Johannes Weickenmeier

Brain stiffness increases with myelin content

UNLABELLED Brain stiffness plays an important role in neuronal development and disease, but reported stiffness values vary significantly for different species, for different brains, and even for different regions within the same brain. Despite extensive research throughout the past decade, the mechanistic origin of these stiffness variations remains elusive. Here we show that brain tissue stiffness is correlated to the underlying tissue microstructure and directly proportional to the local myelin content. In 116 indentation tests of six freshly harvested bovine brains, we found that the cerebral stiffnesses of 1.33±0.63kPa in white matter and 0.68±0.20kPa in gray matter were significantly different (p<0.01). Strikingly, while the inter-specimen variation was rather moderate, the minimum and maximum cerebral white matter stiffnesses of 0.59±0.19 kPa and 2.36±0.64kPa in each brain varied by a factor of four on average. To provide a mechanistic interpretation for this variation, we performed a histological characterization of the tested brain regions. We stained the samples with hematoxylin and eosin and luxol fast blue and quantified the local myelin content using image analysis. Interestingly, we found that the cerebral white matter stiffness increased with increasing myelin content, from 0.72kPa at a myelin content of 64-2.45kPa at a myelin content of 89%, with a Pearson correlation coefficient of ρ=0.91 (p<0.01). This direct correlation could have significant neurological implications. During development, our results could help explain why immature, incompletely myelinated brains are softer than mature, myelinated brains and more vulnerable to mechanical insult as evident, for example, in shaken baby syndrome. During demyelinating disease, our findings suggest to use stiffness alterations as clinical markers for demyelination to quantify the onset of disease progression, for example, in multiple sclerosis. Taken together, our study indicates that myelin might play a more important function than previously thought: It not only insulates signal propagation and improves electrical function of single axons, it also provides structural support and mechanical stiffness to the brain as a whole. STATEMENT OF SIGNIFICANCE Increasing evidence suggests that the mechanical environment of the brain plays an important role in neuronal development and disease. Reported stiffness values vary significantly, but the origin of these variations remains unknown. Here we show that stiffness of our brain is correlated to the underlying tissue microstructure and directly proportional to the local myelin content. Myelin has been discovered in 1854 as an insulating layer around nerve cells to improve electric signal propagation. Our study now shows that it also plays an important mechanical role: Using a combined mechanical characterization and histological characterization, we found that the white matter stiffness increases linearly with increasing myelin content, from 0.5kPa at a myelin content of 63-2.5kPa at 92%.

Suction based mechanical characterization of superficial facial soft tissues

The present study is aimed at a combined experimental and numerical investigation of the mechanical response of superficial facial tissues. Suction based experiments provide the location, time, and history dependent behavior of skin and SMAS (superficial musculoaponeurotic system) by means of Cutometer and Aspiration measurements. The suction method is particularly suitable for in vivo, multi-axial testing of soft biological tissue including a high repeatability in subsequent tests. The campaign comprises three measurement sites in the face, i.e. jaw, parotid, and forehead, using two different loading profiles (instantaneous loading and a linearly increasing and decreasing loading curve), multiple loading magnitudes, and cyclic loading cases to quantify history dependent behavior. In an inverse finite element analysis based on anatomically detailed models an optimized set of material parameters for the implementation of an elastic-viscoplastic material model was determined, yielding an initial shear modulus of 2.32kPa for skin and 0.05kPa for SMAS, respectively. Apex displacements at maximum instantaneous and linear loading showed significant location specificity with variations of up to 18% with respect to the facial average response while observing variations in repeated measurements in the same location of less than 12%. In summary, the proposed parameter sets for skin and SMAS are shown to provide remarkable agreement between the experimentally observed and numerically predicted tissue response under all loading conditions considered in the present study, including cyclic tests.

Elastic–viscoplastic modeling of soft biological tissues using a mixed finite element formulation based on the relative deformation gradient

The characteristic highly nonlinear, time-dependent, and often inelastic material response of soft biological tissues can be expressed in a set of elastic-viscoplastic constitutive equations. The specific elastic-viscoplastic model for soft tissues proposed by Rubin and Bodner (2002) is generalized with respect to the constitutive equations for the scalar quantity of the rate of inelasticity and the hardening parameter in order to represent a general framework for elastic-viscoplastic models. A strongly objective integration scheme and a new mixed finite element formulation were developed based on the introduction of the relative deformation gradient-the deformation mapping between the last converged and current configurations. The numerical implementation of both the generalized framework and the specific Rubin and Bodner model is presented. As an example of a challenging application of the new model equations, the mechanical response of facial skin tissue is characterized through an experimental campaign based on the suction method. The measurement data are used for the identification of a suitable set of model parameters that well represents the experimentally observed tissue behavior. Two different measurement protocols were defined to address specific tissue properties with respect to the instantaneous tissue response, inelasticity, and tissue recovery.

A physically motivated constitutive model for 3D numerical simulation of skeletal muscles.

A detailed numerical implementation within the FEM is presented for a physically motivated three-dimensional constitutive model describing the passive and active mechanical behaviors of the skeletal muscle. The derivations for the Cauchy stress tensor and the consistent material tangent are provided. For nearly incompressible skeletal muscle tissue, the strain energy function may be represented either by a coupling or a decoupling of the distortional and volumetric material response. In the present paper, both functionally different formulations are introduced allowing for a direct comparison between the coupled and decoupled isochoric-volumetric approach. The numerical validation of both implementations revealed significant limitations for the decoupled approach. For an extensive characterization of the model response to different muscle contraction modes, a benchmark model is introduced. Finally, the proposed implementation is shown to provide a reliable tool for the analysis of complex and highly nonlinear problems through the example of the human mastication system by studying bite force and three-dimensional muscle shape changes during mastication.

The mechanical importance of myelination in the central nervous system

Neurons in the central nervous system are surrounded and cross-linked by myelin, a fatty white substance that wraps around axons to create an electrically insulating layer. The electrical function of myelin is widely recognized; yet, its mechanical importance remains underestimated. Here we combined nanoindentation testing and histological staining to correlate brain stiffness to the degree of myelination in immature, pre-natal brains and mature, post-natal brains. We found that both gray and white matter tissue stiffened significantly (p≪0.001) upon maturation: the gray matter stiffness doubled from 0.31±0.20kPa pre-natally to 0.68±0.20kPa post-natally; the white matter stiffness tripled from 0.45±0.18kPa pre-natally to 1.33±0.64kPa post-natally. At the same time, the white matter myelin content increased significantly (p≪0.001) from 58±2% to 74±9%. White matter stiffness and myelin content were correlated with a Pearson correlation coefficient of ρ=0.92 (p≪0.001). Our study suggests that myelin is not only important to ensure smooth electrical signal propagation in neurons, but also to protect neurons against physical forces and provide a strong microstructural network that stiffens the white matter tissue as a whole. Our results suggest that brain tissue stiffness could serve as a biomarker for multiple sclerosis and other forms of demyelinating disorders. Understanding how tissue maturation translates into changes in mechanical properties and knowing the precise brain stiffness at different stages of life has important medical implications in development, aging, and neurodegeneration.

Magnetic resonance elastography of the brain: A comparison between pigs and humans

Magnetic resonance elastography holds promise as a non-invasive, easy-to-use, in vivo biomarker for neurodegenerative diseases. Throughout the past decade, pigs have gained increased popularity as large animal models for human neurodegeneration. However, the volume of a pig brain is an order of magnitude smaller than the human brain, its skull is 40% thicker, and its head is about twice as big. This raises the question to which extent established vibration devices, actuation frequencies, and analysis tools for humans translate to large animal studies in pigs. Here we explored the feasibility of using human brain magnetic resonance elastography to characterize the dynamic properties of the porcine brain. In contrast to humans, where vibration devices induce an anterior-posterior displacement recorded in transverse sections, the porcine anatomy requires a dorsal-ventral displacement recorded in coronal sections. Within these settings, we applied a wide range of actuation frequencies, from 40Hz to 90Hz, and recorded the storage and loss moduli for human and porcine brains. Strikingly, we found that optimal actuation frequencies for humans translate one-to-one to pigs and reliably generate shear waves for elastographic post-processing. In a direct comparison, human and porcine storage and loss moduli followed similar trends and increased with increasing frequency. When translating these frequency-dependent storage and loss moduli into the frequency-independent stiffnesses and viscosities of a standard linear solid model, we found human values of μ1=1.3kPa, μ2=2.1kPa, and η=0.025kPas and porcine values of μ1=2.0kPa, μ2=4.9kPa, and η=0.046kPas. These results suggest that living human brain is softer and less viscous than dead porcine brain. Our study compares, for the first time, magnetic resonance elastography in human and porcine brains, and paves the way towards systematic interspecies comparison studies and ex vivo validation of magnetic resonance elastography as a whole.

Brain stiffens post mortem

Alterations in brain rheology are increasingly recognized as a diagnostic marker for various neurological conditions. Magnetic resonance elastography now allows us to assess brain rheology repeatably, reproducibly, and non-invasively in vivo. Recent elastography studies suggest that brain stiffness decreases one percent per year during normal aging, and is significantly reduced in Alzheimer’s disease and multiple sclerosis. While existing studies successfully compare brain stiffnesses across different populations, they fail to provide insight into changes within the same brain. Here we characterize rheological alterations in one and the same brain under extreme metabolic changes: alive and dead. Strikingly, the storage and loss moduli of the cerebrum increased by 26% and 60% within only three minutes post mortem and continued to increase by 40% and 103% within 45 minutes. Immediate post mortem stiffening displayed pronounced regional variations; it was largest in the corpus callosum and smallest in the brainstem. We postulate that post mortem stiffening is a manifestation of alterations in polarization, oxidation, perfusion, and metabolism immediately after death. Our results suggest that the stiffness of our brain–unlike any other organ–is a dynamic property that is highly sensitive to the metabolic environment Our findings emphasize the importance of characterizing brain tissue in vivo and question the relevance of ex vivo brain tissue testing as a whole. Knowing the true stiffness of the living brain has important consequences in diagnosing neurological conditions, planning neurosurgical procedures, and modeling the brain’s response to high impact loading.

Experimental Characterization and Simulation of Layer Interaction in Facial Soft Tissues

Anatomically detailed modeling of soft tissue structures such as the forehead plays an important role in physics based simulations of facial expressions, for surgery planning, and implant design. We present ultrasound measurements of through-layer tissue deformation in different regions of the forehead. These data were used to determine the local dependence of tissue interaction properties in terms of variations in the relative deformation between individual layers. A physically based finite element model of the forehead is developed and simulations are compared with measurements in order to validate local tissue interaction properties. The model is used for simulation of forehead wrinkling during frontalis muscle contraction.

Location-specific mechanical response and morphology of facial soft tissues

The facial tissue of 9 healthy volunteers (m/f; age: 23-60y) is characterized at three different locations using a procedure combining suction measurements and 18MHz ultrasound imaging. The time-dependent and multilayered nature of skin is accounted for by adopting multiple loading protocols which differ with respect to suction probe opening size and rate of tissue deformation. Over 700 suction measurements were conducted and analyzed according to location-specific mechanical and morphological characteristics. All corresponding data are reported and made available for facial tissue analysis and biomechanical modeling. Higher skin stiffness is measured at the forehead in comparison to jaw and parotid; these two regions are further characterized by lower creep deformation. Thicker tissue regions display a tendency towards a more compliant and less dissipative response. Comparison of superficial layer thickness and corresponding mechanical measurements suggests that connective tissue density determines the resistance to deformation in suction experiments.

Dimensional, Geometrical, and Physical Constraints in Skull Growth

After birth, the skull grows and remodels in close synchrony with the brain to allow for an increase in intracranial volume. Increase in skull area is provided primarily by bone accretion at the sutures. Additional remodeling, to allow for a change in curvatures, occurs by resorption on the inner surface of the bone plates and accretion on their outer surfaces. When a suture fuses too early, normal skull growth is disrupted, leading to a deformed final skull shape. The leading theory assumes that the main stimulus for skull growth is provided by mechanical stresses. Based on these ideas, we first discuss the dimensional, geometrical, and kinematic synchrony between brain, skull, and suture growth. Second, we present two mechanical models for skull growth that account for growth at the sutures and explain the various observed dysmorphologies. These models demonstrate the particular role of physical and geometrical constraints taking place in skull growth.