Sebastian Hirsch

In vivo waveguide elastography of white matter tracts in the human brain

White matter is composed primarily of myelinated axons which form fibrous, organized structures and can act as waveguides for the anisotropic propagation of sound. The evaluation of their elastic properties requires both knowledge of the orientation of these waveguides in space, as well as knowledge of the waves propagating along and through them. Here, we present waveguide elastography for the evaluation of the elastic properties of white matter tracts in the human brain, in vivo, using a fusion of diffusion tensor imaging, magnetic resonance elastography, spatial‐spectral filtering, a Helmholtz decomposition, and anisotropic inversions, and apply this method to evaluate the material parameters of the corticospinal tracts of five healthy human volunteers. We begin with an Orthotropic inversion model and demonstrate that redundancies in the solution for the nine elastic coefficients indicate that the corticospinal tracts can be approximated by a Hexagonal model (transverse isotropy) comprised of five elastic coefficients representative of a medium with fibers aligned parallel to a central axis, and provides longitudinal and transverse wave velocities on the order of 5.7 m/s and 2.1 m/s, respectively. This method is intended as a new modality to assess white matter structure and health by means of the evaluation of the anisotropic elasticity tensor of nerve fibers. Magn Reson Med, 2012.

Multifrequency inversion in magnetic resonance elastography

Time-harmonic shear wave elastography is capable of measuring viscoelastic parameters in living tissue. However, finite tissue boundaries and waveguide effects give rise to wave interferences which are not accounted for by standard elasticity reconstruction methods. Furthermore, the viscoelasticity of tissue causes dispersion of the complex shear modulus, rendering the recovered moduli frequency dependent. Therefore, we here propose the use of multifrequency wave data from magnetic resonance elastography (MRE) for solving the inverse problem of viscoelasticity reconstruction by an algebraic least-squares solution based on the springpot model. Advantages of the method are twofold: (i) amplitude nulls appearing in single-frequency standing wave patterns are mitigated and (ii) the dispersion of storage and loss modulus with drive frequency is taken into account by the inversion procedure, thereby avoiding subsequent model fitting. As a result, multifrequency inversion produces fewer artifacts in the viscoelastic parameter map than standard single-frequency parameter recovery and may thus support image-based viscoelasticity measurement. The feasibility of the method is demonstrated by simulated wave data and MRE experiments on a phantom and in vivo human brain. Implemented as a clinical method, multifrequency inversion may improve the diagnostic value of time-harmonic MRE in a large variety of applications.

MR elastography of the liver and the spleen using a piezoelectric driver, single-shot wave-field acquisition, and multifrequency dual parameter reconstruction.

Viscoelastic properties of the liver are sensitive to fibrosis. This study proposes several modifications to existing magnetic resonance elastography (MRE) techniques to improve the accuracy of abdominal MRE.

Towards an elastographic atlas of brain anatomy.

Cerebral viscoelastic constants can be measured in a noninvasive, image-based way by magnetic resonance elastography (MRE) for the detection of neurological disorders. However, MRE brain maps of viscoelastic constants are still limited by low spatial resolution. Here we introduce three-dimensional multifrequency MRE of the brain combined with a novel reconstruction algorithm based on a model-free multifrequency inversion for calculating spatially resolved viscoelastic parameter maps of the human brain corresponding to the dynamic range of shear oscillations between 30 and 60 Hz. Maps of two viscoelastic parameters, the magnitude and the phase angle of the complex shear modulus, |G*| and φ, were obtained and normalized to group templates of 23 healthy volunteers in the age range of 22 to 72 years. This atlas of the anatomy of brain mechanics reveals a significant contrast in the stiffness parameter |G*| between different anatomical regions such as white matter (WM; 1.252±0.260 kPa), the corpus callosum genu (CCG; 1.104±0.280 kPa), the thalamus (TH; 1.058±0.208 kPa) and the head of the caudate nucleus (HCN; 0.649±0.101 kPa). φ, which is sensitive to the lossy behavior of the tissue, was in the order of CCG (1.011±0.172), TH (1.037±0.173), CN (0.906±0.257) and WM (0.854±0.169). The proposed method provides the first normalized maps of brain viscoelasticity with anatomical details in subcortical regions and provides useful background data for clinical applications of cerebral MRE.

High-resolution mechanical imaging of the human brain by three-dimensional multifrequency magnetic resonance elastography at 7T.

Magnetic resonance elastography (MRE) is capable of measuring the viscoelastic properties of brain tissue in vivo. However, MRE is still limited in providing high-resolution maps of mechanical constants. We therefore introduce 3D multifrequency MRE (3DMMRE) at 7T magnetic field strength combined with enhanced multifrequency dual elasto-visco (MDEV) inversion in order to achieve high-resolution elastographic maps of in vivo brain tissue with 1mm(3) resolution. As demonstrated by phantom data, the new MDEV-inversion method provides two high resolution parameter maps of the magnitude (|G*|) and the phase angle (ϕ) of the complex shear modulus. MDEV inversion applied to cerebral 7T-3DMMRE data of five healthy volunteers revealed structures of brain tissue in greater anatomical details than previous work. The viscoelastic properties of cortical gray matter (GM) and white matter (WM) could be differentiated by significantly lower values of |G*| and ϕ in GM (21% [P<0.01]; 8%, [P<0.01], respectively) suggesting that GM is significantly softer and less viscous than WM. In conclusion, 3DMMRE at ultrahigh magnetic fields and MDEV inversion open a new window into characterizing the mechanical structure of in vivo brain tissue and may aid the detection of various neurological disorders based on their effects to mechanical tissue properties.

In vivo measurement of volumetric strain in the human brain induced by arterial pulsation and harmonic waves

Motion‐sensitive phase contrast magnetic resonance imaging and magnetic resonance elastography are applied for the measurement of volumetric strain and tissue compressibility in human brain. Volumetric strain calculated by the divergence operator using a biphasic effective‐medium model is related to dilatation and compression of fluid spaces during harmonic stimulation of the head or during intracranial passage of the arterial pulse wave. In six volunteers, phase contrast magnetic resonance imaging showed that the central cerebrum expands at arterial pulse wave to strain values of (2.8 ± 1.9)·10−4. The evolution of volumetric strain agrees well with the magnitude of the harmonic divergence measured in eight volunteers by magnetic resonance elastography using external activation of 25 Hz vibration frequency. Intracranial volumetric strain was proven sensitive to venous pressure altered by abdominal muscle contraction. In eight volunteers, an increase in volumetric strain due to abdominal muscle contraction of approximately 45% was observed (P = 0.0001). The corresponding compression modulus in the range of 9.5–13.5 kPa demonstrated that the compressibility of brain tissue at 25 Hz stimulation is much higher than that of water. This pilot study provides the background for compression‐sensitive magnetic resonance imaging with or without external head stimulation. Volumetric strain may be sensitive to fluid flow abnormalities or pressure imbalances between vasculature and parenchyma as seen in hydrocephalus. Magn Reson Med 70:671–683, 2013.

Fractal network dimension and viscoelastic powerlaw behavior: I. A modeling approach based on a coarse-graining procedure combined with shear oscillatory rheometry

Recent advances in dynamic elastography and biorheology have revealed that the complex shear modulus, G*, of various biological soft tissues obeys a frequency-dependent powerlaw. This viscoelastic powerlaw behavior implies that mechanical properties are communicated in tissue across the continuum of scales from microscopic to macroscopic. For deriving constitutive constants from the dispersion of G* in a biological tissue, a hierarchical fractal model is introduced that accounts for multiscale networks. Effective-media powerlaw constants are derived by a constitutive law based on cross-linked viscoelastic clusters embedded in a rigid environment. The spatial variation of G* is considered at each level of hierarchy by an iterative coarse-graining procedure. The establishment of cross-links in this model network is associated with an increasing fractal dimension and an increasing viscoelastic powerlaw exponent. This fundamental relationship between shear modulus dynamics and fractal dimension of the mechanical network in tissue is experimentally reproduced in phantoms by applying shear oscillatory rheometry to layers of tangled paper strips embedded in agarose gel. Both model and experiments demonstrate the sensitivity of G* to the density of the mechanical network in tissue, corroborating disease-related alterations of the viscoelastic powerlaw exponent in human parenchyma demonstrated by in vivo elastography.

Cerebral magnetic resonance elastography in supranuclear palsy and idiopathic Parkinson's disease

Detection and discrimination of neurodegenerative Parkinson syndromes are challenging clinical tasks and the use of standard T1- and T2-weighted cerebral magnetic resonance (MR) imaging is limited to exclude symptomatic Parkinsonism. We used a quantitative structural MR-based technique, MR-elastography (MRE), to assess viscoelastic properties of the brain, providing insights into altered tissue architecture in neurodegenerative diseases on a macroscopic level. We measured single-slice multifrequency MRE (MMRE) and three-dimensional MRE (3DMRE) in two neurodegenerative disorders with overlapping clinical presentation but different neuropathology — progressive supranuclear palsy (PSP: N = 16) and idiopathic Parkinsons disease (PD: N = 18) as well as in controls (N = 18). In PSP, both MMRE (Δμ = − 28.8%, Δα = − 4.9%) and 3DMRE (Δ|G*|: − 10.6%, Δφ: − 34.6%) were significantly reduced compared to controls, with a pronounced reduction within the lentiform nucleus (Δμ = − 34.6%, Δα = − 8.1%; Δ|G*|: − 7.8%, Δφ: − 44.8%). MRE in PD showed a comparable pattern, but overall reduction in brain elasticity was less severe reaching significance only in the lentiform nucleus (Δμ n.s., Δα = − 7.4%; Δ|G*|: − 6.9%, Δφ: n.s.). Beyond that, patients showed a close negative correlation between MRE constants and clinical severity. Our data indicate that brain viscoelasticity in PSP and PD is differently affected by the underlying neurodegeneration; whereas in PSP all MRE constants are reduced and changes in brain softness (reduced μ and |G*|) predominate those of viscosity (α and φ) in PD.

In vivo waveguide elastography: Effects of neurodegeneration in patients with amyotrophic lateral sclerosis

Waveguide elastography (WGE) combines magnetic resonance elastography (MRE), diffusion tensor imaging (DTI), and anisotropic inversions for a determination of the elastic properties of white matter. Previously, the method evaluated the anisotropic elastic properties of the corticospinal tracts (CSTs) of healthy volunteers. Here, the sensitivity of WGE is tested for the detection of pathologic changes in a cohort of patients with Amyotrophic Lateral Sclerosis (ALS).

Fractal network dimension and viscoelastic powerlaw behavior: II. An experimental study of structure-mimicking phantoms by magnetic resonance elastography

The dynamics of the complex shear modulus, G*, of soft biological tissue is governed by the rigidity and topology of multiscale mechanical networks. Multifrequency elastography can measure the frequency dependence of G* in soft biological tissue, providing information about the structure of tissue networks at multiple scales. In this study, the viscoelastic properties of structure-mimicking phantoms containing tangled paper stripes embedded in agarose gel are investigated by multifrequency magnetic resonance elastography within the dynamic range of 40–120 Hz. The effective media viscoelastic properties are analyzed in terms of the storage modulus (the real part of G*), the loss modulus (the imaginary part of G*) and the viscoelastic powerlaw given by the two-parameter springpot model. Furthermore, diffusion tensor imaging is used for investigating the effect of network structures on water mobility. The following observations were made: the random paper networks with fractal dimensions between 2.481 and 2.755 had no or minor effects on the storage modulus, whereas the loss modulus was significantly increased about 2.2 kPa per fractal dimension unit (R = 0.962, P < 0.01). This structural sensitivity of the loss modulus was significantly correlated with the springpot powerlaw exponent (0.965, P < 0.01), while for the springpot elasticity modulus, a trend was discernable (0.895, P < 0.05). No effect of the paper network on water diffusion was observed. The gel phantoms with embedded paper stripes presented here are a feasible way for experimentally studying the effect of network topology on soft-tissue viscoelastic parameters. In the dynamic range of in vivo elastography, the fractal network dimension primarily correlates to the loss behavior of soft tissue as can be seen from the loss modulus or the powerlaw exponent of the springpot model. These findings represent the experimental underpinning of structure-sensitive elastography for an improved characterization of various soft-tissue diseases.