometimes mixing them in the solution of a single problem. In such context merely adopting credibility approaches developed within other research communities might not be appropriate. In this paper we propose a theoretical framing for assessing the credibility of a predictive models for In Silico Trials, which accounts for the epistemic specificity of this research field and is general enough to be used for different type of models.

On fibre dispersion modelling of soft biological tissues: a review

Collagen fibres within fibrous soft biological tissues such as artery walls, cartilage, myocardiums, corneas and heart valves are responsible for their anisotropic mechanical behaviour. It has recently been recognized that the dispersed orientation of these fibres has a significant effect on the mechanical response of the tissues. Modelling of the dispersed structure is important for the prediction of the stress and deformation characteristics in (patho)physiological tissues under various loading conditions. This paper provides a timely and critical review of the continuum modelling of fibre dispersion, specifically, the angular integration and the generalized structure tensor models. The models are used in representative numerical examples to fit sets of experimental data that have been obtained from mechanical tests and fibre structural information from second-harmonic imaging. In particular, patches of healthy and diseased aortic tissues are investigated, and it is shown that the predictions of the models fit very well with the data. It is straightforward to use the models described herein within a finite-element framework, which will enable more realistic (and clinically relevant) boundary-value problems to be solved. This also provides a basis for further developments of material models and points to the need for additional mechanical and microstructural data that can inform further advances in the material modelling.

Modelling the role of redox-related mechanisms in musculoskeletal ageing

The decline in the musculoskeletal system with age is driven at the cellular level by random molecular damage. Cells possess mechanisms to repair or remove damage and many of the pathways involved in this response are regulated by redox signals. However, with ageing there is an increase in oxidative stress which can lead to chronic inflammation and disruption of redox signalling pathways. The complexity of the processes involved has led to the use of computational modelling to help increase our understanding of the system, test hypotheses and make testable predictions. This paper will give a brief background of the biological systems that have been modelled, an introduction to computational modelling, a review of models that involve redox-related mechanisms that are applicable to musculoskeletal ageing, and finally a discussion of the future potential for modelling in this field.

A multiscale model to predict current absolute risk of femoral fracture in a postmenopausal population

Osteoporotic hip fractures are a major healthcare problem. Fall severity and bone strength are important risk factors of hip fracture. This study aims to obtain a mechanistic explanation for fracture risk in dependence of these risk factors. A novel modelling approach is developed that combines models at different scales to overcome the challenge of a large space–time domain of interest and considers the variability of impact forces between potential falls in a subject. The multiscale model and its component models are verified with respect to numerical approximations made therein, the propagation of measurement uncertainties of model inputs is quantified, and model predictions are validated against experimental and clinical data. The main results are model predicted absolute risk of current fracture (ARF0) that ranged from 1.93 to 81.6% (median 36.1%) for subjects in a retrospective cohort of 98 postmenopausal British women (49 fracture cases and 49 controls); ARF0 was computed up to a precision of 1.92 percentage points (pp) due to numerical approximations made in the model; ARF0 possessed an uncertainty of 4.00 pp due to uncertainties in measuring model inputs; ARF0 classified observed fracture status in the above cohort with AUC = 0.852 (95% CI 0.753–0.918), 77.6% specificity (95% CI 63.4–86.5%) and 81.6% sensitivity (95% CI 68.3–91.1%). These results demonstrate that ARF0 can be computed using the model with sufficient precision to distinguish between subjects and that the novel mechanism of fracture risk determination based on fall dynamics, hip impact and bone strength can be considered validated.