Nonlinear Soft Tissue Mechanics Based on Polytopic Tensor Product Modeling

Achieving reliable force control is one of the main design goals of robotic teleoperation. It is essential to grant safe and stable performance of these systems, regarding HMI control, even under major disturbing conditions such as time delay or model parameter uncertainties. This paper discusses the systematic derivation of polytopic qLPV model from the nonlinear dynamics of typical soft tissues of the human body based on recent experimental results. The derivation is based on the Tensor Product (TP) Model Transformation. The presented method is a crucial step in laying the foundations of adequate force control in telesurgery. The proposed approach could form the basis of LMI-based controller design

An explicit model to extract viscoelastic properties of cells from AFM force-indentation curves

Atomic force microscopy (AFM) is widely used for quantifying the mechanical properties of soft materials such as cells. AFM force-indentation curves are conventionally fitted with a Hertzian model to extract elastic properties. These properties solely are, however, insufficient to describe the mechanical properties of cells. Here, we expand the analysis capabilities to describe the viscoelastic behavior while using the same force-indentation curves. Our model gives an explicit relation of force and indentation and extracts physically meaningful mechanical parameters. We first validated the model on simulated force-indentation curves. Then, we applied the fitting model to the force-indentation curves of two hydrogels with different crosslinking mechanisms. Finally, we characterized HeLa cells in two cell cycle phases, interphase and mitosis, and showed that mitotic cells have a higher apparent elasticity and a lower apparent viscosity. Our study provides a simple method, which can be directly integrated into the standard AFM framework for extracting the viscoelastic properties of materials

Viscoelastic Biomarkers of Ex Vivo Liver Samples via TorsionalWave Elastography

We thank the Department of Electronics and Computer Technology of the University of Granada for assistance with the electronic system of the torsional wave sensor.The clinical ultrasound community demands mechanisms to obtain the viscoelastic biomarkers of soft tissue in order to quantify the tissue condition and to be able to track its consistency. Torsional Wave Elastography (TWE) is an emerging technique proposed for interrogating soft tissue mechanical viscoelastic constants. Torsional waves are a particular configuration of shear waves, which propagate asymmetrically in-depth and are radially transmitted by a disc and received by a ring. This configuration is shown to be particularly efficient in minimizing spurious p-waves components and is sensitive to mechanical constants, especially in cylinder-shaped organs. The objective of this work was to validate (TWE) technique against Shear Wave Elasticity Imaging (SWEI) technique through the determination of shear wave velocity, shear moduli, and viscosity of ex vivo chicken liver samples and tissue mimicking hydrogel phantoms. The results of shear moduli for ex vivo liver tissue vary 1.69–4.0kPa using TWE technique and 1.32–4.48kPa using SWEI technique for a range of frequencies from 200 to 800Hz. Kelvin–Voigt viscoelastic parameters reported values of μ = 1.51kPa and η = 0.54Pa·s using TWE and μ = 1.02kPa and η = 0.63Pa·s using SWEI. Preliminary results show that the proposed technique successfully allows reconstructing shear wave velocity, shear moduli, and viscosity mechanical biomarkers from the propagated torsional wave, establishing a proof of principle and warranting further studies.This research was funded by the Ministry of Education grant numbers DPI2017-83859-R, DPI2014-51870-R, and UNGR15-CE-3664; Ministry of Health grant numbers DTS15/00093 and PI16/00339 Carlos III Instituto de Salud y Fondos Feder; and Junta de Andalucía grant numbers, PI-0107-2017 and PIN-0030-2017. Juan de la Cierva Incorporación IJC2018-037167-I

Why Are Viscosity and Nonlinearity Bound to Make an Impact in Clinical Elastographic Diagnosis?

The contributions by Antonio Gomez, Monica Contreras and Francisca S. Molina are gratefully acknowledged.The adoption of multiscale approaches by the biomechanical community has caused a major improvement in quality in the mechanical characterization of soft tissues. The recent developments in elastography techniques are enabling in vivo and non-invasive quantification of tissues’ mechanical properties. Elastic changes in a tissue are associated with a broad spectrum of pathologies, which stems from the tissue microstructure, histology and biochemistry. This knowledge is combined with research evidence to provide a powerful diagnostic range of highly prevalent pathologies, from birth and labor disorders (prematurity, induction failures, etc.), to solid tumors (e.g., prostate, cervix, breast, melanoma) and liver fibrosis, just to name a few. This review aims to elucidate the potential of viscous and nonlinear elastic parameters as conceivable diagnostic mechanical biomarkers. First, by providing an insight into the classic role of soft tissue microstructure in linear elasticity; secondly, by understanding how viscosity and nonlinearity could enhance the current diagnosis in elastography; and finally, by compounding preliminary investigations of those elastography parameters within different technologies. In conclusion, evidence of the diagnostic capability of elastic parameters beyond linear stiffness is gaining momentum as a result of the technological and imaging developments in the field of biomechanics.This research was funded by Ministerio de Educación, Cultura y Deporte grant numbers DPI2017-83859-R, DPI2014-51870-R, UNGR15-CE-3664 and EQC2018-004508-P; Ministerio de Sanidad, Servicios Sociales e Igualdad grant numbers DTS15/00093 and PI16/00339; Instituto de Salud Carlos III y Fondos Feder; Junta de Andalucía grant numbers PI-0107-2017, PIN-0030-2017 and IE2017-5537; Juan de la Cierva Incorporación IJC2018-037167-I, Ministerio de Ciencia, Innovación y Universidades grant number PRE2018-086085

Soft tissue structural assessment using mechanical measurements

The overall aim of the work presented in this thesis is the development of quantitative relationships between the structure (histological make-up and/or tissue architecture) and the mechanical properties of soft biological tissue. The purpose of the research is to contribute towards the assessment of “tissue quality” using mechanical probing (instrumented palpation). The work focuses particularly on two case studies; the eyeball, where tissue quality relates to the corneal stiffness and the intra-ocular pressure (IOP); and the periodontal ligament (PDL), where tissue quality relates to the load displacement-time behaviour of teeth to which external forces are applied (such as in orthodontic treatment). The experimental work involves static and dynamic testing of two porcine tissues (eyeballs and periodontal ligament) and also a mechanical system (mechanical eyeball) devised to investigate separately the components expected to influence mechanical behaviour; cornea stiffness, IOP, fluid inertia and leakage rate. Special test rigs were designed, calibrated and assessed for their measurement and process capabilities and the results were compared with quasi linear visco elastic (QLV) models to identify an appropriate mechanical way of characterising the tissue for comparison with its quality. The larger part of the work concentrated on the eye with the ultimate aim of identifying symptoms of glaucoma more accurately. Dynamic testing identified a suitable indentation frequency range of 20Hz to 24Hz, the amplitude ratio in this range being capable of measuring IOP within an error of ±7mmHg which is only slightly above the ±5mmHg target for the latest tonometers. The cornea tissue was found to have 20% viscous behaviour and 80% elastic behaviour. The data were analysed using dynamic visco elastic models with an additional term for the inertia of the fluid in the eyeball. The work on the mechanical eyeball showed that it is possible to separate the effects of IOP and the stiffness of the cornea, which is of great significance in determining the true IOP, as opposed to one derived from a tonometer reading which makes assumptions about cornea stiffness. The other main contribution is on the assessment of the periodontal ligament, which plays an important shock-absorbing role during mastication and is the initiator for orthodontic tooth movement (OTM), when loads are applied to teeth using orthodontic appliances. The force-relaxation behaviour of one lower premolar in pig mandibles was measured and the resulting force relaxation curves analysed using three different visco elastic spring damper models. The analysis showed that, when longer relaxation times are allowed three or even four parameter models are not adequate to describe the behaviour. It is suggested that a more appropriate model is a multi component Maxwell model which uses more or less Maxwell components depending on the allowed relaxation time. Overall, the work shows that instrumented palpation, supported by the development of suitable models can play a significant role in measuring tissue quality. Also, using simplified models of the stress-strain behaviour, it was possible to demonstrate that the measurements made here were in general accord with those reported in the literature for eyes, corneas and periodontal ligament

Soft tissue viscoelastic properties: measurements, models and interpretation

The quantification of mechanical properties of soft tissues has been of great interest for more than two decades because they have the potential of being used as biomarkers for disease diagnosis. Indentation techniques, the most recognized techniques for characterizing mechanical properties, are widely used for basic science investigations in research labs. The use of elastography techniques coupled with imaging technologies has been growing rapidly in recent years, which is promising for clinical applications. Each technique produces different mechanical behaviors due to the interaction of the stimuli and the structure of the tissue. An appropriate model will parameterize these behaviors to reflect the corresponding tissue microscopic features with high fidelity. The objective of this thesis is to identify combinations of techniques and models that will yield mechanical parameters with diagnostic interpretations about tissue microenvironment. Three techniques for characterizing tissue viscoelastic properties were developed and validated, each offers strengths in a large variety of applications. Indentation based techniques measure low-frequency force-displacement curves under different loading profiles. Ultrasound-based techniques and optical based techniques measure the dispersion behaviors of the propagating wave velocities at mid-to-high frequency ranges. When a material is linear, isotropic, and contains only elastic components, the “intrinsic” elastic modulus of the material can be obtained independently of the technique used when corrections are properly made to eliminate the bias from boundary effects. If the material includes time-dependent components, models must be included in the analysis to provide parametric estimates. Classical models for viscoelastic solids such as the Kelvin-Voigt model do not fully represent mechanical measurements in tissues because they are not material continua. Tissue properties are determined in part by fluid movement in the open- and closed-cell compartments found within a viscoelastic collagen matrix that is actively maintained by the embedded cells to meet programmed needs. These biphasic (solid/fluid) media exhibit multifaceted deformation responses that are particularly difficult to model using a concise feature set. The Kelvin-Voigt fractional derivative (KVFD) model introduced in this study represents the measurement data of a broad range in both time and frequency domain with a small number of parameters, and it yields stable estimates for many types of phantoms and tissues. It is superior to the integer derivative models for the materials and techniques we used in this study. Moreover, the KVFD model provides a three-dimensional feature space of mechanical properties that properly characterizes the composition and structure of a material. This was validated through measurements on gelatin-cream emulsion samples exhibiting viscoelastic behavior, as well as ex vivo liver tissue samples. For the elastic property, KVFD parameter E_0 mainly represents the elasticity of the solid matrix and is approximately equal to the shear modulus no matter which technique is used. For the viscous property, when combined with different measurement techniques, KVFD model parameter α and τ represent different tissue components. The combination of these techniques and the KVFD model have the potential to be able to distinguish between healthy and pathological tissues described by the histological features

Shear wave rheometry with applications in elastography

The goal of elastography is to map the mechanical properties of soft tissues associated with health and disease. The mechanical property of interest in this work is the complex shear modulus, composed of a real part, the storage modulus, which is a measure of elasticity, and an imaginary part, the loss modulus, which is a measure of viscosity. Together, they determine the speed and attenuation of shear waves in the medium. Elastography techniques based on either ultrasound imaging or MRI can image shear wave propagation and thus are capable of measuring shear wave speed and attenuation. Dispersion, or the frequency-dependence of material parameters, is a primary confounding factor when comparing measurements between different shear wave elastography implementations. Prior attempts at quantifying this frequency-dependence suffered from inaccurate modeling assumptions and low signal-to-noise ratios (SNR). To overcome these limitations, a high-fidelity forward model of shear wave propagation in homogeneous media was developed. The model is an exact semi-analytical solution of Navier's equation and is well-suited for acoustic radiation force impulse shear wave elastography (ARFI-SWE) because it does not require precise knowledge of the strength of the source, nor its spatial or temporal distribution. Unlike models used in ARFI-SWE heretofore, it accounts for the vector polarization of shear waves and exactly represents geometric spreading of the shear wavefield, whether spherical, cylindrical, or neither. Furthermore, it is material-model independent, i.e. it makes no assumption about the frequency-dependence of material parameters. It overcomes the problem of low SNR through spatial averaging and enables estimation of the frequency-dependent complex shear modulus over a wider frequency range than has hitherto been possible. This improved ARFI-SWE was named Shear Wave Rheometry (SWR). By combining SWR with a novel torsional vibration rheometry, dispersion in tissue-mimicking gels was quantified from 1--1800 Hz. The measurements show sizable frequency-dependent variation in the shear modulus of gelatin, a material often assumed to be non-dispersive based on narrow-band measurements. SWR measurements in ex vivo bovine liver tissue yielded complex shear modulus estimates from 25--250 Hz and showed that liver tissue exhibits significant dispersion in this frequency range: a factor of 4 increase in the storage modulus and a factor of 10 increase in the loss modulus. Quality metrics showed that liver tissue can be reasonably approximated as homogeneous and isotropic for ARFI-SWE measurements in this frequency range. Results demonstrate that accounting for dispersion is essential for meaningful comparisons of measurements between systems. Moreover, improved tissue characterization enabled by SWR may have clinical relevance, for example, in the diagnosis and monitoring of chronic liver disease

Models for force control in telesurgical robot systems

Surgical robotics is one of the most rapidly developing fields within robotics. Besides general motion control issues, control engineers often find it challenging to design robotic telesurgery systems, as these have to deal with complex environmental constrains. The unique behavior of soft tissues requires special approaches in both robot control and system modeling in the case of robotic tissue manipulation. Precise control depends on the appropriate modeling of the interaction between the manipulated tissues and the instruments held by the robotic arm, frequently referred to as the tool–tissue interaction. Due to the nature of the physiological environment, the mechatronics of the systems and the time delays, it is difficult to introduce a universal model or a general modeling approach. This paper gives an overview of the emerging problems in the design and modeling of telesurgical systems, analyzing each component, and introducing the most widely employed models. The arising control problems are reviewed in the frames of master–slave type teleoperation, proposing a novel oft tissue model and providing an overview of the possible control approaches

Modelling and Analysis of a new Integrated Radiofrequency Ablation and Division Device

Master'sMASTER OF ENGINEERIN