Simon Chatelin

Fifty years of brain tissue mechanical testing: From in vitro to in vivo investigations

Beginning in the 1960s many studies have been performed to investigate the mechanical properties of brain. In this paper we point out the difficulties linked with in vitro experimental protocols as well as the advantages of using recently developed non-invasive in vivo techniques, such as magnetic resonance elastography. Results of in vitro and in vivo work are compared, emphasizing the specificities and disparities of the in vitro as well as the in vivo results. In particular, a detailed discussion of the results obtained from dynamic shear experiments and magnetic resonance elastography is given before arriving at a tentative conclusion on the state of knowledge of the mechanical properties of brain.

Fast porous visco-hyperelastic soft tissue model for surgery simulation: application to liver surgery

Understanding and modeling liver biomechanics represents a significant challenge due to its complex nature. In this paper, we tackle this issue in the context of real-time surgery simulation where a compromise between biomechanical accuracy and computational efficiency must be found. We describe a realistic liver model including hyperelasticity, porosity and viscosity that is implemented within an implicit time integration scheme. To optimize its computation, we introduce the Multiplicative Jacobian Energy Decomposition (MJED) method for discretizing hyperelastic materials on linear tetrahedral meshes which leads to faster matrix assembly than the standard Finite Element Method. Visco-hyperelasticity is modeled by Prony series while the mechanical effect of liver perfusion is represented with a linear Darcy law. Dynamic mechanical analysis has been performed on 60 porcine liver samples in order to identify some viscoelastic parameters. Finally, we show that liver deformation can be simulated in real-time on a coarse mesh and study the relative effects of the hyperelastic, viscous and porous components on the liver biomechanics.

In vivo liver tissue mechanical properties by transient elastography: Comparison with dynamic mechanical analysis

Understanding the mechanical properties of human liver is one of the most critical aspects of its numerical modeling for medical applications or impact biomechanics. Generally, model constitutive laws come from in vitro data. However, the elastic properties of liver may change significantly after death and with time. Furthermore, in vitro liver elastic properties reported in the literature have often not been compared quantitatively with in vivo liver mechanical properties on the same organ. In this study, both steps are investigated on porcine liver. The elastic property of the porcine liver, given by the shear modulus G, was measured by both Transient Elastography (TE) and Dynamic Mechanical Analysis (DMA). Shear modulus measurements were realized on in vivo and in vitro liver to compare the TE and DMA methods and to study the influence of testing conditions on the liver viscoelastic properties. In vitro results show that elastic properties obtained by TE and DMA are in agreement. Liver tissue in the frequency range from 0.1 to 4 Hz can be modeled by a two-mode relaxation model. Furthermore, results show that the liver is homogeneous, isotropic and more elastic than viscous. Finally, it is shown in this study that viscoelastic properties obtained by TE and DMA change significantly with post mortem time and with the boundary conditions.

Towards child versus adult brain mechanical properties.

The characterization of brain tissue mechanical properties is of crucial importance in the development of realistic numerical models of the human head. While the mechanical behavior of the adult brain has been extensively investigated in several studies, there is a considerable paucity of data concerning the influence of age on mechanical properties of the brain. Therefore, the implementation of child and infant head models often involves restrictive assumptions like properties scaling from adult or animal data. The present study presents a step towards the investigation of the effects of age on viscoelastic properties of human brain tissue from a first set of dynamic oscillatory shear experiments. Tests were also performed on three different locations of brain (corona radiata, thalamus and brainstem) in order to investigate regional differences. Despite the limited number of child brain samples a significant increase in both storage and loss moduli occurring between the age of 5 months and the age of 22 months was found, confirmed by statistical Students t-tests (p=0.104,0.038 and 0.054 for respectively corona radiata, thalamus and brain stem samples locations respectively). The adult brain appears to be 3-4 times stiffer than the young child one. Moreover, the brainstem was found to be approximately 2-3 times stiffer than both gray and white matter from corona radiata and thalamus. As a tentative conclusion, this study provides the first rheological data on the human brain at different ages and brain regions. This data could be implemented in numerical models of the human head, especially in models concerning pediatric population.

Experimental in vitro mechanical characterization of porcine Glisson's capsule and hepatic veins.

Understanding the mechanical properties of human liver is the most critical aspect of numerical modeling for medical applications and impact biomechanics. Many researchers work on identifying mechanical properties of the liver both in vivo and in vitro considering the high liver injury percentage in abdominal trauma and for easy detection of fatal liver diseases such as viral hepatitis, cirrhosis, etc. This study is performed to characterize mechanical properties of individual parts of the liver, namely Glissons capsule and hepatic veins, as these parts are rarely characterized separately. The long term objective of this study is to develop a realistic liver model by characterizing individual parts and later integrating them. In vitro uniaxial quasi-static tensile tests are done on fresh unfrozen porcine hepatic parts for large deformations at the rate of 0.1mm/s with a Bose Electroforce 3200 biomaterials test instrument. Results show that mean values of small strain and large strain elastic moduli are 8.22 ± 3.42 and 48.15 ± 4.5 MPa for Glissons capsule (30 samples) and 0.62 ± 0.41 and 2.81 ± 2.23 MPa for veins (20 samples), respectively, and are found to be in good agreement with data in the literature. Finally, a non-linear hyper-elastic constitutive law is proposed for the two separate liver constituents under study.

Anisotropic polyvinyl alcohol hydrogel phantom for shear wave elastography in fibrous biological soft tissue: a multimodality characterization.

Shear wave elastography can provide quantitative evaluation of soft tissues viscoelastic properties based on the measurement of shear wave speed in the medium. Muscular and cerebral tissues are composed of fibers which induce a strong anisotropic effect on the mechanical behavior. Currently, these tissues cannot be accurately represented by existing elastography phantoms and there is an urgent need of developing new anisotropic tissue mimicking phantoms. In the present study we propose an original multimodality imaging characterization of a transverse isotropic (TI) polyvinyl alcohol (PVA) cryogel. The mechanical anisotropy is induced in the PVA hydrogel by stretching the physical crosslinks of the polymeric chains while undergoing freezing cycling [1]. Multiple properties of these phantoms were investigated using a variety of techniques at different scale. The mechanical (dynamic and static) properties were studied using Supersonic Shear wave Imaging (SSI) technique [2] and Full-Field Optical Coherence Tomography (FF-OCT) strain imaging. The optical and ultrasonic spatial coherence properties were measure by FF-OCT volumetric imaging [3] and Backscatter Tensor Imaging (BTI) [4], respectively. The results suggest that this type of phantom (TI) could be used in the development of techniques and equipment to study anisotropy, such as the design of new ultrasound probes for cardiac and musculoskeletal application.

Ultrafast Harmonic Coherent Compound (UHCC) Imaging for High Frame Rate Echocardiography and Shear-Wave Elastography

Transthoracic shear-wave elastography (SWE) of the myocardium remains very challenging due to the poor quality of transthoracic ultrafast imaging and the presence of clutter noise, jitter, phase aberration, and ultrasound reverberation. Several approaches, such as diverging-wave coherent compounding or focused harmonic imaging, have been proposed to improve the imaging quality. In this study, we introduce ultrafast harmonic coherent compounding (UHCC), in which pulse-inverted diverging waves are emitted and coherently compounded, and show that such an approach can be used to enhance both SWE and high frame rate (FR) B-mode Imaging. UHCC SWE was first tested in phantoms containing an aberrating layer and was compared against pulse-inversion harmonic imaging and against ultrafast coherent compounding (UCC) imaging at the fundamental frequency. In vivo feasibility of the technique was then evaluated in six healthy volunteers by measuring myocardial stiffness during diastole in transthoracic imaging. We also demonstrated that improvements in imaging quality could be achieved using UHCC B-mode imaging in healthy volunteers. The quality of transthoracic images of the heart was found to be improved with the number of pulse-inverted diverging waves with a reduction of the imaging mean clutter level up to 13.8 dB when compared against UCC at the fundamental frequency. These results demonstrated that UHCC B-mode imaging is promising for imaging deep tissues exposed to aberration sources with a high FR.

Multiplicative jacobian energy decomposition method for fast porous visco-hyperelastic soft tissue model

Simulating soft tissues in real time is a significant challenge since a compromise between biomechanical accuracy and computational efficiency must be found. In this paper, we propose a new discretization method, the Multiplicative Jacobian Energy Decomposition (MJED) which is an alternative to the classical Galerkin FEM (Finite Element Method) formulation. This method for discretizing non-linear hyperelastic materials on linear tetrahedral meshes leads to faster stiffness matrix assembly for a large variety of isotropic and anisotropic materials. We show that our new approach, implemented within an implicit time integration scheme, can lead to fast and realistic liver deformations including hyperelasticity, porosity and viscosity.

Modelling the impulse diffraction field of shear waves in transverse isotropic viscoelastic medium

The generation of shear waves from an ultrasound focused beam has been developed as a major concept for remote palpation using shear wave elastography (SWE). For muscular diagnostic applications, characteristics of the shear wave profile will strongly depend on characteristics of the transducer as well as the orientation of muscular fibers and the tissue viscoelastic properties. The numerical simulation of shear waves generated from a specific probe in an anisotropic viscoelastic medium is a key issue for further developments of SWE in fibrous soft tissues. In this study we propose a complete numerical tool allowing 3D simulation of a shear wave front in anisotropic viscoelastic media. From the description of an ultrasonic transducer, the shear wave source is simulated by using Fields II software and shear wave propagation described by using the Greens formalism. Finally, the comparison between simulations and experiments are successively performed for both shear wave velocity and dispersion profile in a transverse isotropic hydrogel phantom, in vivo forearm muscle and in vivo biceps brachii.

An automatic differentiation-based gradient method for inversion of the shear wave equation in magnetic resonance elastography: specific application in fibrous soft tissues

Quantitative and accurate measurement of in vivo mechanical properties using dynamic elastography has been the scope of many research efforts over the past two decades. Most of the shear-wave-based inverse approaches for magnetic resonance elastography (MRE) make the assumption of isotropic viscoelasticity. In this paper, we propose a quantitative gradient method for inversion of the shear wave equation in anisotropic media derived from a full waveform description using analytical viscoelastic Green formalism and automatic differentiation. The abilities and performances of the proposed identification method are first evaluated on numerical phantoms calculated in a transversely isotropic medium, and subsequently on experimental MRE data measured on an isotropic hydrogel phantom, on an anisotropic cryogel phantom and on an ex vivo fibrous muscle. The experiments are carried out by coupling circular shear wave profiles generated by acoustic radiation force and MRE acquisition of the wave front. Shear modulus values obtained by our MRE method are compared to those obtained by rheometry in the isotropic hydrogel phantom, and are found to be in good agreement despite non-overlapping frequency ranges. Both the cryogel and the ex vivo muscle are found to be anisotropic. Stiffness values in the longitudinal direction are found to be 1.8 times and 1.9 times higher than those in the transverse direction for the cryogel and the muscle, respectively. The proposed method shows great perspectives and substantial benefits for the in vivo quantitative investigation of complex mechanical properties in fibrous soft tissues.