Effects of fetal position on the loading of the fetal brain during the onset of the second stage of labour.

During vaginal labour, the delivery requires the fetal head to mould to accommodate the geometric constraints of the birth canal. Excessive moulding can produce brain injuries and long-term sequelae. Understanding the loading of the fetal brain during the second stage of labour (fully dilated cervix, active pushing, and expulsion of fetus) could thus help predict the safety of the newborn during vaginal delivery. To this end, this study proposes a finite element model of the fetal head and maternal canal environment that is capable of predicting the stresses experienced by the fetal brain at the onset of the second phase of labour. Both fetal and maternal models were adapted from existing studies to represent the geometry of full-term pregnancy. Two fetal positions were compared: left-occiput-anterior and left-occiput-posterior. The results demonstrate that left-occiput-anterior position reduces the maternal tissue deformation, at the cost of higher stress in the fetal brain. In both cases, stress is concentrated underneath the sutures, though the location varies depending on the presentation. In summary, this study provides a patient-specific simulation platform for the study of vaginal labour and its effect on both the fetal brain and maternal anatomy. Finally, it is suggested that such an approach has the potential to be used by obstetricians to support their decision-making processes through the simulation of various delivery scenarios.

Modelling transcranial ultrasound neuromodulation: an energy-based multiscale framework.

Several animal and human studies have now established the potential of low intensity, low frequency transcranial ultrasound (TUS) for non-invasive neuromodulation. Paradoxically, the underlying mechanisms through which TUS neuromodulation operates are still unclear, and a consensus on the identification of optimal sonication parameters still remains elusive. One emerging hypothesis based on thermodynamical considerations attributes the acoustic-induced nerve activity alterations to the mechanical energy and/or entropy conversions occurring during TUS action. Here, we propose a multiscale modelling framework to examine the energy states of neuromodulation under TUS. First, macroscopic tissue-level acoustic simulations of the sonication of a whole monkey brain are conducted under different sonication protocols. For each one of them, mechanical loading conditions of the received waves in the anterior cingulate cortex region are recorded and exported into a microscopic cell-level 3D viscoelastic finite element model of a neuronal axon embedded in extracellular medium. Pulse-averaged elastically stored and viscously dissipated energy rate densities during axon deformation are finally computed under different sonication incident angles and are mapped against distinct combinations of sonication parameters of the TUS. The proposed multiscale framework allows for the analysis of vibrational patterns of the axons and its comparison against the spectrograms of stimulating ultrasound. The results are in agreement with literature data on neuromodulation, demonstrating the potential of this framework to identify optimised acoustic parameters in TUS neuromodulation. The proposed approach is finally discussed in the context of multiphysics energetic considerations, argued here to be a promising avenue towards a scalable framework for TUS in silico predictions. STATEMENT OF SIGNIFICANCE: Low-intensity transcranial ultrasound (TUS) is poised to become a leading neuromodulation technique for the treatment of neurological disorders. Paradoxically, how it operates at the cellular scale remains unknown, hampering progress in personalised treatment. To this end, models of the multiphysics of neurons able to upscale results to the organ scale are required. We propose here to achieve this by considering an axon submitted to an ultrasound wave extracted from a simulation at the organ scale. Doing so, information pertaining to both stored and dissipated axonal energies can be extracted for a given head/brain morphology. This two-scale multiphysics energetic approach is a promising scalable framework for in silico predictions in the context of personalised TUS treatment.

White matter tract transcranial ultrasound stimulation, a computational study.

Low-intensity transcranial ultrasound stimulation (TUS) is poised to become one of the most promising treatments for neurological disorders. However, while recent animal model experiments have successfully quantified the alterations of the functional activity coupling between a sonicated target cortical region and other cortical regions of interest (ROIs), the varying degree of alteration between these different connections remains unexplained. We hypothesise here that the incidental sonication of the tracts leaving the target region towards the different ROIs could participate in explaining these differences. To this end, we propose a tissue level phenomenological numerical model of the coupling between the ultrasound waves and the white matter electrical activity. The model is then used to reproduce in silico the sonication of the anterior cingulate cortex (ACC) of a macaque monkey and measure the neuromodulation power within the white matter tracts leaving the ACC for five cortical ROIs. The results show that the more induced power a white matter tract proximal to the ACC and connected to a secondary ROI receives, the more altered the connectivity fingerprint of the ACC to this region will be after sonication. These results point towards the need to isolate the sonication to the cortical region and minimise the spillage on the neighbouring tracts when aiming at modulating the target region without losing the functional connectivity with other ROIs. Those results further emphasise the potential role of the white matter in TUS and the need to account for white matter topology when designing TUS protocols.

A Framework for Low-Intensity Low-Frequency Ultrasound Neuromodulation Sonication Parameter Identification from Micromechanical Flexoelectricity Modelling.

Low-intensity, low-frequency ultrasound (LILFU) has recently emerged as a promising technique to modulate non-invasively nerve activities at lower cost than other traditional and more-invasive neuromodulation methods. However, there is currently no consensus on the optimum sonication parameters to be used in LILFU applications, and most of the accepted ranges have arisen from trial-and-error approaches. Here we utilise a recently proposed micromechanics model of membrane flexoelectricity, a potential candidate for neuromodulation, and simulate action potentials/membrane polarisation triggered by acoustic pulses of different pulse frequencies, pulse magnitudes and duty cycles. Results reveal that, at constant duty cycles, increasing the transmit frequency increases the thresholds of both the pulse magnitude and the elastic energy rate density required to mechanically trigger an action potential, whereas at constant frequencies, increasing the duty cycle reduces both. The influence of transmit frequency is weakened at lower duty cycles. Our simulation results offer some guidance on the selections of sonication parameters used in LILFU for neurologic disorder treatments in the context of the flexoelectricity hypothesis.

A Machine Learning Enhanced Mechanistic Simulation Framework for Functional Deficit Prediction in TBI.

Resting state functional magnetic resonance imaging (rsfMRI), and the underlying brain networks identified with it, have recently appeared as a promising avenue for the evaluation of functional deficits without the need for active patient participation. We hypothesize here that such alteration can be inferred from tissue damage within the network. From an engineering perspective, the numerical prediction of tissue mechanical damage following an impact remains computationally expensive. To this end, we propose a numerical framework aimed at predicting resting state network disruption for an arbitrary head impact, as described by the head velocity, location and angle of impact, and impactor shape. The proposed method uses a library of precalculated cases leveraged by a machine learning layer for efficient and quick prediction. The accuracy of the machine learning layer is illustrated with a dummy fall case, where the machine learning prediction is shown to closely match the full simulation results. The resulting framework is finally tested against the rsfMRI data of nine TBI patients scanned within 24 h of injury, for which paramedical information was used to reconstruct in silico the accident. While more clinical data are required for full validation, this approach opens the door to (i) on-the-fly prediction of rsfMRI alterations, readily measurable on clinical premises from paramedical data, and (ii) reverse-engineered accident reconstruction through rsfMRI measurements.

Action potential alterations induced by single F11 neuronal cell loading.

Several research programmes have demonstrated how Transcranial Ultrasound Stimulation (TUS) can non-invasively and reversibly mechanically perturb neuronal functions. However, the mechanisms through which such reversible and a priori non-damaging behaviour can be observed remain largely unknown. While several TUS protocols have demonstrated motor and behavioural alterations in in vivo models, in vitro studies remain scarce. In particular, an experimental framework able to load mechanically an individual neuron in a controlled manner and simultaneously measure the generation and evolution of action potentials before, during and after such load, while allowing for direct microscopy, has not been successfully proposed. To this end, we herein present a multiphysics setup combining nanoindentation and patch clamp systems, assembled in an inverted microscope for simultaneous bright-field or fluorescence imaging. We evaluate the potential of the platform with a set of experiments in which single dorsal root ganglion-derived neuronal cell bodies are compressed while their spontaneous activity is recorded. We show that these transient quasi-static mechanical loads reversibly affect the amplitude and rate of change of the neuronal action potentials, which are smaller and slower upon indentation, while irreversibly altering other features. The ability to simultaneously image, mechanically and electrically manipulate and record single cells in a perturbed mechanical environment makes this system particularly suitable for studying the multiphysics of the brain at the cell level.

Medical imaging based in silico head model for ischaemic stroke simulation.

Stroke is one of the most common causes of death and a leading factor of disability in adults worldwide. It occurs when the blood supply to part of the brain is significantly reduced, potentially leading to the formation of brain oedema. Owing to the rigid nature of the skull, brain expansion results in the shifting of tissue structure, often captured by measurement of the midline shift (MLS). Clinically, MLS has been used in practice as an indication of stroke severity, potential tissue damage and as a way to assess whether decompressive surgery should be performed. However, a growing body of research points towards limitations in such predictive ability. Inspired by the recent progress made in traumatic brain injury simulations, in silico experiments appear as the ideal candidate to elucidate stroke consequences on brain tissues, e.g., morphological changes, in particular in the overarching context of computer model assisted clinical decision making support. To this end, two biologically-informed finite element head models, human and rat, were constructed to support such analysis. The main components of the models include magnetic resonance imaging-derived grey matter, white matter, cerebrospinal fluid and skull, while the human head model also includes the vasculature, additional cerebral components and axonal tractography. Constitutive models representing the mechanical behaviour of each component account in particular for the behaviour of brain tissues during the swelling process accompanying oedema development. The rat model was leveraged for the calibration of the swelling parameters, in turn used for the simulation of human stroke. Human oedema development as a result of stroke was simulated at three frequent locations: basal ganglia, fronto-opercular/anterior insula and temporo-parietal. All three cases exhibit a quadratic MLS evolution with time with the basal ganglia and temporo-parietal showing the largest and smallest values, respectively, at any given time. A proposed injury criterion for axonal tract damage was shown to be larger in the temporo-parietal case. Taken together, these results point towards i) the importance of considering stroke location when using the MLS as an indication of stroke severity, and ii) the potential lack of correlation between MLS value and tissue damage. Ultimately, we propose an in silico methodology that may hold promise in predicting stroke evolution based on an estimate of MLS and stroke location at a given time.

Datasets for multi-scale diffraction analysis (synchrotron XRD and EBSD) of twinning-detwinning during tensile-compressive deformation of AZ31B magnesium alloy samples.

Diffraction data were collected using synchrotron X-ray scattering (sXRD) and electron back-scattered diffraction (EBSD) during in situ tensile-compressive deformation of Mg alloy AZ31B dogbone samples. The onset and evolution of twinning and detwinning were monitored based on intensity changes in sXRD 2D scattering patterns (which also provided average elastic strain values through the calculation of orientation-specific lattice spacing changes), and EBSD, that revealed the micro-scale grain morphology changes. The observations were interpreted and analysed with the help of crystal plasticity finite element modelling (CP-FEM), as reported in the published article (https://doi.org/10.1016/j.ijplas.2019.02.018).

Two mechanisms regulate directional cell growth in Arabidopsis lateral roots.

Morphogenesis in plants depends critically on directional (anisotropic) growth. This occurs principally perpendicular to the net orientation of cellulose microfibrils (CMFs), which is in turn controlled by cortical microtubules (CMTs). In young lateral roots of Arabidopsis thaliana, growth anisotropy also depends on RAB-A5c, a plant-specific small GTPase that specifies a membrane trafficking pathway to the geometric edges of cells. Here we investigate the functional relationship between structural anisotropy at faces and RAB-A5c activity at edges during lateral root development. We show that surprisingly, inhibition of RAB-A5c function is associated with increased CMT/CMF anisotropy. We present genetic, pharmacological, and modelling evidence that this increase in CMT/CMF anisotropy partially compensates for loss of an independent RAB-A5c-mediated mechanism that maintains anisotropic growth in meristematic cells. We show that RAB-A5c associates with CMTs at cell edges, indicating that CMTs act as an integration point for both mechanisms controlling cellular growth anisotropy in lateral roots.

Electrophysiological-mechanical coupling in the neuronal membrane and its role in ultrasound neuromodulation and general anaesthesia.

The current understanding of the role of the cell membrane is in a state of flux. Recent experiments show that conventional models, considering only electrophysiological properties of a passive membrane, are incomplete. The neuronal membrane is an active structure with mechanical properties that modulate electrophysiology. Protein transport, lipid bilayer phase, membrane pressure and stiffness can all influence membrane capacitance and action potential propagation. A mounting body of evidence indicates that neuronal mechanics and electrophysiology are coupled, and together shape the membrane potential in tight coordination with other physical properties. In this review, we summarise recent updates concerning electrophysiological-mechanical coupling in neuronal function. In particular, we aim at making the link with two relevant yet often disconnected fields with strong clinical potential: the use of mechanical vibrations-ultrasound-to alter the electrophysiogical state of neurons, e.g., in neuromodulation, and the theories attempting to explain the action of general anaesthetics. STATEMENT OF SIGNIFICANCE: General anaesthetics revolutionised medical practice; now an apparently unrelated technique, ultrasound neuromodulation-aimed at controlling neuronal activity by means of ultrasound-is poised to achieve a similar level of impact. While both technologies are known to alter the electrophysiology of neurons, the way they achieve it is still largely unknown. In this review, we argue that in order to explain their mechanisms/effects, the neuronal membrane must be considered as a coupled mechano-electrophysiological system that consists of multiple physical processes occurring concurrently and collaboratively, as opposed to sequentially and independently. In this framework the behaviour of the cell membrane is not the result of stereotypical mechanisms in isolation but instead emerges from the integrative behaviour of a complexly coupled multiphysics system.

Computational model of the mechanoelectrophysiological coupling in axons with application to neuromodulation.

For more than half a century, the action potential (AP) has been considered a purely electrical phenomenon. However, experimental observations of membrane deformations occurring during APs have revealed that this process also involves mechanical features. This discovery has recently fuelled a controversy on the real nature of APs: whether they are mechanical or electrical. In order to examine some of the modern hypotheses regarding APs, we propose here a coupled mechanoelectrophysiological membrane finite-element model for neuronal axons. The axon is modeled as an axisymmetric thin-wall cylindrical tube. The electrophysiology of the membrane is modeled using the classic Hodgkin-Huxley (H-H) equations for the Nodes of Ranvier or unmyelinated axons and the cable theory for the internodal regions, whereas the axonal mechanics is modeled by means of viscoelasticity theory. Membrane potential changes induce a strain gradient field via reverse flexoelectricity, whereas mechanical pulses result in an electrical self-polarization field following the direct flexoelectric effect, in turn influencing the membrane potential. Moreover, membrane deformation also alters the values of membrane capacitance and resistance in the H-H equation. These three effects serve as the fundamental coupling mechanisms between the APs and mechanical pulses in the model. A series of numerical studies was systematically conducted to investigate the consequences of interaction between the APs and mechanical waves on both myelinated and unmyelinated axons. Simulation results illustrate that the AP is always accompanied by an in-phase propagating membrane displacement of ≈1nm, whereas mechanical pulses with enough magnitude can also trigger APs. The model demonstrates that mechanical vibrations, such as the ones arising from ultrasound stimulations, can either annihilate or enhance axonal electrophysiology depending on their respective directionality and frequency. It also shows that frequency of pulse repetition can also enhance signal propagation independently of the amplitude of the signal. This result not only reconciles the mechanical and electrical natures of the APs but also provides an explanation for the experimentally observed mechanoelectrophysiological phenomena in axons, especially in the context of ultrasound neuromodulation.

Ion current and action potential alterations in peripheral neurons subject to uniaxial strain.

Peripheral nerves, subject to continuous elongation and compression during everyday movement, contain neuron fibers vital for movement and sensation. At supraphysiological strains resulting from trauma, chronic conditions, aberrant limb positioning, or surgery, conduction blocks occur which may result in chronic or temporary loss of function. Previous in vitro stretch models, mainly focused on traumatic brain injury modelling, have demonstrated altered electrophysiological behavior during localized deformation applied by pipette suction. Our aim was to evaluate the changes in voltage-activated ion channel function during uniaxial straining of neurons applied by whole-cell deformation, more physiologically relevant model of peripheral nerve trauma. Here, we quantified experimentally the changes in inwards and outwards ion currents and action potential (AP) firing in dorsal root ganglion-derived neurons subject to uniaxial strains, using a custom-built device allowing simultaneous cell deformation and patch clamp recording. Peak inwards sodium currents and rectifying potassium current magnitudes were found to decrease in cells under stretch, channel reversal potentials were found to be left-shifted, and half-maximum activation potentials right-shifted. The threshold for AP firing was increased in stretched cells, although neurons retained the ability to fire induced APs. Overall, these results point to ion channels being damaged directly and immediately by uniaxial strain, affecting cell electrophysiological activity, and can help develop prevention and treatment strategies for peripheral neuropathies caused by mechanical trauma.

Engineering a uniaxial substrate-stretching device for simultaneous electrophysiological measurements and imaging of strained peripheral neurons.

Peripheral nerves are continuously subjected to mechanical strain during everyday movements, but excessive stretch can lead to damage and neuronal cell functionality can also be impaired. To better understand cellular processes triggered by stretch, it is necessary to develop in vitro experimental methods that allow multiple concurrent measurements and replicate in vivo mechanical conditions. Current commercially available cell stretching devices do not allow flexible experimental design, restricting the range of possible multi-physics measurements. Here, we describe and characterise a custom-built uniaxial substrate-straining device, with which neurons cultured on aligned patterned surfaces (50 µm wide grooves) can be strained up to 70% and simultaneously imaged with widefield and confocal imaging (up to 100x magnification). Furthermore, direct and indirect electrophysiological measurements by patch clamping and calcium imaging can be made during strain application. We characterise the strain applied to cells cultured in deformable wells by using finite element method simulations and experimental data, showing local surface strains of up to 60% with applied strains of up to 25%. We also show how patterned substrates do not alter the mechanical properties of the system compared to unpatterned surfaces whilst still inducing a homogeneous cell response to strain. The characterisation of this device will be useful for research into investigating the effect of whole-cell mechanical stretch on neurons at both single cell and network scales, with applications found in peripheral neuropathy modelling and in platforms for preventive and regenerative studies.

Rapid and efficient differentiation of functional motor neurons from human iPSC for neural injury modelling.

Primary rodent neurons and immortalised cell lines have overwhelmingly been used for in vitro studies of traumatic injury to peripheral and central neurons, but have some limitations of physiological accuracy. Motor neurons (MN) derived from human induced pluripotent stem cells (iPSCs) enable the generation of cell models with features relevant to human physiology. To facilitate this, it is desirable that MN protocols both rapidly and efficiently differentiate human iPSCs into electrophysiologically active MNs. In this study, we present a simple, rapid protocol for differentiation of human iPSCs into functional spinal (lower) MNs, involving only adherent culture and use of small molecules for directed differentiation, with the ultimate aim of rapid production of electrophysiologically functional cells for short-term neural injury experiments. We show successful differentiation in two unrelated iPSC lines, by quantifying neural-specific marker expression, and by evaluating cell functionality at different maturation stages by calcium imaging and patch clamping. Differentiated neurons were shown to be electrophysiologically altered by uniaxial mechanical deformation. Spontaneous network activity decreased with applied stretch, indicating aberrant network connectivity. These results demonstrate the feasibility of this rapid, simple protocol for differentiating iPSC-derived MNs, suitable for in vitro neural injury studies focussing on electrophysiological alterations caused by mechanical deformation or trauma.

Cognition based bTBI mechanistic criteria; a tool for preventive and therapeutic innovations.

Blast-induced traumatic brain injury has been associated with neurodegenerative and neuropsychiatric disorders. To date, although damage due to oxidative stress appears to be important, the specific mechanistic causes of such disorders remain elusive. Here, to determine the mechanical variables governing the tissue damage eventually cascading into cognitive deficits, we performed a study on the mechanics of rat brain under blast conditions. To this end, experiments were carried out to analyse and correlate post-injury oxidative stress distribution with cognitive deficits on a live rat exposed to blast. A computational model of the rat head was developed from imaging data and validated against in vivo brain displacement measurements. The blast event was reconstructed in silico to provide mechanistic thresholds that best correlate with cognitive damage at the regional neuronal tissue level, irrespectively of the shape or size of the brain tissue types. This approach was leveraged on a human head model where the prediction of cognitive deficits was shown to correlate with literature findings. The mechanistic insights from this work were finally used to propose a novel protective device design roadmap and potential avenues for therapeutic innovations against blast traumatic brain injury.

Mechanistic models versus machine learning, a fight worth fighting for the biological community?

Ninety per cent of the world's data have been generated in the last 5 years (Machine learning: the power and promise of computers that learn by example Report no. DES4702. Issued April 2017. Royal Society). A small fraction of these data is collected with the aim of validating specific hypotheses. These studies are led by the development of mechanistic models focused on the causality of input-output relationships. However, the vast majority is aimed at supporting statistical or correlation studies that bypass the need for causality and focus exclusively on prediction. Along these lines, there has been a vast increase in the use of machine learning models, in particular in the biomedical and clinical sciences, to try and keep pace with the rate of data generation. Recent successes now beg the question of whether mechanistic models are still relevant in this area. Said otherwise, why should we try to understand the mechanisms of disease progression when we can use machine learning tools to directly predict disease outcome?

3D multicellular model of shock wave-cell interaction.

Understanding the interaction between shock waves and tissue is critical for advancing the use of shock waves for medical applications, such as cancer therapy. This work aims to study shock wave-cell interaction in a more realistic environment, relevant to in vitro and in vivo studies, by using 3D computational models of healthy and cancerous cells. The results indicate that for a single cell embedded in an extracellular environment, the cellular geometry does not influence significantly the membrane strain but does influence the von Mises stress. On the contrary, the presence of neighbouring cells has a strong effect on the cell response, by increasing fourfold both quantities. The membrane strain response of a cell converges with more than three neighbouring cell layers, indicating that a cluster of four layers of cells is sufficient to model the membrane strain in a large domain of tissue. However, a full 3D tissue model is needed if the stress evaluation is of main interest. A tumour mimicking multicellular spheroid model is also proposed to study mutual interaction between healthy and cancer cells and shows that cancer cells can be specifically targeted in an early stage tumour-mimicking environment. STATEMENT OF SIGNIFICANCE: This work presents 3D computational models of shock-wave/cell interaction in a biophysically realistic environment using real cell morphology in tissue-mimicking phantoms and multicellular spheroids. Results show that cell morphology does not strongly influence the membrane strain but influences the von Mises stress. While the presence of neighbouring cells significantly increases the cell response, four cell layers are enough to capture the membrane strain change in tissue. However, a full tissue model is necessary if accurate stress analysis is needed. The work also shows that cancer cells can be specifically targeted in early stage tumour mimicking environment. This work is a step towards realistic modelling of shock-wave/cell interactions in tissues and provides insight on the use of 3D models for different scenarios.

Response of Single Cells to Shock Waves and Numerically Optimized Waveforms for Cancer Therapy.

Shock waves are used clinically for breaking kidney stones and treating musculoskeletal indications. The mechanisms by which shock waves interact with tissue are still not well understood. Here, ultra-high-speed imaging was used to visualize the deformation of individual cells embedded in a tissue-mimicking phantom when subject to shock-wave exposure from a clinical source. Three kidney epithelial cell lines were considered to represent normal healthy (human renal epithelial), cancer (CAKI-2), and virus-transformed (HK-2) cells. The experimental results showed that during the compressive phase of the shock waves, there was a small (<2%) decrease in the projected cell area, but during the tensile phase, there was a relatively large (∼10%) increase in the projected cell area. The experimental observations were captured by a numerical model with a constitutive material framework consisting of an equation of state for the volumetric response and hyper-viscoelasticity for the deviatoric response. To model the volumetric cell response, it was necessary to change from a higher bulk modulus during the compression to a lower bulk modulus during the tensile shock loading. It was discovered that cancer cells showed a smaller deformation but faster response to the shock-wave tensile phase compared to their noncancerous counterparts. Cell viability experiments, however, showed that cancer cells suffered more damage than other cell types. These data suggest that the cell response to shock waves is specific to the type of cell and waveforms that could be tailored to an application. For example, the model predicts that a shock wave with a tensile stress of 4.59 MPa would increase cell membrane permeability for cancer cells with minimal impact on normal cells.

Molecular dynamics simulations of heterogeneous cell membranes in response to uniaxial membrane stretches at high loading rates.

The chemobiomechanical signatures of diseased cells are often distinctively different from that of healthy cells. This mainly arises from cellular structural/compositional alterations induced by disease development or therapeutic molecules. Therapeutic shock waves have the potential to mechanically destroy diseased cells and/or increase cell membrane permeability for drug delivery. However, the biomolecular mechanisms by which shock waves interact with diseased and healthy cellular components remain largely unknown. By integrating atomistic simulations with a novel multiscale numerical framework, this work provides new biomolecular mechanistic perspectives through which many mechanosensitive cellular processes could be quantitatively characterised. Here we examine the biomechanical responses of the chosen representative membrane complexes under rapid mechanical loadings pertinent to therapeutic shock wave conditions. We find that their rupture characteristics do not exhibit significant sensitivity to the applied strain rates. Furthermore, we show that the embedded rigid inclusions markedly facilitate stretch-induced membrane disruptions while mechanically stiffening the associated complexes under the applied membrane stretches. Our results suggest that the presence of rigid molecules in cellular membranes could serve as "mechanical catalysts" to promote the mechanical destructions of the associated complexes, which, in concert with other biochemical/medical considerations, should provide beneficial information for future biomechanical-mediated therapeutics.

Publisher's Note: Growth, collapse, and stalling in a mechanical model for neurite motility [Phys. Rev. E 93, 032410 (2016)].

This corrects the article DOI: 10.1103/PhysRevE.93.032410.