Quantitative imaging methods for the development and validation of brain biomechanics models

Abstract

Rapid deformation of brain tissue in response to head impact or acceleration can lead to numerous pathological changes, both immediate and delayed. Modeling and simulation hold promise for illuminating the mechanisms of traumatic brain injury (TBI) and for developing preventive devices and strategies. However, mathematical models have predictive value only if they satisfy two conditions. First, they must capture the biomechanics of the brain as both a material and a structure, including the mechanics of brain tissue and its interactions with the skull. Second, they must be validated by direct comparison with experimental data. Emerging imaging technologies and recent imaging studies provide important data for these purposes. This review describes these techniques and data, with an emphasis on magnetic resonance imaging approaches. In combination, these imaging tools promise to extend our understanding of brain biomechanics and improve our ability to study TBI in silico.

Figure 1

The technology underlying the physical discretization of computational models of the human head can now produce remarkable anatomic accuracy and predictions of mechanical fields at very fine spatial resolution. However, mathematical models and material data for the tissues, structures, and interactions within the brain have lagged behind, as have data for validation of model predictions. This review summarizes the state of the art in the collection of such data on brain biomechanics in vivo. Adapted from Reference 28, with permission.

Figure 2

The earliest estimates of acceleration-induced shear strain fields within the human brain are those of Holbourn (40), who observed shear deformation patterns within gelatin-filled skulls due to occipital impact and angular acceleration/lateral impact. The scale bar represents the relative magnitude of shear in arbitrary units. Recent magnetic resonance imaging data have shown that shear strain patterns within a gelatin-filled skull differ fundamentally from those within a living human owing to several factors including brain architecture, vasculature, and attachment to the skull. Adapted from Reference 40.

Figure 3

High-speed and high-resolution videography techniques have enabled studies of physical models of the brain that undergo large deformations at high strain rates. The skull of a miniature pig was filled with two layers of silicone gel; a grid pattern was painted between the layers. The assembly was subjected to angular accelerations of 50,000–200,000 rad s⁻² while grid deformation was recorded at 1,000 frames per second. Adapted from Reference 42.

Figure 4

Progress on understanding acceleration-induced strain in the animal brain in situ has been made through high-speed video studies. The exposed flat surface of the hemisected brain of a juvenile pig was marked with India ink (a), and the skull and brain were covered by a layer of lubricant and by a transparent Plexiglas cover plate. Strain fields were estimated from marker positions (b) during an angular acceleration pulse with a peak magnitude of ∼10,000 m s⁻². Reproduced from Reference 43.

Figure 5

High-speed video techniques have been applied to image thin slices of brain tissue subjected to high accelerations in vitro, to gain information about their mechanical response at high strains and strain rates. The trade-off is the absence of the natural structural attachments and mechanical environment of the brain. Here, displacement (a) and strain fields (b) are shown at 12 ms (top) and 23 ms (bottom) postimpact, measured in sagittal slices (4 mm thick) of a pig brain encapsulated with artificial cerebrospinal fluid in a rigid cavity and subjected to linear accelerations of approximately 2,000 m s⁻². In panel a, the uppercase letters A–E indicate areas where tissue heterogeneity is observed to affect the displacement field; in panel b, the letters F and G indicate vertical (F) and horizontal (G) sulci. Adapted from Reference 44.

Figure 6

Tagged magnetic resonance (MR) images provide the ability to track displacement of tissue in human volunteers. These images are obtained by modulating the longitudinal magnetization of spin packets. Transient sinusoidal patterns of longitudinal magnetization are produced noninvasively in tissue by the combination of radiofrequency pulses and magnetic field gradients; the remainder of the MR pulse sequence is a standard fast gradient-echo scheme. The resulting tagged image (c) is a product of the spin-density image (a) and the sinusoidal pattern (b).

Figure 7

Magnetic resonance (MR) tagging approaches provide data on the relative motion and interactions of structures within the brain. Shown here is the first-ever evidence of relative rotations of brain structures during a normal physiological motion. Cerebellar displacement was measured from tagged MR images of the brain acquired in vivo during voluntary quasi-static flexion of the neck, and the cerebellum was found to rotate relative to both the skull and surrounding tissue. Reproduced from Reference 57.

Figure 8

Mechanical strains can be extracted semiautomatically from tagged magnetic resonance images. Here, the procedure is applied to estimate intracranial strains resulting from angular deceleration of the skull. The reference images acquired prior to initiation of head motion (a–d) are compared with the deformed images (e–h). The centers of taglines in the images shown in panels a and e are detected by the harmonic phase algorithm and superimposed in yellow in panels b and f. Triangular meshes (c,g) are compared to estimate deformation gradients, and (dimensionless) strain fields (d,h) are estimated from the deformation gradients. In panels d and h, the displacements are amplified by a factor of 5 for illustration. Adapted from Reference 60. See also Supplemental Movie 1 (follow the Supplemental Materials link from the Annual Reviews home page at http://www.annualreviews.org).

Figure 9

Deformations associated with mild, physiological impact result in peak strains of up to 5%. The (dimensionless) strain fields shown (color bar) were superimposed over displacement fields in tagged images of the brain acquired during mild occipital impact. (a–c) Sagittal images. (a) Baseline shear strain, E_xy (undeformed). (b) Normal strain, E_xx. (c) Shear strain, E_xy . (d–f) Transverse images. (d) Baseline shear strain, E_xy (undeformed). (e, f) Deformed brain normal strain E_yy and shear strain E_xy. Adapted from Reference 59.

Figure 10

Magnetic resonance (MR) studies have shown that sliding of the brain relative to the skull is attenuated at regions of attachment between the brain and meninges, and that rotation is a dominant mode of the response of the brain to physiological linear acceleration of the head. Relative displacements of the brain with respect to the skull are shown, estimated from tagged MR images acquired during mild frontal impact. (a) Tagged reference image with markers (yellow dots) on reference points that move with the skull. (b) Summed tagged images acquired at 6-ms intervals during the head drop and deceleration. The trajectories of the marker points are shown as red arrows; the position and orientation of a skull-fixed coordinate system are shown as green lines. (c) Contour maps of the relative displacement of the brain with respect to the skull-fixed coordinate system. See Supplemental Movie 2. Adapted from Reference 62.

Figure 11

Phase-contrast MRI allows high spatial resolution imaging of the three-dimensional displacement and strain fields in the moving brains of live human subjects. Shown here is the strain tensor field in the human brain due to normal pulsatile motion of the brain parenchyma. Box icons are color coded and scaled to represent the eigenvalues λ_i and scaled eigenvectors υ_i(λ_i) of the strain rate tensor at each voxel. Adapted from Reference 68.

Figure 12

Magnetic resonance elastography (MRE) produces estimates of intracranial displacement fields observed in response to dynamic pressure loading of the skull. These can be inverted to estimate spatially varying mechanical properties of brain tissue. Example displacement fields shown here are obtained from a single-slice multifrequency MRE experiment. (a) Standard MR anatomical images: T1-weighted (T1w), proton density (PD), and T2-weighted (T2w) contrast. (b) Wave images and parameter fields. U′ and U″ denote the real and imaginary parts of the first harmonic component U(x, y, ω) of the displacement field. The complex modulus images (G′ and G″) denote the real and imaginary parts of the complex shear modulus G(x, y, ω). The driving frequencies are given above the columns. Reproduced from Reference 99.

Figure 13

Magnetic resonance elastography (MRE) provides noninvasive estimates of living brain tissue in human volunteers. MRE-based estimates of brain tissue shear modulus vary among different studies but lie within the range of estimates obtained in vitro by direct mechanical tests. Adapted from Reference 104.

Figure 14

Intracranial strain and strain rate fields are important in understanding the response of brain tissue to mechanical trauma, but injury mechanisms are complicated. Although strain fields are clearly related to apoptotic cell death in a closed-head model of traumatic brain injury in the juvenile rat, cell death is not directly colocalized with strain, and much injury occurs downstream of regions of high strain. (a, b) Schematic depictions of coronal (a) and sagittal (b) sections of the juvenile (P7) rat brain, illustrating the pattern of (dimensionless) strain magnitude during parasagittal indentation of the flexible skull. The location of the impactor tip is shown by the solid horizontal line. (c,d,e) Activated caspase-3-stained sections from a P8 rat brain 24 h postimpact; caspase-3 is a sensitive indicator of apoptosis. Arrows in panels c and e indicate the direction of impact and the center of the impact site. Panels c and d are coronal sections cut in a rostrocaudal plane slightly caudal to the impact site (c), or at a much more caudal level (d). These sections show that the delayed pathological reaction at the cerebrocortical level is primarily concentrated medial to the point of impact. Panel e is a sagittal section revealing that this cerebrocortical delayed pathological reaction extends in a caudal (but not rostral) direction. Reproduced from Reference 45.