Mechanical Characterization and Modeling of the Porcine Cerebral Meninges

Investigation of direction- and age-dependent prestretch in mouse cranial dura mater

Cranial dura mater is a dense interwoven vascularized connective tissue that helps regulate neurocranial remodeling by responding to strains from the growing brain. Previous ex vivo experimentation has failed to account for the role of prestretch in the mechanical behavior of the dura. Here we aim to estimate the prestretch in mouse cranial dura mater and determine its dependency on direction and age. We performed transverse and longitudinal incisions in parietal dura excised from newborn (day ∼ 4) and mature (12 weeks) mice and calculated the ex vivo normalized incision opening (measured width over length). Then, similar incisions were simulated under isotropic stretching within Abaqus/Standard. Finally, prestretch was estimated by comparing the ex vivo and in silico normalized openings. There were no significant differences between the neonatal and adult mice when comparing cuts in the same direction, but adult mice were found to have significantly greater stretch in the anterior-posterior direction than in the medial-lateral direction, while neonatal dura was essentially isotropic. Additionally, our simulations show that increasing curvature impacts the incision opening, indicating that flat in silico models may overestimate prestretch.

Sample size considerations in soft tissue biomechanics

Biomechanical experiments help link tissue morphology with load-deformation characteristics. A tissue-dependent minimum sample number is indispensable to obtain accurate material properties. Stress-strain properties were retrieved from human dura mater and scalp skin, exemplifying two distinct soft tissues. Minimum sample sizes necessary for a stable estimation of material properties were obtained in a simulation study. One-thousand random samples were sequentially drawn for calculating the point at which a majority of the estimators settled within a corridor of stability at given tolerance levels around a 'complete' reference for the mean, median and coefficient of variation. Stable estimations of means and medians can be achieved below sample sizes of 30 at a ± 20%-tolerance within 80%-conformity for scalp skin and dura. Lower tolerance levels or higher conformity dramatically increase the required sample size. Conformity was barely ever reached for the coefficient of variation. The parameter type appears decisive for achieving conformity. STATEMENT OF SIGNIFICANCE: Biomechanical trials utilizing human tissues are needed to obtain material properties for surgical repair, tissue engineering and modeling purposes. Linking tissue mechanics with morphology helps elucidate form-function relationships, the 'morpho-mechanical link'. For material properties to be accurate, it is vital to examine a minimum number of samples. This number may vary between tissues, and the effects of intrinsic tissue characteristics on data accuracy are unclear to date. This study used data obtained from human dura and skin to compute minimum sample sizes required for estimating material properties at a stable level. It was shown that stable estimations are possible at a ± 20%-tolerance within 80%-conformity below sample sizes of 30. Higher accuracy warrants much higher sample sizes for most material properties.

Tensile properties of human spinal dura mater and pericranium

Autologous pericranium is a promising dural graft material. An optimal graft should exhibit similar mechanical properties to the native dura, but the mechanical properties of human pericranium have not been characterized, and studies of the biomechanical performance of human spinal dura are limited. The primary aim of this study was to measure the tensile structural and material properties of the pericranium, in the longitudinal and circumferential directions, and of the dura in each spinal region (cervical, thoracic and lumbar) and in three directions (longitudinal anterior and posterior, and circumferential). The secondary aim was to determine corresponding constitutive stress-strain equations using a one-term Ogden model. A total of 146 specimens were tested from 7 cadavers. Linear regression models assessed the effect of tissue type, region, and orientation on the structural and material properties. Pericranium was isotropic, while spinal dura was anisotropic with higher stiffness and strength in the longitudinal than the circumferential direction. Pericranium had lower strength and modulus than spinal dura across all regions in the longitudinal direction but was stronger and stiffer than dura in the circumferential direction. Spinal dura and pericranium had similar strain at peak force, toe, and yield, across all regions and directions. Human pericranium exhibits isotropic mechanical behavior that lies between that of the longitudinal and circumferential spinal dura. Further studies are required to determine if pericranium grafts behave like native dura under in vivo loading conditions. The Ogden parameters reported may be used for computational modeling of the central nervous system. Graphical abstract.

Experimental Bi-axial tensile tests of spinal meningeal tissues and constitutive models comparison

Introduction This study aims at identifying mechanical characteristics under bi-axial loading conditions of extracted swine pia mater (PM) and dura and arachnoid complex (DAC). Methods 59 porcine spinal samples have been tested on a bi-axial experimental device with a pre-load of 0.01 N and a displacement rate of 0.05 mm·s^-1. Post-processing analysis included an elastic modulus, as well as constitutive model identification for Ogden model, reduced Gasser Ogden Holzapfel (GOH) model, anisotropic GOH model, transverse isotropic and anisotropic Gasser models as well as a Mooney-Rivlin model including fiber strengthening for PM. Additionally, micro-structure of the tissue was investigated using a bi-photon microscopy. Results Linear elastic moduli of 108 ± 40 MPa were found for DAC longitudinal direction, 53 ± 32 MPa for DAC circumferential direction, with a significant difference between directions (p < 0.001). PM presented significantly higher longitudinal than circumferential elastic moduli (26 ± 13 MPa vs 13 ± 9 MPa, p < 0.001). Transversely isotropic and anisotropic Gasser models were the most suited models for DAC (r²  =  0.99 and RMSE:0.4 and 0.3 MPa) and PM (r² = 1 and RMSE:0.06 and 0.07 MPa) modelling. Conclusion This work provides reference values for further quasi-static bi-axial studies, and is the first for PM. Collagen structures observed by two photon microscopy confirmed the use of anisotropic Gasser model for PM and the existence of fenestration. The results from anisotropic Gasser model analysis depicted the best fit to experimental data as per this protocol. Further investigations are required to allow the use of meningeal tissue mechanical behaviour in finite element modelling with respect to physiological applications. STATEMENT OF SIGNIFICANCE: This study is the first to present biaxial tensile test of pia mater as well as constitutive model comparisons for dura and arachnoid complex tissue based on such tests. Collagen structures observed by semi-quantitative analysis of two photon microscopy confirmed the use of anisotropic Gasser model for pia mater and existence of fenestration. While clear identification of fibre population was not possible in DAC, results from anisotropic Gasser model depicted better fitting on experimental data as per this protocol. Bi-axial mechanical testing allows quasi-static characterization under conditions closer to the physiological context and the results presented could be used for further simulations of physiology. Indeed, the inclusion of meningeal tissue in finite element models will allow more accurate and reliable numerical simulations.

A 3-D Finite-Element Minipig Model to Assess Brain Biomechanical Responses to Blast Exposure

Despite years of research, it is still unknown whether the interaction of explosion-induced blast waves with the head causes injury to the human brain. One way to fill this gap is to use animal models to establish “scaling laws” that project observed brain injuries in animals to humans. This requires laboratory experiments and high-fidelity mathematical models of the animal head to establish correlates between experimentally observed blast-induced brain injuries and model-predicted biomechanical responses. To this end, we performed laboratory experiments on Göttingen minipigs to develop and validate a three-dimensional (3-D) high-fidelity finite-element (FE) model of the minipig head. First, we performed laboratory experiments on Göttingen minipigs to obtain the geometry of the cerebral vasculature network and to characterize brain-tissue and vasculature material properties in response to high strain rates typical of blast exposures. Next, we used the detailed cerebral vasculature information and species-specific brain tissue and vasculature material properties to develop the 3-D high-fidelity FE model of the minipig head. Then, to validate the model predictions, we performed laboratory shock-tube experiments, where we exposed Göttingen minipigs to a blast overpressure of 210 kPa in a laboratory shock tube and compared brain pressures at two locations. We observed a good agreement between the model-predicted pressures and the experimental measurements, with differences in maximum pressure of less than 6%. Finally, to evaluate the influence of the cerebral vascular network on the biomechanical predictions, we performed simulations where we compared results of FE models with and without the vasculature. As expected, incorporation of the vasculature decreased brain strain but did not affect the predictions of brain pressure. However, we observed that inclusion of the cerebral vasculature in the model changed the strain distribution by as much as 100% in regions near the interface between the vasculature and the brain tissue, suggesting that the vasculature does not merely decrease the strain but causes drastic redistributions. This work will help establish correlates between observed brain injuries and predicted biomechanical responses in minipigs and facilitate the creation of scaling laws to infer potential injuries in the human brain due to exposure to blast waves.

Mechanical properties of porcine spinal dura mater and pericranium

BACKGROUND

The objective of this study was to characterize and compare the mechanical properties of porcine pericranium and spinal dura mater, to evaluate the mechanical suitability of pericranium as a dural graft.

METHOD

Eighty-eight spinal dura (cervical, thoracic, and lumbar regions, in ventral longitudinal, dorsal longitudinal and circumferential orientations) and eighteen pericranium samples (ventral-dorsal, and lateral orientations) from four pigs, were harvested and subjected to uniaxial loading while hydrated. The stiffness, strain at toe-linear regions transition, strain at linear-yield regions transition and other structural and mechanical properties were measured. Stress-strain curves were fitted to a one-term Ogden model and Ogden parameters were calculated. Linear regression models with cluster-robust standard errors were used to assess the effect of region and orientation on material and structural properties.

RESULTS

Both spinal dura and pericranium exhibited distinct anisotropy and were stiffer in the longitudinal direction. The tissues exhibited structural and mechanical similarities especially in terms of stiffness and strains in the linear region. Stiffness ranged from 1.28 to 5.32 N/mm for spinal dura and 2.42-3.90 N/mm for pericranium. In the circumferential and longitudinal directions, the stiffness of spinal dura specimens was statistically similar to that of pericranium in the same orientation. The strain at the upper bound of the linear region of longitudinal pericranium (28.0%) was statistically similar to that of any spinal dura specimens (24.4-32.9%).

CONCLUSIONS

Autologous pericranium has advantageous physical properties for spinal duraplasty. The present study demonstrated that longitudinally oriented pericranium is mechanically compatible with spinal duraplasty procedures. Autologous pericranium grafts will likely support the mechanical loads transmitted from the spinal dura, but further biomechanical analyses are required to study the effect of the lower yield strain of circumferential pericranium compared to spinal dura. Finally, the Ogden parameters calculated for pericranium, and the spinal dura at each spinal level, will be useful for computational models incorporating these soft tissues.

A Machine Learning Approach to Investigate the Uncertainty of Tissue-Level Injury Metrics for Cerebral Contusion

Controlled cortical impact (CCI) on porcine brain is often utilized to investigate the pathophysiology and functional outcome of focal traumatic brain injury (TBI), such as cerebral contusion (CC). Using a finite element (FE) model of the porcine brain, the localized brain strain and strain rate resulting from CCI can be computed and compared to the experimentally assessed cortical lesion. This way, tissue-level injury metrics and corresponding thresholds specific for CC can be established. However, the variability and uncertainty associated with the CCI experimental parameters contribute to the uncertainty of the provoked cortical lesion and, in turn, of the predicted injury metrics. Uncertainty quantification via probabilistic methods (Monte Carlo simulation, MCS) requires a large number of FE simulations, which results in a time-consuming process. Following the recent success of machine learning (ML) in TBI biomechanical modeling, we developed an artificial neural network as surrogate of the FE porcine brain model to predict the brain strain and the strain rate in a computationally efficient way. We assessed the effect of several experimental and modeling parameters on four FE-derived CC injury metrics (maximum principal strain, maximum principal strain rate, product of maximum principal strain and strain rate, and maximum shear strain). Next, we compared the in silico brain mechanical response with cortical damage data from in vivo CCI experiments on pig brains to evaluate the predictive performance of the CC injury metrics. Our ML surrogate was capable of rapidly predicting the outcome of the FE porcine brain undergoing CCI. The now computationally efficient MCS showed that depth and velocity of indentation were the most influential parameters for the strain and the strain rate-based injury metrics, respectively. The sensitivity analysis and comparison with the cortical damage experimental data indicate a better performance of maximum principal strain and maximum shear strain as tissue-level injury metrics for CC. These results provide guidelines to optimize the design of CCI tests and bring new insights to the understanding of the mechanical response of brain tissue to focal traumatic brain injury. Our findings also highlight the potential of using ML for computationally efficient TBI biomechanics investigations.