Multiscale layered biomechanical model of the pacinian corpuscle

The Impact of Differential Knee Laxity on Brain Activation During Passive Knee Joint Loading

Although higher anterior knee laxity is an established risk factor of ACL injury, underlying mechanisms are uncertain. While decreased proprioception and altered movement patterns in individuals with anterior knee laxity have been identified, the potential impact of higher laxity on brain activity is not well understood. Thus, the purpose of this study is to identify the impact of different magnitudes of knee laxity on brain function during anterior knee joint loading. Twenty-seven healthy and active female college students without any previous severe lower leg injuries volunteered for this study. Anterior knee laxity was measured using a knee arthrometer KT-2000 to assign participants to a higher laxity (N=15) or relatively lower laxity group (N=12). Functional magnetic resonance images were obtained during passive anterior knee joint loading in a task-based design using a 3T MRI scanner. Higher knee laxity individuals demonstrated diminished cortical activation in the left superior parietal lobe during passive anterior knee joint loading. Less brain activation in the regions associated with awareness of bodily movements in females with higher knee laxity may indicate a possible connection between brain activity and knee laxity. The results of this study may help researchers and clinicians develop effective rehabilitation programs for individuals with increased knee laxity. This article is protected by copyright. All rights reserved.

In silico evaluation of the mechanical stimulation effect on the regenerative rehabilitation for the articular cartilage local defects

Osteoarthritis is one of the most severe diseases of the human musculoskeletal system, and therefore, for many years, special attention has been paid to the search for effective methods of its treatment. However, even the most modern methods only in a limited number of cases in the early or intermediate stages of osteoarthritis lead to positive treatment results. In the later stages of development, osteoarthritis is practically incurable and most often ends with disability or the need for joint replacement for a large number of people. One of the main reasons hindering the development of osteoarthritis treatment methods is the peculiarities of articular cartilage, in which there is practically no vascular network and tissue homeostasis is carried out mainly due to the diffusion of nutrients present in the synovial fluid. In modern medicine, for the treatment of osteoarthritis, tissue engineering strategies have been developed based on the implantation of scaffolds populated with chondrogenic cells into the area of the defect. In vitro studies have established that these cells are highly mechanosensitive and, under the influence of mechanical stimuli of a certain type and intensity, their ability to proliferate and chondrogenesis increases. This property can be used to improve the efficiency of regenerative rehabilitation technologies based on the synergistic combination of cellular technologies, tissue engineering strategies, and mechanical tissue stimulation. In this work, using a regenerative rehabilitation mathematical model of local articular cartilage defects, numerical experiments were performed, the results of which indicate that the micro-and macro environment of the restored tissue, which changes during mechanical stimulation, has a significant effect on the formation of the extracellular matrix, and, consequently, cartilage tissue generally. The results obtained can be used to plan strategies for mechanical stimulation, based on the analysis of the results of cell proliferation experimental assessment after each stimulation procedure in vivo.

Printing a Pacinian Corpuscle: Modeling and Performance

The Pacinian corpuscle is a highly sensitive mammalian sensor cell that exhibits a unique band-pass sensitivity to vibrations. The cell achieves this band-pass response through the use of 20 to 70 elastic layers entrapping layers of viscous fluid. This paper develops and explores a scalable mechanical model of the Pacinian corpuscle and uses the model to predict the response of synthetic corpuscles, which could be the basis for future vibration sensors. The -3dB point of the biological cell is accurately mimicked using the geometries and materials available with off-the-shelf 3D printers. The artificial corpuscles here are constructed using uncured photoresist within structures printed in a commercial stereolithography (SLA) 3D printer, allowing the creation of trapped fluid layers analogous to the biological cell. Multi-layer artificial Pacinian corpuscles are vibration tested over the range of 20-3000 Hz and the response is in good agreement with the model.

Vibrotactile perception in Dupuytren disease

PURPOSE

Dupuytren disease (DD) has been associated with enlarged Pacinian corpuscles (PCs) and with PCs having a greater number of lamellae. Based on these associations, we hypothesized that subjects with DD would have altered sensitivity to high-frequency vibrations and that the changes would be more prominent at 250 Hz, where healthy subjects demonstrate the highest sensitivity.

METHODS

A novel device was created to deliver vibrations of specific frequencies and amplitudes to the fingers and palm. Using a Psi-marginal adaptive algorithm, vibrotactile perception thresholds (VPTs) were determined in 36 subjects with DD and 74 subjects without DD. Experiments were performed at 250 Hz and 500 Hz at the fingertip and palm. The VPTs were statistically analyzed with respect to disease status, age, gender, location tested, and frequency tested.

RESULTS

We found that VPT increases with age, which agrees with findings by others. Women showed greater sensitivity (i.e. lower VPT) than men. Men exhibited lower sensitivity in DD versus healthy subjects, but the results were not statistically significant. In subjects with DD presenting unilaterally, the unaffected hand was more sensitive than the affected hand, in particular for a 250 Hz stimulus applied to the finger.

CONCLUSIONS

The data on vibration sensitivity obtained from a large group of subjects with and without DD present interesting trends that may serve as a useful reference to future DD researchers. Understanding additional symptoms of DD may facilitate development of novel diagnostic or prognostic protocols.

An inter-species computational analysis of vibrotactile sensitivity in Pacinian and Herbst corpuscles

Vibration sensing is ubiquitous among vertebrates, with the sensory end organ generally being a multilayered ellipsoidal structure. There is, however, a wide range of sizes and structural arrangements across species. In this work, we applied our earlier computational model of the Pacinian corpuscle to predict the sensory response of different species to various stimulus frequencies, and based on the results, we identified the optimal frequency for vibration sensing and the bandwidth over which frequencies should be most detectable. We found that although the size and layering of the corpuscles were very different, almost all of the 19 species studied showed very similar sensitivity ranges. The human and goose were the notable exceptions, with their corpuscle tuned to higher frequencies (130-170 versus 40-50 Hz). We observed no correlation between animal size and any measure of corpuscle geometry in our model. Based on the results generated by our computational model, we hypothesize that lamellar corpuscles across different species may use different sizes and structures to achieve similar frequency detection bands.

Coding source localization through inter-spike delay: modelling a cluster of Pacinian Corpuscles using time-division multiplexing approach

The Pacinian Corpuscle (PC) is the most sensitive mechanoreceptor in the human body found in clusters of two or three. We extended our previous model of an isolated-PC to a cluster-PC focussing on relative spike delay and displacement threshold for understanding how the stimulus location is coded. In our model, two PCs with Gaussian overlapping receptive fields are arranged beneath the skin model. For a spatiotemporal stimulus (vibration), the model response is proposed to be a time-division multiplexing of responses from two PCs within the cluster. While the spike rate characteristics and pole-zero plot of cluster-PC model show similarities with the isolated-PC model, the frequency response shows ripples after 1 kHz as the distance (d) between the PCs increases. The stimulus location [Formula: see text] and d influence the relative spike delay and the displacement threshold, but not the spike rate. The novel contributions from our model include prediction of (i) relative spike delay for various d, stimulus frequency (f), and ψ, (ii) spike rate characteristics for varying f, and (iii) displacement threshold curve as a function of frequency for various d. Although the physiological validation of the novel predictions is impractical, we have validated the relative spike delay and the displacement threshold curves with experimental data in the literature.

Layered patterns in nature, medicine, and materials: quantifying anisotropic structures and cyclicity

Various natural patterns-such as terrestrial sand dune ripples, lamellae in vertebrate bones, growth increments in fish scales and corals, aortas and lamellar corpuscles in humans and animals-comprise layers of different thicknesses and lengths. Microstructures in manmade materials-such as alloys, perlite steels, polymers, ceramics, and ripples induced by laser on the surface of graphen-also exhibit layered structures. These layered patterns form a record of internal and external factors regulating pattern formation in their various systems, making it potentially possible to recognize and identify in their incremental sequences trends, periodicities, and events in the formation history of these systems. The morphology of layered systems plays a vital role in developing new materials and in biomimetic research. The structures and sizes of these two-dimensional (2D) patterns are characteristically anisotropic: That is, the number of layers and their absolute thicknesses vary significantly in different directions. The present work develops a method to quantify the morphological characteristics of 2D layered patterns that accounts for anisotropy in the object of study. To reach this goal, we use Boolean functions and an N-partite graph to formalize layer structure and thickness across a 2D plane and to construct charts of (1) "layer thickness vs. layer number" and (2) "layer area vs. layer number." We present a parameter disorder of layer structure (DStr) to describe the deviation of a study object's anisotropic structure from an isotropic analog and illustrate that charts and DStr could be used as local and global morphological characteristics describing various layered systems such as images of, for example, geological, atmospheric, medical, materials, forensic, plants, and animals. Suggested future experiments could lead to new insights into layered pattern formation.

Computational and Psychophysical Experiments on the Pacinian Corpuscle's Ability to Discriminate Complex Stimuli

Recognizing and discriminating vibrotactile stimuli is an essential function of the Pacinian corpuscle. This function has been studied at length in both a computational and an experimental setting, but the two approaches have rarely been compared, especially when the computational model has a high level of structural detail. In this paper, we explored whether the predictions of a multiscale, multiphysical computational model of the Pacinian corpuscle can predict the outcome of a corresponding psychophysical experiment. The discrimination test involved either two simple stimuli with frequency in the 160-500 Hz range, or two complex stimuli formed by combining the waveforms for a 100-Hz stimulus with a second stimulus in the 160-500 Hz range. The subjects' ability to distinguish between the simple stimuli increased as the frequency increased, a result consistent with the model predictions for the same stimuli. The model also predicted correctly that subjects would find the complex stimuli more difficult to distinguish than the simple ones and also that the discriminability of the complex stimuli would show no trend with frequency difference.

Mechanics to pre-process information for the fine tuning of mechanoreceptors

Non-nervous auxiliary structures play a significant role in sensory biology. They filter the stimulus and transform it in a way that fits the animal's needs, thereby contributing to the avoidance of the central nervous system's overload with meaningless stimuli and a corresponding processing task. The present review deals with mechanoreceptors mainly of invertebrates and some remarkable recent findings stressing the role of mechanics as an important source of sensor adaptedness, outstanding performance, and diversity. Instead of organizing the review along the types of stimulus energy (force) taken up by the sensors, processes associated with a few basic and seemingly simple mechanical principles like lever systems, viscoelasticity, resonance, traveling waves, and impedance matching are taken as the guideline. As will be seen, nature makes surprisingly competent use of such "simple mechanics".

Computational Parametric Analysis of the Mechanical Response of Structurally Varying Pacinian Corpuscles

The Pacinian corpuscle (PC) is a cutaneous mechanoreceptor that senses low-amplitude, high-frequency vibrations. The PC contains a nerve fiber surrounded by alternating layers of solid lamellae and interlamellar fluid, and this structure is hypothesized to contribute to the PC's role as a band-pass filter for vibrations. In this study, we sought to evaluate the relationship between the PC's material and geometric parameters and its response to vibration. We used a spherical finite element mechanical model based on shell theory and lubrication theory to model the PC's outer core. Specifically, we analyzed the effect of the following structural properties on the PC's frequency sensitivity: lamellar modulus (E), lamellar thickness (h), fluid viscosity (μ), PC outer radius (Ro), and number of lamellae (N). The frequency of peak strain amplification (henceforth "peak frequency") and frequency range over which strain amplification occurred (henceforth "bandwidth") increased with lamellar modulus or lamellar thickness and decreased with an increase in fluid viscosity or radius. All five structural parameters were combined into expressions for the relationship between the parameters and peak frequency, ωpeak=1.605×10-6N3.475(Eh/μRo), or bandwidth, B=1.747×10-6N3.951(Eh/μRo). Although further work is needed to understand how mechanical variability contributes to functional variability in PCs and how factors such as PC eccentricity also affect PC behavior, this study provides two simple expressions that can be used to predict the impact of structural or material changes with aging or disease on the frequency response of the PC.

Structure of the Pacinian Corpuscle: Insights Provided by Improved Mechanical Modeling

An improved model of the Pacinian corpuscle includes corrections for lamellar curvature. Results suggest that outer-zone lamellae produce a focusing effect whereby stimuli are channeled radially inwards. The requirements for this effect (large outer-surface area and thin, closely spaced lamellae) provide a rationale for the complexity of the outer-zone structure.

Micropipette aspiration of the Pacinian corpuscle

The Pacinian corpuscle (PC) is a cutaneous mechanoreceptor sensitive to high-frequency vibrations (20-1000Hz). The PC is of importance due to its integral role in somatosensation and the critical need to understand PC function for haptic feedback system development. Previous theoretical and computational studies have modeled the physiological response of the PC to sustained or vibrating mechanical stimuli, but they have used estimates of the receptor's mechanical properties, which remain largely unmeasured. In this study, we used micropipette aspiration (MPA) to determine an apparent Young's modulus for PCs isolated from a cadaveric human hand. MPA was applied in increments of 5mm H₂O (49Pa), and the change in protrusion length of the PC into the pipette was recorded. The protrusion length vs. suction pressure data were used to calculate the apparent Young's modulus. Using 10 PCs with long-axis lengths of 2.99±0.41mm and short-axis lengths of 1.45±0.22mm, we calculated a Young's modulus of 1.40±0.86kPa. Our measurement is on the same order of magnitude as those approximated in previous models, which estimated the PC to be on the same order of magnitude as skin or isolated cells, so we recommend that a modulus in the kPa range be used in future studies.

Multiscale modeling methods in biomechanics

More and more frequently, computational biomechanics deals with problems where the portion of physical reality to be modeled spans over such a large range of spatial and temporal dimensions, that it is impossible to represent it as a single space-time continuum. We are forced to consider multiple space-time continua, each representing the phenomenon of interest at a characteristic space-time scale. Multiscale models describe a complex process across multiple scales, and account for how quantities transform as we move from one scale to another. This review offers a set of definitions for this emerging field, and provides a brief summary of the most recent developments on multiscale modeling in biomechanics. Of all possible perspectives, we chose that of the modeling intent, which vastly affect the nature and the structure of each research activity. To the purpose we organized all papers reviewed in three categories: 'causal confirmation,' where multiscale models are used as materializations of the causation theories; 'predictive accuracy,' where multiscale modeling is aimed to improve the predictive accuracy; and 'determination of effect,' where multiscale modeling is used to model how a change at one scale manifests in an effect at another radically different space-time scale. Consistent with how the volume of computational biomechanics research is distributed across application targets, we extensively reviewed papers targeting the musculoskeletal and the cardiovascular systems, and covered only a few exemplary papers targeting other organ systems. The review shows a research subdomain still in its infancy, where causal confirmation papers remain the most common. WIREs Syst Biol Med 2017, 9:e1375. doi: 10.1002/wsbm.1375 For further resources related to this article, please visit the WIREs website.

Feeling force: physical and physiological principles enabling sensory mechanotransduction

Organisms as diverse as microbes, roundworms, insects, and mammals detect and respond to applied force. In animals, this ability depends on ionotropic force receptors, known as mechanoelectrical transduction (MeT) channels, that are expressed by specialized mechanoreceptor cells embedded in diverse tissues and distributed throughout the body. These cells mediate hearing, touch, and proprioception and play a crucial role in regulating organ function. Here, we attempt to integrate knowledge about the architecture of mechanoreceptor cells and their sensory organs with principles of cell mechanics, and we consider how engulfing tissues contribute to mechanical filtering. We address progress in the quest to identify the proteins that form MeT channels and to understand how these channels are gated. For clarity and convenience, we focus on sensory mechanobiology in nematodes, fruit flies, and mice. These themes are emphasized: asymmetric responses to applied forces, which may reflect anisotropy of the structure and mechanics of sensory mechanoreceptor cells, and proteins that function as MeT channels, which appear to have emerged many times through evolution.

Investigation of mechanosensation in C. elegans using light field calcium imaging

We describe a new experimental approach to investigate touch sensation in the model organism C. elegans using light field deconvolution microscopy. By combining fast volumetric image acquisition with controlled indentation of the organism using a high sensitivity force transducer, we are able to simultaneously measure activity in multiple touch receptor neurons expressing the calcium ion indicator GCaMP6s. By varying the applied mechanical stimulus we show how this method can be used to quantify touch sensitivity in C. elegans. We describe some of the challenges of performing light field calcium imaging in moving samples and demonstrate that they can be overcome by simple data processing.

A multiphysics model of the Pacinian corpuscle

This study integrates mechanics and neuroscience to model the mechanoelectrochemical transduction of vibrations into neural signals in the Pacinian corpuscle.

Multiscale Mechanical Model of the Pacinian Corpuscle Shows Depth and Anisotropy Contribute to the Receptor's Characteristic Response to Indentation

Cutaneous mechanoreceptors transduce different tactile stimuli into neural signals that produce distinct sensations of touch. The Pacinian corpuscle (PC), a cutaneous mechanoreceptor located deep within the dermis of the skin, detects high frequency vibrations that occur within its large receptive field. The PC is comprised of lamellae that surround the nerve fiber at its core. We hypothesized that a layered, anisotropic structure, embedded deep within the skin, would produce the nonlinear strain transmission and low spatial sensitivity characteristic of the PC. A multiscale finite-element model was used to model the equilibrium response of the PC to indentation. The first simulation considered an isolated PC with fiber networks aligned with the PC's surface. The PC was subjected to a 10 μm indentation by a 250 μm diameter indenter. The multiscale model captured the nonlinear strain transmission through the PC, predicting decreased compressive strain with proximity to the receptor's core, as seen experimentally by others. The second set of simulations considered a single PC embedded epidermally (shallow) or dermally (deep) to model the PC's location within the skin. The embedded models were subjected to 10 μm indentations at a series of locations on the surface of the skin. Strain along the long axis of the PC was calculated after indentation to simulate stretch along the nerve fiber at the center of the PC. Receptive fields for the epidermis and dermis models were constructed by mapping the long-axis strain after indentation at each point on the surface of the skin mesh. The dermis model resulted in a larger receptive field, as the calculated strain showed less indenter location dependence than in the epidermis model.