A variational constitutive model for soft biological tissues

In this paper, a fully variational constitutive model of soft biological tissues is formulated in the finite strain regime. The model includes Ogden-type hyperelasticity, finite viscosity, deviatoric and volumetric plasticity, rate and microinertia effects. Variational updates are obtained via time discretization and pre-minimization of a suitable objective function with respect to internal variables. Genetic algorithms are used for model parameter identification due to their suitability for non-convex, high dimensional optimization problems. The material behavior predicted by the model is compared to available tests on swine and human brain tissue. The ability of the model to predict a wide range of experimentally observed behavior, including hysteresis, cyclic softening, rate effects, and plastic deformation is demonstrated

Efficient techniques for soft tissue modeling and simulation

Performing realistic deformation simulations in real time is a challenging problem in computer graphics. Among numerous proposed methods including Finite Element Modeling and ChainMail, we have implemented a mass spring system because of its acceptable accuracy and speed. Mass spring systems have, however, some drawbacks such as, the determination of simulation coefficients with their iterative nature. Given the correct parameters, mass spring systems can accurately simulate tissue deformations but choosing parameters that capture nonlinear deformation behavior is extremely difficult. Since most of the applications require a large number of elements i. e. points and springs in the modeling process it is extremely difficult to reach realtime performance with an iterative method. We have developed a new parameter identification method based on neural networks. The structure of the mass spring system is modified and neural networks are integrated into this structure. The input space consists of changes in spring lengths and velocities while a "teacher" signal is chosen as the total spring force, which is expressed in terms of positional changes and applied external forces. Neural networks are trained to learn nonlinear tissue characteristics represented by spring stiffness and damping in the mass spring algorithm. The learning algorithm is further enhanced by an adaptive learning rate, developed particularly for mass spring systems. In order to avoid the iterative approach in deformation simulations we have developed a new deformation algorithm. This algorithm defines the relationships between points and springs and specifies a set of rules on spring movements and deformations. These rules result in a deformation surface, which is called the search space. The deformation algorithm then finds the deformed points and springs in the search space with the help of the defined rules. The algorithm also sets rules on each element i. e. triangle or tetrahedron so that they do not pass through each other. The new algorithm is considerably faster than the original mass spring systems algorithm and provides an opportunity for various deformation applications. We have used mass spring systems and the developed method in the simulation of craniofacial surgery. For this purpose, a patient-specific head model was generated from MRI medical data by applying medical image processing tools such as, filtering, the segmentation and polygonal representation of such model is obtained using a surface generation algorithm. Prism volume elements are generated between the skin and bone surfaces so that different tissue layers are included to the head model. Both methods produce plausible results verified by surgeons

A K-BKZ Formulation for Soft-Tissue Viscoelasticity

A viscoelastic model of the K-BKZ (Kaye 1962; Bernstein et al. 1963) type is developed for isotropic biological tissues, and applied to the fat pad of the human heel. To facilitate this pursuit, a class of elastic solids is introduced through a novel strain-energy function whose elements possess strong ellipticity, and therefore lead to stable material models. The standard fractional-order viscoelastic (FOV) solid is used to arrive at the overall elastic/viscoelastic structure of the model, while the elastic potential via the K-BKZ hypothesis is used to arrive at the tensorial structure of the model. Candidate sets of functions are proposed for the elastic and viscoelastic material functions present in the model, including a regularized fractional derivative that was determined to be the best. The Akaike information criterion (AIC) is advocated for performing multi-model inference, enabling an objective selection of the best material function from within a candidate set

Robotics-Assisted Needle Steering for Percutaneous Interventions: Modeling and Experiments

Needle insertion and guidance plays an important role in medical procedures such as brachytherapy and biopsy. Flexible needles have the potential to facilitate precise targeting and avoid collisions during medical interventions while reducing trauma to the patient and post-puncture issues. Nevertheless, error introduced during guidance degrades the effectiveness of the planned therapy or diagnosis. Although steering using flexible bevel-tip needles provides great mobility and dexterity, a major barrier is the complexity of needle-tissue interaction that does not lend itself to intuitive control. To overcome this problem, a robotic system can be employed to perform trajectory planning and tracking by manipulation of the needle base. This research project focuses on a control-theoretic approach and draws on the rich literature from control and systems theory to model needle-tissue interaction and needle flexion and then design a robotics-based strategy for needle insertion/steering. The resulting solutions will directly benefit a wide range of needle-based interventions. The outcome of this computer-assisted approach will not only enable us to perform efficient preoperative trajectory planning, but will also provide more insight into needle-tissue interaction that will be helpful in developing advanced intraoperative algorithms for needle steering. Experimental validation of the proposed methodologies was carried out on a state of-the-art 5-DOF robotic system designed and constructed in-house primarily for prostate brachytherapy. The system is equipped with a Nano43 6-DOF force/torque sensor (ATI Industrial Automation) to measure forces and torques acting on the needle shaft. In our setup, an Aurora electromagnetic tracker (Northern Digital Inc.) is the sensing device used for measuring needle deflection. A multi-threaded application for control, sensor readings, data logging and communication over the ethernet was developed using Microsoft Visual C 2005, MATLAB 2007 and the QuaRC Toolbox (Quanser Inc.). Various artificial phantoms were developed so as to create a realistic medium in terms of elasticity and insertion force ranges; however, they simulated a uniform environment without exhibiting complexities of organic tissues. Experiments were also conducted on beef liver and fresh chicken breast, beef, and ham, to investigate the behavior of a variety biological tissues

Numerical modelling of the growth and remodelling phenomena in biological tissues

Living biological tissues are complex structures that have the capacity of evolving in response to external loads and environmental stimuli. The adequate modelling of soft biological tissue behaviour is a key issue in successfully reproducing biomechanical problems through computational analysis. This study presents a general constitutive formulation capable of representing the behaviour of these tissues through finite element simulation. It is based on phenomenological models that, used in combination with the generalized mixing theory, can numerically reproduce a wide range of material behaviours. First, the passive behaviour of tissues is characterized by means of hyperelastic and finite-strain damage models. A new generalized damage model is proposed, providing a flexible and versatile formulation that can reproduce a wide range of tissue behaviour. It can be particularized to any hyperelastic model and requires identifying only two material parameters. Then, the use of these constitutive models with generalized mixing theory in a finite-strain framework is described and tools to account for the anisotropic behaviour of tissues are put forth. The active behaviour of tissues is characterized through constitutive models capable of reproducing the growth and remodelling phenomena. These are built on the hyperelastic and damage formulations described above and, thus, represent the active extension of the passive tissue behaviour. A growth model considering biological availability is used and extended to include directional growth. In addition, a novel constitutive model for homeostatic-driven turnover remodelling is presented and discussed. This model captures the stiffness recovery that occurs in healing tissues, understood as a recovery or reversal of damage in the tissue, which is driven by both mechanical and biochemical stimuli. Finally, the issue of correctly identifying the material parameters for computational modelling is addressed. An inverse method using optimization techniques is developed to facilitate the identification of these parameters.Els teixits biològics vius són estructures complexes que tenen la capacitat d'evolucionar en resposta a càrregues externes i estímuls ambientals. El modelat adequat del comportament del teixit biològic tou és un tema clau per poder reproduir amb èxit problemes biomecànics mitjançant anàlisi computacional. Aquest estudi presenta una formulació constitutiva general capaç de representar el comportament d'aquests teixits mitjançant la simulació amb elements finits. Es basa en models fenomenològics que, usats en combinació amb la teoria de mescles generalitzada, permeten reproduir numèricament un ampli ventall de comportaments materials. Primer, el comportament passiu dels teixits es caracteritza amb models hiperelàstics i de dany en grans deformacions. Es proposa un model generalitzat de dany que proporciona una formulació versàtil i flexible per poder reproduir una extensa gamma de conductes de teixits. Pot ser particularitzat amb qualsevol model hiperelàstic i requereix identificar tan sols dos paràmetres materials. Llavors, es descriu l'ús d'aquests models constitutius en conjunt amb la teoria generalitzada de mescles, desenvolupada en el marc de grans deformacions, i es presenten eines que permeten incorporar les propietats anisòtropes dels teixits. El comportament actiu dels teixits es caracteritza mitjançant models constitutius capaços de reproduir els fenòmens de creixement i remodelació. Aquests es construeixen sobre les formulacions d'hiperelasticitat i dany descrites anteriorment i, per tant, suposen l'extensió activa del comportament passiu del teixit. Es fa servir un model de creixement que té en compte la disponibilitat biològica de l'organisme, que després s'amplia per incloure dany direccional en el model. També es presenta i analitza un nou model constitutiu per al remodelat per renovació tendint a l’homeòstasi (homeostatic-driven turnover remodelling). Aquest model captura la recuperació de rigidesa que s'observa en teixits que es guareixen. Aquí, el remodelat s'entén com la recuperació o inversió del dany en el teixit i és motivat tant per estímuls mecànics com bioquímics. Finalment, s'aborda el tema de la identificació correcta dels paràmetres materials per al modelat computacional. Es desenvolupa un mètode invers que fa ús de tècniques d'optimització per facilitar la identificació d'aquests paràmetre

Mathematical modelling with experimental validation of viscoelastic properties in non-Newtonian fluids

The paper proposes a mathematical framework for the use of fractional-order impedance models to capture fluid mechanics properties in frequency-domain experimental datasets. An overview of non-Newtonian (NN) fluid classification is given as to motivate the use of fractional-order models as natural solutions to capture fluid dynamics. Four classes of fluids are tested: oil, sugar, detergent and liquid soap. Three nonlinear identification methods are used to fit the model: nonlinear least squares, genetic algorithms and particle swarm optimization. The model identification results obtained from experimental datasets suggest the proposed model is useful to characterize various degree of viscoelasticity in NN fluids. The advantage of the proposed model is that it is compact, while capturing the fluid properties and can be identified in real-time for further use in prediction or control applications. This article is part of the theme issue 'Advanced materials modelling via fractional calculus: challenges and perspectives'

Fractional order models of the human respiratory system

The fractional calculus is a generalization of classical integer-order integration and derivation to fractional (non-integer) order operators. Fractional order (FO) models are those models which contain such fractional order operators. A common representation of these models is in frequency domain, due to its simplicity. The dynamical systems whose model can be approximated in a natural way using FO terms, exhibit specific features, such as viscoelasticity, diffusion and a fractal structure; hence the respiratory system is an ideal application for FO models. Although viscoelastic and diffusive properties were intensively investigated in the respiratory system, the fractal structure was ignored. Probably one of the reasons is that the respiratory system does not pose a perfect symmetry, hence failing to satisfy one of the conditions for being a typical fractal structure. In the 70s, the respiratory impedance determined by the ratio of air-pressure and air-flow, has been introduced in a model structure containing a FO term. It has also been shown that the fractional order models outperform integer-order models on input impedance measurements. However, there was a lack of underpinning theory to clarify the appearance of the fractional order in the FO model structure. The thesis describes a physiologically consistent approach to reach twofold objectives: 1. to provide a physiologically-based mathematical explanation for the necessity of fractional order models for the input impedance, and 2. to determine the capability of the best fractional order model to classify between healthy and pathological cases. Rather than dealing with a specific case study, the modelling approach presents a general method which can be used not only in the respiratory system application, but also in other similar systems (e.g. leaves, circulatory system, liver, intestines). Furthermore, we consider also the case when symmetry is not present (e.g. deformations in the thorax - kyphoscoliose) as well as various pathologies. We provide a proof-of-concept for the appearance of the FO model from the intrinsic structure of the respiratory tree. Several clinical studies are then conducted to validate the sensitivity and specificity of the FO model in healthy groups and in various pathological groups

Dual modality optical coherence tomography : Technology development and biomedical applications

Optical coherence tomography (OCT) is a cross-sectional imaging modality that is widely used in clinical ophthalmology and interventional cardiology. It is highly promising for in situ characterization of tumor tissues. OCT has high spatial resolution and high imaging speed to assist clinical decision making in real-time. OCT can be used in both structural imaging and mechanical characterization. Malignant tumor tissue alters morphology. Additionally, structural OCT imaging has limited tissue differentiation capability because of the complex and noisy nature of the OCT signal. Moreover, the contrast of structural OCT signal derived from tissue’s light scattering properties has little chemical specificity. Hence, interrogating additional tissue properties using OCT would improve the outcome of OCT’s clinical applications. In addition to morphological difference, pathological tissue such as cancer breast tissue usually possesses higher stiffness compared to the normal healthy tissue, which indicates a compelling reason for the specific combination of structural OCT imaging with stiffness assessment in the development of dual-modality OCT system for the characterization of the breast cancer diagnosis. This dissertation seeks to integrate the structural OCT imaging and the optical coherence elastography (OCE) for breast cancer tissue characterization. OCE is a functional extension of OCT. OCE measures the mechanical response (deformation, resonant frequency, elastic wave propagation) of biological tissues under external or internal mechanical stimulation and extracts the mechanical properties of tissue related to its pathological and physiological processes. Conventional OCE techniques (i.e., compression, surface acoustic wave, magnetomotive OCE) measure the strain field and the results of OCE measurement are different under different loading conditions. Inconsistency is observed between OCE characterization results from different measurement sessions. Therefore, a robust mechanical characterization is required for force/stress quantification. A quantitative optical coherence elastography (qOCE) that tracks both force and displacement is proposed and developed at NJIT. qOCE instrument is based on a fiber optic probe integrated with a Fabry-Perot force sensor and the miniature probe can be delivered to arbitrary locations within animal or human body. In this dissertation, the principle of qOCE technology is described. Experimental results are acquired to demonstrate the capability of qOCE in characterizing the elasticity of biological tissue. Moreover, a handheld optical instrument is developed to allow in vivo real-time OCE characterization based on an adaptive Doppler analysis algorithm to accurately track the motion of sample under compression. For the development of the dual modality OCT system, the structural OCT images exhibit additive and multiplicative noises that degrade the image quality. To suppress noise in OCT imaging, a noise adaptive wavelet thresholding (NAWT) algorithm is developed to remove the speckle noise in OCT images. NAWT algorithm characterizes the speckle noise in the wavelet domain adaptively and removes the speckle noise while preserving the sample structure. Furthermore, a novel denoising algorithm is also developed that adaptively eliminates the additive noise from the complex OCT using Doppler variation analysis