Frontiers in Applied Mathematics and Statistics

Pulmonary embolism (PE) is a sudden blockage of lung arteries, usually caused by a blood clot that travels from the deep veins of the legs. As the world becomes more sedentary and lifestyle diseases emerge, deaths from PE are expected to rise in the next 20 years. For instance, the United States records annual deaths of 60 per 100,000 people. The degree to which these deaths are affected by demographic, socioeconomic and environmental predisposing factors as well as how they vary across time and space remains an open science question. In this paper, we conduct a detailed statistical and spatial-temporal study PE mortality counts across US counties from 2005 to 2022. Our study shows that study shows that PE mortality is not randomly distributed in space and time but concentrated in most counties in Arkansas, Mississippi, Kansas, Missouri, Oklahoma, Louisiana, Nebraska, Tennessee, and Texas. We also established that age is a statistically significant predictor (mean coefficient of 0.52) of PE mortality especially in counties of Mississippi, Kansas, Missouri, Tennessee, Illinois, Kentucky, Texas and Virginia. Our results thus provide empirical support for prioritizing regionally targeted PE prevention policies. Furthermore, the adopted county-level analysis uncovered granular geographic patterns that are usually obscured in state or national level analysis. Our study thus provides actionable evidence to support geographically tailored strategies aimed at reducing mortality by pinpointing counties with consistently elevated PE mortality risk at different timescales.

BackgroundTo control leishmaniasis, chemotherapy drugs are currently under development. However, these drugs often exhibit poor efficacy and are associated with toxicity, adverse effects, and drug resistance. At present, no specific drug is available for the treatment of leishmaniasis. Meanwhile, vaccine research is ongoing. Recent studies have analysed some experimental vaccines using mathematical models. AimIn previous work, drug targeting was focused on the entire human body rather than specifically addressing infected macrophages and parasites. In our current approach, we aim to eliminate infected macrophages and parasites through nano-drug design. Specifically, we utilise two types of nanoparticles: iron oxide and citric acid-coated iron oxide. Moving forward, we plan to advance this strategy using mathematical modelling of macrophage-parasite interactions. MethodsWe design PDE-based models of macrophages and parasites, incorporating cytokine dynamics, to support nano-drug development. Drug efficacy is estimated using posterior distributions to analyse phenotypic fluctuations of macrophages and parasites during the design phase. We investigate implicit and semi-implicit treatment schemes, focusing on energy decay properties. To model drug flow during treatment, we introduce a three-phase moving boundary problem. Comparative analyses are conducted to evaluate macrophage and parasite behaviour with and without treatment. Finally, the entire framework is implemented within a virtual lab environment. ResultsThe results show that the nano-drug exhibits better efficacy compared to combined drug doses. We analysed and compared two types of nano-drug particles: iron oxide and citric acid-coated iron oxide. We discuss how the drug effectively targets and eliminates infected macrophages and parasites. ConclusionOur models results and simulations will support researchers conducting further studies in nano-drug design for leishmaniasis. These simulations are performed within a virtual lab environment.

This work focuses on the global and partial identification problem for fractional differential equations. We provide a general numerical procedure based on global and local optimization algorithms with two refinements for biological systems that ensure solution positivity and homogeneous parameter units. The method is applied to a new fractional model of Dengue outbreak called the Fractional Homogeneous Nishiura (FHN) model, calibrated using data of newly infected people in Cape Verde. We show that our identification method yields a better fit between data and model solutions than previous approaches and that our FHN model captures the dynamics of Dengue more closely than existing systems.

With Japans rapidly aging population, demand for home healthcare is projected to increase by 62% by 2040. This study quantitatively evaluated accessibility to 24-hour home healthcare and regional disparities across all 335 secondary medical areas (SMAs) in Japan using the Enhanced Two-Step Floating Catchment Area (E2SFCA) method. We conducted a nationwide cross-sectional study analyzing approximately 430,000 population points at 500-meter mesh resolution. The E2SFCA integrated demand (age-adjusted population), supply (24-hour home care support clinics and hospitals), and transportation (road networks). Accessibility scores (ASs) and Gini coefficients were calculated for each SMA. Wards hierarchical cluster analysis classified regional types, and multiple regression based on the Penchansky and Thomas five-dimensional access framework identified factors associated with the median AS (ASM) and Gini coefficient. The median ASM was 45.71 (0.00-153.49), and the median Gini coefficient was 0.33 (0.06-0.93). Cluster analysis identified six types ranked by descending ASM, from C1 (high access, equitable; n = 48) to C6 (access desert; n = 23). C6 had a median ASM of 0.00 and Gini coefficient of 0.74, indicating virtually no access within a 30-minute catchment. Home-visit standardized claim ratios, used as external validation, declined monotonically from C1 (125.6) to C6 (17.6). For ASM, 24-hour visiting nursing stations ({beta} = +0.369) and clinic physicians ({beta} = +0.342) showed the strongest positive associations, with non-residential area negatively associated ({beta} = -0.273). For the Gini coefficient, non-residential area showed the strongest positive association ({beta} = +0.523). Taxable income per taxpayer was not significantly associated with either outcome. Non-residential area was associated with both lower accessibility and greater intra-regional inequality, suggesting that geographic constraints may limit the effectiveness of resource investment alone. Uniform nationwide implementation of policies shifting care from long-term care beds to home healthcare may not be feasible; region-specific approaches considering geographic characteristics are necessary.

Stroke, as an acute cerebrovascular disease with significant public health implications, is influenced by a complex interplay of meteorological conditions, air quality, and socioeconomic factors. However, the inherent challenges of mixed-frequency data from diverse sources and high-dimensional variable spaces limit the effectiveness of traditional regression models. This study develops a Lasso-MIDAS model framework to identify the key multidimensional drivers of stroke admissions. Using this approach, 21 candidate variables encompassing meteorological, environmental, and economic indicators were screened. The empirical results identified 11 core influencing factors. In the meteorological and environmental dimensions, Wind Speed, Carbon Monoxide (CO), and Sulfur Dioxide (SO2) were identified as significant positive drivers, with Temperature Difference also positively correlating with admission risks. Conversely, Nitrogen Dioxide (NO2) exhibited a negative correlation, potentially reflecting behavioral adaptation and exposure reduction during peak pollution periods. In the socioeconomic dimension, the Consumer Price Index (CPI) for Food, Tobacco, and Alcohol emerged as a major risk factor, highlighting the impact of living cost pressures on public health. The findings demonstrate the superiority of the Lasso-MIDAS model in handling large-scale healthcare data. It effectively addresses the frequency mismatch problem while enhancing the robustness of causal identification through variable shrinkage. These conclusions provide a scientific basis for health authorities to establish early warning systems and optimize public health policy interventions.

Sylvatic Yellow Fever (YF) is an infectious mosquito-borne disease with significant epidemiological relevance due to its widespread distribution and high lethality for human and non-human primates, particularly in tropical regions of the planet such as in Brazil. Identifying regions and periods of high environmental suitability for the occurrence of YF is essential for preventing or mitigating its burden, as it enables the efficient allocation of surveillance efforts, prevention, and implementation of control measures. Environmental modeling of YF occurrence has proven to be an effective approach toward this goal; however, its effectiveness strongly depends on the modeling framework's capabilities as well as the spatial and temporal precision of all associated data. We propose a fine-scale geospatial modeling of YF environmental suitability that is based on a generative machine-learning ensemble method built on a large set of high-resolution environmental covariates. First, we take the spatiotemporal statistical description of the environment of each of the 545 YF cases from 2019--2024 up to 30 m/monthly resolution at three buffer scales: 100 m, 500 m, and 1000 m ratios. Then, we perform a feature selection and train hundreds of One-Class Support Vector Machine submodels to form a robust ensemble model, whose predictions are projected to a 1x1 km resolution grid of Brazil under several metrics, exceeding seven million ensemble evaluations. The predictions ranked the Southern Brazil region with the highest mean suitability for YF, with a level of 0.64; Southeast comes next with 0.46, followed closely by Central-West region (0.44), North (0.39), and finally Northeast (0.28). The model exhibited high uncertainty for the North region, indicating that data collection efforts are much needed in this region. As for the environmental covariates, a feature analysis pointed out that Land use and cover accounts for the largest influence in the model output.

Fraud in the health landscape is an aggravating issue, with far-reaching consequences burdening the financial stability of the health industry and threatening the quality of medical care. It results from vulnerabilities within the current healthcare framework that are exploited by the fraudsters in their favor. In spite of many developed models that aim to detect fraudulent patterns in insurance claims, the accuracy of such models frequently suffers as a result of the imbalance issue of the Medicare dataset and irrelevant features. This study ventures to improve detection performance and accuracy by employing a deep learning model along with data sampling and feature selection techniques. Comparative analysis among different combinations is conducted to determine their efficacy to enhance the accuracy of the fraud detection model. Hence, the suggested model clearly demonstrates that a combination of myriad data sampling and feature selection techniques is helping to improve accuracy and performance. The accuracy was thus 95.4%, with negligible evidence of overfitting detected using both Chi-square and Synthetic Minority Over-sampling (SMOTE) techniques. Ultimately, the study findings underscore the significance of employing combined techniques instead of using only the baseline deep learning model for better performance in detecting Medicare insurance fraud.

Variability in gene expression among single cells and growing cell populations can arise from the stochastic nature of protein synthesis, which often occurs in random bursts. This study investigates the variability in the expression of a growth-sustaining protein, whose concentration is regulated by a negative feedback loop due to cell growth-induced dilution. We model the distribution of protein concentration using a Chapman-Kolmogorov equation for single cells and a population balance equation for growing cell populations. For single cells, we derive an explicit solution for the protein concentration distribution in state space and represent it as a Bessel function in Laplace space. For growing populations, we find that the distribution satisfies a Heun differential equation with singular boundary conditions. By addressing the central connection problem for the Heun equation, we quantify the population-level protein distribution and determine the Mathusian parameter, which characterizes population growth. This work provides a comprehensive analytical framework for understanding how stochastic protein synthesis impacts gene expression variability and population dynamics.

This retrospective study aims to explore the interactive effects of biological maturation and relative age effect (RAE) on talent identification. 56 male elite soccer players matched for chronological age (15.08{+/-}0.41 years) were studied. Test items included anthropometry (height, body mass, sitting height, leg length, BMI and Quetelet index), physiology (power, speed, agility, speed endurance and aerobic performance), soccer-specific skills (passing, shooting and dribbling), psychology (achievement motivation, orientation and resilience) and biological maturation (APHV) tests. The test results were analyzed independent sample t-test, Pearson correlation analysis, and stratified regression. Conclusion: Biological maturation significantly influences anthropometry (height, weight and Quetelet index), lower limb explosive, and speed (single-leg jump, standing triple jump, and 30-m sprint) in U16 male elite soccer players in Shanghai. The relative age effect shows no significant impact on talent selection indicators, which is attributed to the accumulated training load effect. The mechanisms of biological maturation and RAE in youth soccer talent selection are distinct and operate independently.

During embryogenesis, as cells proliferate and assemble into tissues, they undergo a sequence of transitions between distinct molecular states eventually giving rise to a cellular population consisting of an appropriate distribution of specific functional cell types. Recent progress on the dynamics underlying decision-making in developmental landscape makes it feasible to start analysing the amount of information involved in constructing such systems. To explore this we introduce the notion of potency of a developmental landscape and attempt to calculate it for two development systems of current interest, in-vitro differentiation of epiblast-like cells into neural and mesodermal progenitors and the worm vulva patterning system. Our approach integrates concepts from developmental biology, information theory and dynamical systems to estimate both the number and identity of signalling regimes that give rise to distinguishable temporal response patterns.

The opioid crisis has severely impacted Ohio, with overdose death rates surpassing national averages and disproportionately affecting rural and Appalachian regions. Accurately predicting county-level opioid overdose deaths (OD) is critical for timely intervention but remains challenging due to the wide differences in opioid OD between large and small counties. We propose a Spatial-Temporal Graph Neural Network (ST-GNN) framework that integrates graph neural networks (GNNs) to capture spatial relationships between counties and Long Short-Term Memory (LSTM) networks to model temporal dynamics. Using quarterly OD data from Q1 2017 to Q2 2023 for 88 Ohio counties, we incorporate a nine-dimensional dynamic feature set, including naloxone administration events and high-risk opioid prescribing, along with a static Social Determinants of Health (SDoH) index. Compared to traditional statistical models and temporal deep learning baselines, our ST-GNN demonstrates superior performance, particularly in larger counties, while classification-based strategy improve predictions for small counties, leading to more stable and reliable results. Our findings emphasize the need for spatial-temporal modeling and customized training to enhance public health decision-making in addressing the opioid crisis.

BackgroundDengue has been a major health threat globally in recent years. In particular, dengue incidences continue to increase annually and the epidemic area has expanded primarily due to global warming. Therefore, effective case detection and surveillance strategies are crucial to tackle this global health challenge. In clinical practice, the rapid test kit detecting dengue non-structural protein 1 antigen and commonly referred as NS1, is widely employed for early diagnosis. However, real-world studies revealed that the sensitivity of the NS1 test kit ranged from approximately 61% to 95%. Since early diagnosis is really critical for disease surveillance in the early stage of a dengue epidemic, scientists have been working hard to develop novel diagnosis methods that can provide higher sensitivity levels. Methodology/Principal FindingsIn response to this challenge, in this study, we have developed a novel diagnosis procedure that integrates machine learning technologies with the NS1 test kit. Our experimental results revealed that we would be able to raise the sensitivity of the dengue diagnosis procedure to higher than 99% by incorporating machine learning based prediction models to screen the suspected patients with a negative NS1 result. Furthermore, the relative risks between the suspected patients who were predicted to be positive and those who were predicted to be negative exceeded 4.8. Conclusions/SignificanceThese results illustrate that the proposed approach provides an effective and efficient diagnosis procedure to address the global health challenge caused by spread of dengue. Author SummaryThis study has aimed to enhance surveillance of the dengue disease by integrating machine learning technologies with the rapid test kit commonly employed in early diagnosis. In clinical practice, the NS1 rapid test kit is widely employed for early diagnosis. However, real-world studies revealed that a certain percentage of the patients with a negative NS1 test result, ranging from 5% to 39%, were actually infected by dengue. Since early diagnosis is critical for disease control in the early stage of a dengue epidemic, scientists have been working hard to tackle this challenge. Based on this observation, this study was launched to investigate the effects of incorporating machine learning based prediction models to further screen those patients with a negative NS1 test result. The experimental results revealed that the proposed approach was able to identify over 99% of the patients who were infected by the dengue disease. Furthermore, the risk of the suspected patients who were predicted to be positive was 4.8 times higher than the risk of those who were predicted to be negative. The experimental results illustrate that the proposed approach provides an effective and efficient diagnosis procedure to enhance surveillance of the dengue disease.

Mental health challenges among university students have increased due to academic pressure, lifestyle changes, and continuous digital engagement. Existing approaches for mental health assessment often rely either on self-reported psychological scales or isolated behavioral indicators, limiting their ability to capture complex temporal and contextual patterns. This study proposes an interpretable multimodal framework for student mental health risk assessment using behavioral sensing, academic information, ecological momentary assessments (EMA), and psychometric survey data. A bidirectional Long Short-Term Memory autoencoder is employed to learn latent temporal representations from day-level behavioral sequences, while graph embeddings capture structural relationships among students using similarity-based neighborhood graphs. These representations are fused with academic and survey-derived features and reduced using Principal Component Analysis and Uniform Manifold Approximation and Projection. K-means clustering is then applied to identify behaviorally distinct student groups. Experimental analysis on the StudentLife dataset demonstrates meaningful clustering performance with a Silhouette Score of 0.4209 and Adjusted Rand Index stability of 0.6869. The identified clusters correspond to low-risk, moderate-risk, and high-risk behavioral profiles. To improve interpretability and practical usability, a fuzzy inference system is introduced to compute mental risk, academic risk, and wellbeing indices using psychometric indicators including PHQ-9, PSS, PANAS, VR-12, and Big Five personality traits. The results demonstrate the potential of combining multimodal behavioral modeling with interpretable fuzzy reasoning to support early mental health risk assessment in educational settings.

Experimental studies show that tumor cells adopt migratory or proliferative phenotypes depending on the local extracellular matrix (ECM). In this work, we propose a minimal go-or-grow invasion model, comprising two specialist cell phenotypes: proliferating and migratory, with phenotypic switching and cell migration depending on local ECM density. Numerical simulations of this model reveal that the spatial arrangement of proliferative and migratory cells depends on the choice of phenotypic switching function. We then ask whether this specialist cell-phenotype model can be reduced to a generalist cell-phenotype model. We derive a relationship between the reduced model and go-or-grow model in the fast phenotypic switching regime. We observe that the reduced model captures the dynamics of the original model, for a range of realistic phenotypic switching functions. We analytically derive the minimum traveling wave speed of the reduced model in a homogeneous ECM bed. Moreover, using linear stability analysis on the go-or-grow model, we recover the same wave speed expression. In addition, we numerically explore how the key parameters influence the traveling wave speed profile. Our analysis indicated the counter-intuitive result that the wave speed is independent of the matrix degradation rate, and our simulations show that, at most, the speed is weakly dependent on this parameter.

Hemodynamic forces play a key role in early cardiac morphogenesis, yet many computational studies assume Newtonian blood behavior. Here, we evaluate the impact of nonNewtonian shearthinning rheology on flow patterns, pressure distributions, and wall shear stress (WSS) during cardiac looping using idealized threedimensional models of the embryonic heart tube. Five geometries representing progressive looping stages, from a linear tube to an Sshaped configuration with ventricular ballooning, were analyzed under pulsatile flow using both Newtonian and powerlaw viscosity models. Across all stages, Reynolds numbers (Re {approx} 1-7) and Womersley numbers (Wo {approx} 0.3) indicated laminar, quasisteady flow consistent with embryonic conditions. Incorporating shearthinning rheology produced substantial deviations from Newtonian predictions, with peak systolic WSS differing by up to [~]40% and pressure drops by up to [~]20%. These effects were most pronounced in regions of increased curvature and geometric complexity. These findings demonstrate that nonNewtonian rheology significantly influences predicted hemodynamic environments during cardiac looping and should be incorporated into computational models aimed at understanding mechanobiological regulation of early heart development.

The emergence of a hantavirus variant aboard a commercial cruise ship presents a significant public health concern. This study develops a discrete-time stochastic Susceptible-Exposed-Infectious-Recovered-Dead model to estimate transmission dynamics, hidden exposed infections, and outbreak risk among passengers and crew. Epidemiological parameters and latent disease states were inferred using an Ensemble Adjustment Kalman Filter calibrated to reported case data from WHO and ECDC situation reports. The estimated basic reproduction number was 2.76, with a 95% confidence interval of 2.52-2.99, indicating substantial potential for sustained onboard transmission before strict quarantine measures. Simulations further suggest that several exposed individuals may remain unidentified during the early outbreak phase, creating a hidden reservoir that symptom-based surveillance alone may fail to detect. These findings highlight the importance of rapid surveillance, widespread testing, targeted quarantine, and active monitoring of exposed individuals in confined travel settings. The proposed modeling framework can support timely outbreak assessment and intervention planning for infectious-disease events in similarly dense and spatially constrained populations.

BackgroundCOCOA, Japans Bluetooth-based COVID-19 contact tracing app, was widely regarded as ineffective due to persistently low key-match counts. However, this assessment may have conflated two distinct phenomena: (1) a structurally suppressed positive registration rate caused by administrative friction in the HER-SYS linkage, and (2) genuine epidemiological inefficacy. ObjectiveTo empirically examine whether the correlation between individual COCOA key-match counts and regional COVID-19 case numbers depended on positive registration rate, using a unique longitudinal dataset from a single observer with a rigorously controlled behavioral pattern. MethodsThe corresponding author (S.N.) recorded daily key-match counts from his personal iPhone from January 10 to October 8, 2022, encompassing the Sixth Wave (January 10-April 20, 2022) and Seventh Wave (July 9-September 2, 2022). Daily reported COVID-19 cases in Tokyo were obtained from publicly available NHK data. Pearson correlation coefficients were calculated for each wave period separately. ResultsDuring the Sixth Wave, no meaningful correlation was observed between key-match counts and daily case numbers (r2 = 0.018, p = 0.059, n = 194). In contrast, during the Seventh Wave, a strong positive correlation emerged (r2 = 0.530, p < 0.001, n = 56). This correlation disappeared abruptly after September 12, 2022, coinciding with Japans revision of the mandatory full case reporting (Zenshu Todokedashi) policy, which substantially reduced positive registrations in COCOA. ConclusionsCOCOAs utility as an individual infection risk indicator was critically dependent on positive registration rate rather than app installation rate. These findings provide the first real-world empirical evidence supporting the threshold effect predicted by prior simulation studies, and offer important lessons for the design of digital tools in future pandemic preparedness.

Infectious disease surveillance systems in tropical countries show that respiratory disease incidence generally manifests as year-round activity with weak fluctuations and irregular seasonality. Previously, using a ten-year time series of influenza-like illness (ILI) collected from outpatient clinics in Ho Chi Minh City (HCMC), Vietnam, we found a combination of nonannual and annual signals driving these dynamics, but with unknown mechanisms. In this study, we use seven stochastic dynamical models incorporating humidity, temperature, and school term to investigate plausible mechanisms behind these annual and nonannual incidence trends. We use iterated filtering to fit the models and evaluate the models by comparing how well they replicate the combination of annual and nonannual signals. We find that a model including specific humidity, temperature, and school term best fits our observed data from HCMC and partially reproduces the irregular seasonality. The estimated effects from specific humidity and temperature on transmission are nonlinearly negative but weak. School dismissal is associated with decreased transmission, but also with low magnitude. Under these weak external drivers, we hypothesize that stochasticity makes a strong sub-annual cycle more likely to be observed in ILI disease dynamics. Our study shows a possible mechanism for respiratory disease dynamics in the tropics. When the external drivers are weak, the seasonality of respiratory disease dynamics is prone to the influence of stochasticity. Author SummaryAlthough the mechanisms driving seasonality of respiratory disease dynamics have been well-studied in temperate regions, they are unknown in the tropics. In this study, we used a 10-year influenza-like-illness (ILI) daily-reporting data set collected from outpatient clinics in Ho Chi Minh City (HCMC) in Vietnam to investigate the mechanisms associated with annual and nonannual ([~]215 days) periodic patterns in the data. By comparing seven mechanistic models against the data, we showed that the mechanism that best explains respiratory disease dynamics in HCMC is a stochastic susceptible-infected-recovered-susceptible (SIRS) model weakly driven by external drivers including specific humidity, temperature, and school term. The nonannual cycles duration is consistent with the inferred duration of immunity of the model. By showing the nonannual cycle as strong as in the data is only observed in stochastic model, we showed that the observed respiratory disease dynamics in HCMC is under the influence of stochasticity when external drivers are weak.

Vertebrate gastrulating mesoderm is a prototypic example of a mesenchymal-like tissue undergoing extensive remodelling. While the tissue may be globally represented as a viscoelastic material, the actual biological material is intrinsically complex. To get to a real understanding of its properties, one needs to move to the mesoscale, linking cellular properties to collective phenomena. Vertebrate embryos also display a remarkable variability in mechanical properties, despite which they robustly complete gastrulation. This study attempts to explore these aspects by dissecting Xenopus mesoderm cell behaviour in a minimal system, using aspiration through a microfluidic system to impose controlled stress to a mesoderm aggregate. We show that beyond estimating global rheology at the tissue scale, it is possible to infer a wealth of information based on cell morphology and dynamics. Our data are consistent with collective behaviour being mostly dictated by the balance between the capacity of cells to stretch and the resistance to cell-cell contacts, which limits cell-cell intercalation and thus tissue remodelling. Importantly, tissues are not only able to transmit stress over a distance, they also clearly react to it through actively reinforcing cell-cell mechanical coupling. This adaptative property is found through a broad range of tissue stiffness, and adhesion strength appears to scale with the elastic modulus, suggesting that cell stiffness may ultimately be the key parameter setting mesoderm rheology and accounting for the large differences observed between embryo batches.

Functional spinal cord repair in zebrafish is governed by regeneration-favorable biochemical and mechanical cues within the lesion microenvironment. Alterations in extracellular matrix composition and stiffness are closely associated with axon regeneration. However, experimentally dissecting the interplay between mechanical signals and axonal regrowth in vivo remains technically challenging. Here, we present an agent-based modeling framework to simulate stiffness-mediated axonal growth trajectories across the lesion. We use this model to explore potential mechanisms underlying the characteristic growth patterns observed during zebrafish spinal cord regeneration. Computational predictions were qualitatively compared with confocal imaging data obtained from larval zebrafish. These phenomenological comparisons revealed a close agreement between simulated and experimentally observed axon growth, indicating that experimentally observed patterns could be governed by transient changes in the stiffness profile of the spinal cord and lesion microenvironment. Hence, our computational framework provides an in silico platform for investigating the role of mechanical cues in axon regeneration in the injured spinal cord.