Viscoelastic Tissue Model Research Articles

Wave Propagation in a Fractional Viscoelastic Tissue Model: Application to Transluminal Procedures.

In this article, a wave propagation model is presented as the first step in the development of a new type of transluminal procedure for performing elastography. Elastography is a medical imaging modality for mapping the elastic properties of soft tissue. The wave propagation model is based on a Kelvin Voigt Fractional Derivative (KVFD) viscoelastic wave equation, and is numerically solved using a Finite Difference Time Domain (FDTD) method. Fractional rheological models, such as the KVFD, are particularly well suited to model the viscoelastic response of soft tissue in elastography. The transluminal procedure is based on the transmission and detection of shear waves through the luminal wall. Shear waves travelling through the tissue are perturbed after encountering areas of altered elasticity. These perturbations carry information of medical interest that can be extracted by solving the inverse problem. Scattering from prostate tumours is used as an example application to test the model. In silico results demonstrate that shear waves are satisfactorily transmitted through the luminal wall and that echoes, coming from reflected energy at the edges of an area of altered elasticity, which are feasibly detectable by using the transluminal approach. The model here presented provides a useful tool to establish the feasibility of transluminal procedures based on wave propagation and its interaction with the mechanical properties of the tissue outside the lumen.

Sensor-free Force Control of Tendon-driven Ablation Catheters through Position Control and Contact Modeling.

In the present study, a sensor-free force control framework for tendon-driven steerable catheters was proposed and validated. The hypothesis of this study was that the contact force between the catheter tip and the tissue could be controlled using the estimated force with a previously validated displacement-based viscoelastic tissue model. The tissue model was used in a feedback control loop. The model estimated the contact force based on a realtime estimation of catheter-tissue indentation depth performed by a data-driven inverse kinematic model. To test the hypothesis, a tendon-driven catheter (φ6 × 40mm) and a robotic catheter intervention system were prototyped and characterized. Three validation studies were performed to test the performance of the proposed system with static and dynamic inputs. The results showed that the system was capable of reaching to the desired force with a root-mean-square error of 0.03 ± 0.02N for static tests and 0.05 ± 0.04N for dynamic inputs. The main contribution of this study was providing a computationally efficient and sensor-free force control schema for tendon-driven catheters.

Virtual Breast Quasi-static Elastography (VBQE).

Viscoelasticity Imaging (VEI) has been proposed to measure relaxation time constants for characterization of in vivo breast lesions. In this technique, an external compression force on the tissue being imaged is maintained for a fixed period of time to induce strain creep. A sequence of ultrasound echo signals is then utilized to generate time-resolved strain measurements. Relaxation time constants can be obtained by fitting local time-resolved strain measurements to a viscoelastic tissue model (e.g., a modified Kevin-Voigt model). In this study, our primary objective is to quantitatively evaluate the contrast transfer efficiency (CTE) of VEI, which contains useful information regarding image interpretations. Using an open-source simulator for virtual breast quasi-static elastography (VBQE), we conducted a case study of contrast transfer efficiency of VEI. In multiple three-dimensional (3D) numerical breast phantoms containing various degrees of heterogeneity, finite element (FE) simulations in conjunction with quasi-linear viscoelastic constitutive tissue models were performed to mimic data acquisition of VEI under freehand scanning. Our results suggested that there were losses in CTE, and the losses could be as high as -18 dB. FE results also qualitatively corroborated clinical observations, for example, artifacts around tissue interfaces.

A Bayesian approach for characterization of soft tissue viscoelasticity in acoustic radiation force imaging.

Biomechanical imaging techniques based on acoustic radiation force (ARF) have been developed to characterize the viscoelasticity of soft tissue by measuring the motion excited by ARF non-invasively. The unknown stress distribution in the region of excitation limits an accurate inverse characterization of soft tissue viscoelasticity, and single degree-of-freedom simplified models have been applied to solve the inverse problem approximately. In this study, the ARF-induced creep imaging is employed to estimate the time constant of a Voigt viscoelastic tissue model, and an inverse finite element (FE) characterization procedure based on a Bayesian formulation is presented. The Bayesian approach aims to estimate a reasonable quantification of the probability distributions of soft tissue mechanical properties in the presence of measurement noise and model parameter uncertainty. Gaussian process metamodeling is applied to provide a fast statistical approximation based on a small number of computationally expensive FE model runs. Numerical simulation results demonstrate that the Bayesian approach provides an efficient and practical estimation of the probability distributions of time constant in the ARF-induced creep imaging. In a comparison study with the single degree of freedom models, the Bayesian approach with FE models improves the estimation results even in the presence of large uncertainty levels of the model parameters.

Three-dimensional finite difference models of shear wave propagation in isotropic, homogeneous soft tissue

Shear wave elastography with ultrasound applies an acoustic radiation force to generate shear waves in viscoelastic soft tissue. To address the need for more effective simulation tools that model shear waves generated by an applied acoustic radiation force, three-dimensional (3D) finite difference programs that simulate propagation of shear waves in an isotropic, homogeneous medium have been created. These programs simulate shear wave propagation in elastic and viscoelastic soft tissue models. The 3D finite difference implementation combines an explicit time-stepping approach and a staggered spatial grid with an absorbing boundary condition that reduces boundary reflections. The acoustic radiation force in these simulations is quickly and accurately simulated in FOCUS (http://www.egr.msu.edu/ ~fultras-web) for a focused linear ultrasound array with an f/# of 2. The compressional wave speed is 1500 m/s and the shear wave speed is 1.5m/s in the elastic and viscoelastic tissue models, and the shear viscosity is 1 Pa·s in the viscoelastic model. The simulation completes 90,000 time steps of a 10 ms simulation in an 80 mm × 80 mm × 80 mm region with spatial sampling equal to the wavelength of compressional component in three days on a 3.4 MHz Intel i7 processor. [Supported in part by NIH Grants R01EB012079 and R01DK092255.]

Rapid method for assessing relative tissue stiffness using MR acoustic radiation force imaging

ABSTRACTAcoustic radiation force imaging (ARFI) has been suggested as a tool for remote palpation. In this study an MR‐ARFI sequence, based on echo‐planar‐imaging, is introduced, for remote semi‐quantitative assessment of local tissue stiffness. The focal zone of a high intensity focused ultrasound (HIFU) is positioned at the region of interest and a single HIFU burst is transmitted. The method then measures the entire time integral of the resulting displacement at the focal zone. Combining this measurement with the Kelvin–Voigt viscoelastic tissue model, a local stiffness index is obtained. The method was implemented on gel phantoms, ex‐vivo bovine brain and chicken liver specimens. The results have demonstrated the ability to evaluate the relative local stiffness within 600 ms and to distinguish between different tissues on the basis of their stiffness index. The method may potentially be used for remote palpation of suspicious regions for diagnostic purposes, or for providing a mechanical feedback during therapeutic procedures, such as thermal ablation.

Force Control for Robotic-Assisted Surgery Based on Viscoelastic Tissue Model

Usually, force control algorithms developed for medical applications use a basic elastic model to represent the interaction between the robot and soft tissue. It is known that soft tissues are complex structures with viscoelastic properties as well as nonheterogeneity and hysteresis behavior. This work intends to improve the performance and the robustness of a force control scheme using a more realistic interaction model. The proposed force control is a model based algorithm using a Kelvin-Boltzmann viscoelastic model as the interaction model.

Monitored steady-state excitation and recovery (MSSR) radiation force imaging using viscoelastic models

Acoustic radiation force imaging methods distinguish tissue structure and composition by monitoring tissue responses to applied radiation force excitations. Although these responses are a complex, multidimensional function of the geometric and viscoelastic nature of tissue, simplified discrete biomechanical models offer meaningful insight to the physical phenomena that govern induced tissue motion. Applying Voigt and standard linear viscoelastic tissue models, we present a new radiation force technique - monitored steady-state excitation and recovery (MSSER) imaging - that tracks both steady-state displacement during prolonged force application and transient response following force cessation to estimate tissue mechanical properties such as elasticity and viscosity. In concert with shear wave elasticity imaging (SWEI) estimates for Young's modulus, MSSER methods are useful for estimating tissue mechanical properties independent of the applied force magnitude. We test our methods in gelatin phantoms and excised pig muscle, with confirmation through mechanical property measurement. Our results measured 10.6 kPa, 14.7 kPa, and 17.1 kPa (gelatin) and 122.4 kPa (pig muscle) with less than 10% error. This work demonstrates the feasibility of MSSER imaging and merits further efforts to incorporate relevant mechanical tissue models into the development of novel radiation force imaging techniques.

Constitutive modelling of brain tissue: Experiment and theory

Recent developments in computer-integrated and robot-aided surgery—in particular, the emergence of automatic surgical tools and robots—as well as advances in virtual reality techniques, call for closer examination of the mechanical properties of very soft tissues (such as brain, liver, kidney, etc.). The ultimate goal of our research into the biomechanics of these tissues is the development of corresponding, realistic mathematical models. This paper contains experimental results of in vitro, uniaxial, unconfined compression of swine brain tissue and discusses a single-phase, non-linear, viscoelastic tissue model. The experimental results obtained for three loading velocities, ranging over five orders of magnitude, are presented. The applied strain rates have been much lower than those applied in previous studies, focused on injury modelling. The stress-strain curves are concave upward for all compression rates containing no linear portion from which a meaningful elastic modulus might be determined. The tissue response stiffened as the loading speed increased, indicating a strong stress-strain rate dependence. The use of the single-phase model is recommended for applications in registration, surgical operation planning and training systems as well as a control system of an image-guided surgical robot. The material constants for the brain tissue are evaluated. Agreement between the proposed theoretical model and experiment is good for compression levels reaching 30% and for loading velocities varying over five orders of magnitude.

Effect of methacholine on low-frequency mechanics of canine airways and lung tissue.

We measured tracheal flow, tracheal pressure, and alveolar capsule pressure in four anesthetized paralyzed tracheostomized open-chest dogs. Lung impedance between 0.12 and 4.88 Hz was measured with a forced volume oscillation technique before and after the intravenous administration of methacholine (MCh). Before MCh administration, lung impedance was well described by a model featuring a single airway leading to an alveolar region surrounded by tissue with a continuous distribution of viscoelastic time constants as used by Hantos et al. (J. Appl. Physiol. 68: 849-860, 1990). After MCh, however, this model gave a poor fit to the impedances. The impedances were well accounted for, however, when the model was enhanced to include an extra time constant term, which we suspect is required to account for the uneven ventilation distribution produced by MCh. Airway impedance before MCh administration was well described by a simple resistance-inertance model, but a model incorporating serial inhomogeneity of ventilation was again required after MCh. Our results support those of previous studies indicating that the impedance of the normal dog lung is well described by a homogeneously ventilated viscoelastic tissue model. In contrast, our results after MCh administration show strong evidence of marked regional ventilation inhomogeneity in addition to the rheological properties of the tissues.