Development and validation of subject-specific 3D human head models based on a nonlinear visco-hyperelastic constitutive framework

Abstract

Computational head models are promising tools for understanding and predicting traumatic brain injuries. Most available head models are developed using inputs (i.e. head geometry, material properties and boundary conditions) from experiments on cadavers or animals and employ hereditary integral-based constitutive models that assume linear viscoelasticity in part of the rate-sensitive material response. This leads to high uncertainty and poor accuracy in capturing the nonlinear brain tissue response. To resolve these issues, a framework for the development of subject-specific three-dimensional head models is proposed, in which all inputs are derived in vivo from the same living human subject: head geometry via magnetic resonance imaging (MRI), brain tissue properties via magnetic resonance elastography (MRE), and full-field strain-response of the brain under rapid head rotation via tagged MRI. A nonlinear, viscous dissipation-based visco-hyperelastic constitutive model is employed to capture brain tissue response. Head models are validated using quantitative metrics that compare spatial strain distribution, temporal strain evolution, and the magnitude of strain maxima, with the corresponding experimental observations from tagged MRI. Results show that our head models accurately capture the strain-response of the brain. Further, employment of the nonlinear visco-hyperelastic constitutive framework provides improvements in the prediction of peak strains and temporal strain evolution over hereditary integral-based models.

The white matter fiber tract deforms most in the perpendicular direction duringin vivovolunteer impacts

“…This may be particularly relevant for those models with intended usage to predict the brain response under non-injurious impacts. Emerging attempts have been noted in validating the computational head model against in vivo brain responses in the form of brain-skull relative displacement [69], maximum principal strain [21, 22, 67, 70], maximum shear strain [67], and tract-oriented normal strain [21, 22]. Our study computes 3D normal and shear strains along and perpendicular to the fiber tract (spatial resolution: 1 mm or 2 mm, temporal resolution: 18 ms, 19.5 ms,or 20 ms) across the whole WM from 44 volunteer impacts.…”

Physics-informed data-driven discovery of constitutive models with application to strain-rate-sensitive soft materials

“…Here, limited memory means that the viscous material behavior is dependent only on the instantaneous deformation rate (i.e., very recent history), and dependence on the entire previous loading history (often described via a hereditary-integral) is neglected. First proposed by Pioletti et al [39], constitutive models within this framework have been employed to successfully capture the rate-dependent response of numerous soft materials under rapid loading: human ligaments and tendons [41,47,48], skeletal muscles [49], hydrogels and elastomers [30,33], tongue tissue [50], and the brain and pericardium [22,51,52], among others. These studies assume specific mathematical forms for U (J ), Wh ( Ī1 , Ī2 ) and Wv ( Ī1 , Ī2 , J1 , J2 , J3 , J4 , J5 , J6 , J7 ) based on expert knowledge and experience.…”

“…Superscripts i, j, and k denote a particular data point in the datasets D vol , D h,iso , and D v,iso , respectively. A dataset like D for a soft material can be obtained in practice by compiling its hydrostatic stress-strain data as D vol [53,54], quasi-static stress-strain data under uniaxial and/or shear deformations as D h,iso [55,56], and viscous overstress (total stress minus stress under quasi-static loading)-strain data from high strain rate testing at multiple strain rate levels under uniaxial and/or shear deformations as D v,iso [21,33,54,55,57]. For every data point in the dataset D, the inputs C and Ċ can be used to compute the set of invariants (using Eqs.…”

“…In Eqs. (32)(33)(34), the accent symbols • over stress and coefficients of the integrity basis denote that these are predicted values from the surrogate models. Note, for any given input strain and strain rate, the components of the integrity basis G can be obtained using Eq.…”

“…Note that strain rate-dependence in visco-hyperelasticity can be classified into short-time (e.g., high strain rate deformation) and long-time (e.g., creep and relaxation) responses [30]. This work focuses only on the short-time response, which is of special interest in the field of injury biomechanics (e.g., simulations of crashes, blast, and ballistic impact) and in the design of protective equipment [31][32][33][34].…”