Is the time right for a new initiative in mathematical modeling of the lower urinary tract? ICI-RS 2023

INTRODUCTION

A session at the 2023 International Consultation on Incontinence - Research Society (ICI-RS) held in Bristol, UK, focused on the question: Is the time right for a new initiative in mathematical modeling of the lower urinary tract (LUT)? The LUT is a complex system, comprising various synergetic components (i.e., bladder, urethra, neural control), each with its own dynamic functioning and high interindividual variability. This has led to a variety of different types of models for different purposes, each with advantages and disadvantages.

METHODS

When addressing the LUT, the modeling approach should be selected and sized according to the specific purpose, the targeted level of detail, and the available computational resources. Four areas were selected as examples to discuss: utility of nomograms in clinical use, value of fluid mechanical modeling, applications of models to simplify urodynamics, and utility of statistical models.

RESULTS

A brief literature review is provided along with discussion of the merits of different types of models for different applications. Remaining research questions are provided.

CONCLUSIONS

Inadequacies in current (outdated) models of the LUT as well as recent advances in computing power (e.g., quantum computing) and methods (e.g., artificial intelligence/machine learning), would dictate that the answer is an emphatic "Yes, the time is right for a new initiative in mathematical modeling of the LUT."

Modeling of the PHEMA-gelatin scaffold enriched with graphene oxide utilizing finite element method for bone tissue engineering

The development of computer-aided facilities has contributed to the optimization of tissue engineering techniques due to the reduction in necessary practical assessments and the removal of animal or human-related ethical issues. Herein, a bone scaffold based on poly (2-hydroxyethyl methacrylate) (PHEMA), gelatin and graphene oxide (GO), was simulated by SOLIDWORKS and ABAQUS under a normal compression force using finite element method (FEM). Concerning the mechanotransduction impact, GO could support the stability of the structure and reduce the possibility of the failure resulting in the integrity and durability of the scaffold efficiency which would be beneficial for osteogenic differentiation.

Generic Cutting Force Modeling with Comprehensively Considering Tool Edge Radius, Tool Flank Wear and Tool Runout in Micro-End Milling

Accurate cutting force prediction is crucial in improving machining precision and surface quality in the micro-milling process, in which tool wear and runout are essential factors. A generic analytic cutting force model considering the effect of tool edge radius on tool flank wear and tool runout in the micro-end milling process is proposed. Based on the analytic modeling of the cutting part of the cutting edge in the end face of the micro-end mill bottom, the actual radius model of the worn tool is established, considering the tool edge radius and tool flank wear. The tool edge radius, tool wear, tool runout, trochoidal trajectories of the current cutting edge, and all cutting edges in the previous cycle are comprehensively considered in the instantaneous uncut chip thickness calculation and the cutter-workpiece engagement determination. The cutting force coefficient model including tool wear is established. A series of milling experiments are performed to verify the accuracy and effectiveness of the proposed cutting force model. The results show that the predicted cutting forces are in good agreement with the experimental cutting forces, and it is necessary to consider tool wear in the micro-milling force modeling. The results indicate that tool wear has a significant influence on the cutting forces and cutting force coefficients in the three directions, and the influences of tool wear on the axial cutting force and axial force coefficient are the largest, respectively. The proposed cutting force model can contribute to real-time machining process monitoring, cutting parameters optimization and ensuring machining quality.

Mechanical limitation of bacterial motility mediated by growing cell chains

Contrasting most known bacterial motility mechanisms, a bacterial sliding motility discovered in at least two Gram-positive bacterial families does not depend on designated motors. Instead, the cells maintain end-to-end connections following cell divisions to form long chains and exploit cell growth and division to push the cells forward. To investigate the dynamics of this motility mechanism, we constructed a mechanical model that depicts the interplay of the forces acting on and between the cells comprising the chain. Due to the exponential growth of individual cells, the tips of the chains can, in principle, accelerate to speeds faster than any known single-cell motility mechanism can achieve. However, analysis of the mechanical model shows that the exponential acceleration comes at the cost of an exponential buildup in mechanical stress in the chain, making overly long chains prone to breakage. Additionally, the mechanical model reveals that the dynamics of the chain expansion hinges on a single non-dimensional parameter. Perturbation analysis of the mechanical model further predicts the critical stress leading to chain breakage and its dependence on the non-dimensional parameter. Finally, we developed a simplistic population expansion model that uses the predicted breaking behavior to estimate the physical limit of chain-mediated population expansion. Predictions from the models provide critical insights into how this motility depends on key physical properties of the cell and the substrate. Overall, our models present a generically applicable theoretical framework for cell chain-mediated bacterial sliding motility and provide guidance for future experimental studies on such motility.

Theoretical Model of Bending Moment for Straight Mortise-and-Tenon Joints with Wooden Pegs Involving a Gap

The stress mechanism of a straight mortise-and-tenon joint with wooden pegs in traditional residential wooden structures was analyzed, and a theoretical moment-rotation model of the joint was derived. To verify the model, three full-scale joint specimens were fabricated and subjected to low-cycle reversed loading tests. All specimens showed tensile cracking parallel to the grain at the top or bottom of the tenon neck. The theoretical calculation results are consistent with the experimental results. The results of the parametric analysis based on the theoretical model show the following: the rotational stiffness and bending moment of the joint increase as the beam width increases; as the beam height increases, the moment increases, but the initial stiffness of the joint is only slightly impacted; as the column diameter increases, the initial stiffness and moment increase, and the free rotation of the joint decreases; as the gap between the mortise and tenon increases, the initial stiffness and moment decrease; as the sliding friction coefficient increases, both the rotational stiffness and moment of the joint increase, and the increase is greater after the joint yields than before.

Mechanical Properties of Nanoporous Metallic Ultrathin Films: A Paradigmatic Case

Nanoporous ultrathin films, constituted by a slab less than 100 nm thick and a certain void volume fraction provided by nanopores, are emerging as a new class of systems with a wide range of possible applications, including electrochemistry, energy storage, gas sensing and supercapacitors. The film porosity and morphology strongly affect nanoporous films mechanical properties, the knowledge of which is fundamental for designing films for specific applications. To unveil the relationships among the morphology, structure and mechanical response, a comprehensive and non-destructive investigation of a model system was sought. In this review, we examined the paradigmatic case of a nanoporous, granular, metallic ultrathin film with comprehensive bottom-up and top-down approaches, both experimentals and theoreticals. The granular film was made of Ag nanoparticles deposited by gas-phase synthesis, thus providing a solvent-free and ultrapure nanoporous system at room temperature. The results, bearing generality beyond the specific model system, are discussed for several applications specific to the morphological and mechanical properties of the investigated films, including bendable electronics, membrane separation and nanofluidic sensing.

Analytical Compliance Equations of Generalized Elliptical-Arc-Beam Spherical Flexure Hinges for 3D Elliptical Vibration-Assisted Cutting Mechanisms

Elliptical vibration-assisted cutting technology has been widely applied in complicated functional micro-structured surface texturing. Elliptical-arc-beam spherical flexure hinges have promising applications in the design of 3D elliptical vibration-assisted cutting mechanisms due to their high motion accuracy and large motion ranges. Analytical compliance matrix formulation of flexure hinges is the basis for achieving high-precision positioning performance of these mechanisms, but few studies focus on this topic. In this paper, analytical compliance equations of spatial elliptic-arc-beam spherical flexure hinges are derived, offering a convenient tool for analysis at early stages of mechanism design. The mechanical model of a generalized flexure hinge is firstly established based on Castigliano's Second Theorem. By introducing the eccentric angle as the integral variable, the compliance matrix of the elliptical-arc-beam spherical flexure hinge is formulated. Finite element analysis is carried out to verify the accuracy of the derived analytical compliance matrix. The compliance factors calculated by the analytical equations agree well with those solved in the finite element analysis for the maximum error; average relative error and relative standard deviation are 8.25%, 1.83% and 1.78%, respectively. This work lays the foundations for the design and modeling of 3D elliptical vibration-assisted cutting mechanisms based on elliptical-arc-beam spherical flexure hinges.

Development of a Material Design Space for 4D-Printed Bio-Inspired Hygroscopically Actuated Bilayer Structures with Unequal Effective Layer Widths

(1) Significance of geometry for bio-inspired hygroscopically actuated bilayer structures is well studied and can be used to fine-tune curvatures in many existent material systems. We developed a material design space to find new material combinations that takes into account unequal effective widths of the layers, as commonly used in fused filament fabrication, and deflections under self-weight. (2) For this purpose, we adapted Timoshenko’s model for the curvature of bilayer strips and used an established hygromorphic 4D-printed bilayer system to validate its ability to predict curvatures in various experiments. (3) The combination of curvature evaluation with simple, linear beam deflection calculations leads to an analytical solution space to study influences of Young’s moduli, swelling strains and densities on deflection under self-weight and curvature under hygroscopic swelling. It shows that the choice of the ratio of Young’s moduli can be crucial for achieving a solution that is stable against production errors. (4) Under the assumption of linear material behavior, the presented development of a material design space allows selection or design of a suited material combination for application-specific, bio-inspired bilayer systems with unequal layer widths.

Soft Skin Layers Enable Area-Specific, Multiscale Graphene Wrinkles with Switchable Orientations

This paper reports a method to realize crack-free graphene wrinkles with variable spatial wavelengths and switchable orientations. Graphene supported on a thin fluoropolymer and prestrained elastomer substrate can exhibit conformal wrinkling after strain relief. The wrinkle orientation could be switched beyond the intrinsic fracture limit of graphene for hundreds of cycles of stretching and releasing without forming cracks. Mechanical modeling revealed that the fluoropolymer layer mediated the structural evolution of the graphene wrinkles without crack formation or delamination. Patterned fluoropolymer layers with different thicknesses produced wrinkles with controlled wavelengths and orientations while maintaining the mechanical integrity of graphene under high tensile strain.

Methods to quantify primary plant cell wall mechanics

The primary plant cell wall is a dynamically regulated composite material of multiple biopolymers that forms a scaffold enclosing the plant cells. The mechanochemical make-up of this polymer network regulates growth, morphogenesis, and stability at the cell and tissue scales. To understand the dynamics of cell wall mechanics, and how it correlates with cellular activities, several experimental frameworks have been deployed in recent years to quantify the mechanical properties of plant cells and tissues. Here we critically review the application of biomechanical tool sets pertinent to plant cell mechanics and outline some of their findings, relevance, and limitations. We also discuss methods that are less explored but hold great potential for the field, including multiscale in silico mechanical modeling that will enable a unified understanding of the mechanical behavior across the scales. Our overview reveals significant differences between the results of different mechanical testing techniques on plant material. Specifically, indentation techniques seem to consistently report lower values compared with tensile tests. Such differences may in part be due to inherent differences among the technical approaches and consequently the wall properties that they measure, and partly due to differences between experimental conditions.

Optical Properties and Mechanical Modeling of Acetylated Transparent Wood Composite Laminates

Transparent wood composites (TWCs) are a new class of light-transmitting wood-based materials composed of a delignified wood template that is infiltrated with a refractive- index-matched polymer resin. Recent research has focused primarily on the fabrication and characterization of single-ply TWCs. However, multi-ply composite laminates are of interest due to the mechanical advantages they impart compared to the single ply. In this work, 1- and 2-ply [0°/90°] TWC laminates were fabricated using a delignified wood template (C) and an acetylated delignified wood template (AC). The optical and mechanical properties of resultant C and AC TWC laminates were determined using ultraviolet-visible spectroscopy (UV-Vis) and tensile testing (5× replicates), respectively. In addition, the ability of classical lamination plate theory and simple rule of mixtures to predict multi-ply tensile modulus and strength, respectively, from ply-level mechanical properties were investigated and are reported herein. Experimental results highlight tradeoffs that exist between the mechanical and optical responses of both unmodified and chemically modified TWCs. Template acetylation reduced the stiffness and strength in the 0° fiber direction by 2.4 GPa and 58.9 MPa, respectively, compared to the unmodified samples. At high wavelengths of light (>515 nm), AC samples exhibited higher transmittance than the C samples. Above 687 nm, the 2-ply AC sample exhibited a higher transmittance than the 1-ply C sample, indicating that thickness-dependent optical constraints can be overcome with improved interfacial interactions. Finally, both predictive models were successful in predicting the elastic modulus and tensile strength response for the 2-ply C and AC samples.

Skeletal Muscle Adaptations and Passive Muscle Stiffness in Cerebral Palsy: A Literature Review and Conceptual Model

This literature review focuses on the primary morphological and structural characteristics, and mechanical properties identified in muscles affected by spastic cerebral palsy (CP). CP is a non-progressive neurological disorder caused by brain damage and is commonly diagnosed at birth. Although the brain damage is not progressive, subsequent neuro-physiological developmental adaptations may initiate changes in muscle structure, function, and composition, causing abnormal muscle activity and coordination. The symptoms of CP vary among patients. However, muscle spasticity is commonly present and is one of the most debilitating effects of CP. Here, we present the current knowledge regarding the mechanical properties of skeletal tissue affected by spastic CP. An increase in sarcomere length, collagen content, and fascicle diameter, and a reduction in the number of satellite cells within spastic CP muscle were consistent findings in the literature. Studies differed, however, in changes in fascicle lengths and fiber diameters. We also present a conceptual mechanical model of fascicle force transmission that incorporates mechanisms that impact both serial and lateral force production, highlighting the connections between the macro and micro structures of muscle to assist in deducing specific mechanisms for property changes and reduced force production.

Advanced and Rationalized Atomic Force Microscopy Analysis Unveils Specific Properties of Controlled Cell Mechanics

The cell biomechanical properties play a key role in the determination of the changes during the essential cellular functions, such as contraction, growth, and migration. Recent advances in nano-technologies have enabled the development of new experimental and modeling approaches to study cell biomechanics, with a level of insights and reliability that were not possible in the past. The use of atomic force microscopy (AFM) for force spectroscopy allows nanoscale mapping of the cell topography and mechanical properties under, nearly physiological conditions. A proper evaluation process of such data is an essential factor to obtain accurate values of the cell elastic properties (primarily Young's modulus). Several numerical models were published in the literature, describing the depth sensing indentation as interaction process between the elastic surface and indenting probe. However, many studies are still relying on the nowadays outdated Hertzian model from the nineteenth century, or its modification by Sneddon. The lack of comparison between the Hertz/Sneddon model with their modern modifications blocks the development of advanced analysis software and further progress of AFM promising technology into biological sciences. In this work, we applied a rationalized use of mechanical models for advanced postprocessing and interpretation of AFM data. We investigated the effect of the mechanical model choice on the final evaluation of cellular elasticity. We then selected samples subjected to different physicochemical modulators, to show how a critical use of AFM data handling can provide more information than simple elastic modulus estimation. Our contribution is intended as a methodological discussion of the limitations and benefits of AFM-based advanced mechanical analysis, to refine the quantification of cellular elastic properties and its correlation to undergoing cellular processes in vitro.

Hybrid Analytical and Data-Driven Modeling for Feed-Forward Robot Control

Feed-forward model-based control relies on models of the controlled plant, e.g., in robotics on accurate knowledge of manipulator kinematics or dynamics. However, mechanical and analytical models do not capture all aspects of a plant’s intrinsic properties and there remain unmodeled dynamics due to varying parameters, unmodeled friction or soft materials. In this context, machine learning is an alternative suitable technique to extract non-linear plant models from data. However, fully data-based models suffer from inaccuracies as well and are inefficient if they include learning of well known analytical models. This paper thus argues that feed-forward control based on hybrid models comprising an analytical model and a learned error model can significantly improve modeling accuracy. Hybrid modeling here serves the purpose to combine the best of the two modeling worlds. The hybrid modeling methodology is described and the approach is demonstrated for two typical problems in robotics, i.e., inverse kinematics control and computed torque control. The former is performed for a redundant soft robot and the latter for a rigid industrial robot with redundant degrees of freedom, where a complete analytical model is not available for any of the platforms.

Method for the quantification of rupture probability in soft collagenous tissues

A computational method is presented for the assessment of rupture probabilities in soft collagenous tissues. This may in particular be important for the quantitative analysis of medical diseases such as atherosclerotic arteries or abdominal aortic aneurysms, where an unidentified rupture has in most cases fatal consequences. The method is based on the numerical minimization and maximization of probabilities of failure, which arise from random input quantities, for example, tissue properties. Instead of assuming probability distributions for these quantities, which are typically unknown especially for soft collagenous tissues, only restricted knowledge of these distributions is taken into account. Given this limited statistical input data, the minimized/maximized probabilities represent optimal bounds on the rupture probability, which enable a quantitative estimation of potential risks of performing or not performing medical treatment. Although easily extendable to all kinds of mechanical rupture criteria, the approach presented here incorporates stretch-based and damage-based criteria. These are evaluated based on numerical simulations of loaded tissues, where continuum mechanical material formulations are considered, which capture the supra-physiological behavior of soft collagenous tissues. Numerical examples are provided demonstrating the applicability of the method in an overstretched atherosclerotic artery. Copyright © 2016 John Wiley & Sons, Ltd.

Microstructure and mechanics of human resistance arteries

Vascular diseases such as diabetes and hypertension cause changes to the vasculature that can lead to vessel stiffening and the loss of vasoactivity. The microstructural bases of these changes are not presently fully understood. We present a new methodology for stain-free visualization, at a microscopic scale, of the morphology of the main passive components of the walls of unfixed resistance arteries and their response to changes in transmural pressure. Human resistance arteries were dissected from subcutaneous fat biopsies, mounted on a perfusion myograph, and imaged at varying transmural pressures using a multimodal nonlinear microscope. High-resolution three-dimensional images of elastic fibers, collagen, and cell nuclei were constructed. The honeycomb structure of the elastic fibers comprising the internal elastic layer became visible at a transmural pressure of 30 mmHg. The adventitia, comprising wavy collagen fibers punctuated by straight elastic fibers, thinned under pressure as the collagen network straightened and pulled taut. Quantitative measurements of fiber orientation were made as a function of pressure. A multilayer analytical model was used to calculate the stiffness and stress in each layer. The adventitia was calculated to be up to 10 times as stiff as the media and experienced up to 8 times the stress, depending on lumen diameter. This work reveals that pressure-induced reorganization of fibrous proteins gives rise to very high local strain fields and highlights the unique mechanical roles of both fibrous networks. It thereby provides a basis for understanding the micromechanical significance of structural changes that occur with age and disease.

Anticipatory Postural Control of Stability during Gait Initiation Over Obstacles of Different Height and Distance Made Under Reaction-Time and Self-Initiated Instructions

Despite the abundant literature on obstacle crossing in humans, the question of how the central nervous system (CNS) controls postural stability during gait initiation with the goal to clear an obstacle remains unclear. Stabilizing features of gait initiation include anticipatory postural adjustments (APAs) and lateral swing foot placement. To answer the above question, 14 participants initiated gait as fast as possible in three conditions of obstacle height, three conditions of obstacle distance and one obstacle-free (control) condition. Each of these conditions was performed with two levels of temporal pressure: reaction-time (high-pressure) and self-initiated (low-pressure) movements. A mechanical model of the body falling laterally under the influence of gravity and submitted to an elastic restoring force is proposed to assess the effect of initial (foot-off) center-of-mass position and velocity (or “initial center-of-mass set”) on the stability at foot-contact. Results showed that the anticipatory peak of mediolateral (ML) center-of-pressure shift, the initial ML center-of-mass velocity and the duration of the swing phase, of gait initiation increased with obstacle height, but not with obstacle distance. These results suggest that ML APAs are scaled with swing duration in order to maintain an equivalent stability across experimental conditions. This statement is strengthened by the results obtained with the mechanical model, which showed how stability would be degraded if there was no adaptation of the initial center-of-mass set to swing duration. The anteroposterior (AP) component of APAs varied also according to obstacle height and distance, but in an opposite way to the ML component. Indeed, results showed that the anticipatory peak of backward center-of-pressure shift and the initial forward center-of-mass set decreased with obstacle height, probably in order to limit the risk to trip over the obstacle, while the forward center-of-mass velocity at foot-off increased with obstacle distance, allowing a further step to be taken. These effects of obstacle height and distance were globally similar under low and high-temporal pressure. Collectively, these findings imply that the CNS is able to predict the potential instability elicited by the obstacle clearance and that it scales the spatiotemporal parameters of APAs accordingly.

Integrating cell biology, image analysis, and computational mechanical modeling to analyze the contributions of cellulose and xyloglucan to stomatal function

Cell walls are likely to be essential determinants of the amazing strength and flexibility of the guard cells that surround each stomatal pore in plants, but surprisingly little is known about cell wall composition, organization, and dynamics in guard cells. Recent analyses of cell wall organization and stomatal function in the guard cells of Arabidopsis thaliana mutants with defects in cellulose and xyloglucan have allowed for the development of new hypotheses about the relative contributions of these components to guard cell function. Advanced image analysis methods can allow for the automated detection of key structures, such as microtubules (MTs) and Cellulose Synthesis Complexes (CSCs), in guard cells, to help determine their contributions to stomatal function. A major challenge in the mechanical modeling of dynamic biological structures, such as guard cell walls, is to connect nanoscale features (e.g., wall polymers and their molecular interactions) with cell-scale mechanics; this challenge can be addressed by applying multiscale computational modeling that spans multiple spatial scales and physical attributes for cell walls.

Mechanically, the Shoot Apical Meristem of Arabidopsis Behaves like a Shell Inflated by a Pressure of About 1 MPa

In plants, the shoot apical meristem contains the stem cells and is responsible for the generation of all aerial organs. Mechanistically, organogenesis is associated with an auxin-dependent local softening of the epidermis. This has been proposed to be sufficient to trigger outgrowth, because the epidermis is thought to be under tension and stiffer than internal tissues in all the aerial part of the plant. However, this has not been directly demonstrated in the shoot apical meristem. Here we tested this hypothesis in Arabidopsis using indentation methods and modeling. We considered two possible scenarios: either the epidermis does not have unique properties and the meristem behaves as a homogeneous linearly-elastic tissue, or the epidermis is under tension and the meristem exhibits the response of a shell under pressure. Large indentation depths measurements with a large tip (~size of the meristem) were consistent with a shell-like behavior. This also allowed us to deduce a value of turgor pressure, estimated at 0.82±0.16 MPa. Indentation with atomic force microscopy provided local measurements of pressure in the epidermis, further confirming the range of values obtained from large deformations. Altogether, our data demonstrate that the Arabidopsis shoot apical meristem behaves like a shell under a MPa range pressure and support a key role for the epidermis in shaping the shoot apex.