Soft tissue modelling for applications in virtual surgery and surgical robotics

Soft tissue modelling has gained a great deal of importance, for a large part due to its application in surgical training simulators for minimally invasive surgery (MIS). This article provides a structured overview of different continuum-mechanical models that have been developed over the years. It aims at facilitating model choice for specific soft tissue modelling applications. According to the complexity of the model, different features of soft biological tissue will be incorporated, i.e. nonlinearity, viscoelasticity, anisotropy, heterogeneity and finally, tissue damage during deformation. A brief summary of experimental methods for material characterisation and an introduction to methods for geometric modelling are also provided. The overview is non-exhaustive, focusing on the most important general models and models with specific biological applications. A trade-off in complexity must be made for enabling real-time simulation, but still maintaining realistic representation of the organ deformation. Depending on the organ and tissue types, different models with emphasis on certain features will prove to be more appropriate, meaning the optimal model choice is organ and tissue-dependent.     

The modelling of interactions between organs and medical tools: a volumetric mass-spring chain algorithm

This paper adds volume deformation capability to the mass-spring chain method using tetrahedral elements in order to obtain more realistic deformations, which occur during the interactions between medical tools and soft tissues. The mass-spring chain method originally does not consider volume information and performs deformation by moving and deforming individual springs of a deformable model. However, most of the applications in computer graphics require volume modelling using tetrahedrons. In the proposed method, the deformation algorithm loops through tetrahedrons and performs deformation based on defined rules similar to those of the original mass-spring chain method. This method can handle not only ordinary deformation applications but also those with topology changes, such as cutting and tearing, as it does not rely on any pre-computed quantities. A method to preserve the volume and the shape of the tetrahedral elements is also developed. In order to speed up the new version of the algorithm, a tetrahedral propagation for deformation is developed. The detailed implementation of the algorithm and the various applications of the organ–surgery tool interactions are presented. The paper also provides the animations of the different models obtained by the proposed method.     

Version control of pathway models using XML patches

Background  

Computational modelling has become an important tool in understanding biological systems such as signalling pathways. With an increase in size complexity of models comes a need for techniques to manage model versions and their relationship to one another. Model version control for pathway models shares some of the features of software version control but has a number of differences that warrant a specific solution.     

Gene regulatory network inference: Data integration in dynamic models—A review

Systems biology aims to develop mathematical models of biological systems by integrating experimental and theoretical techniques. During the last decade, many systems biological approaches that base on genome-wide data have been developed to unravel the complexity of gene regulation. This review deals with the reconstruction of gene regulatory networks (GRNs) from experimental data through computational methods. Standard GRN inference methods primarily use gene expression data derived from microarrays. However, the incorporation of additional information from heterogeneous data sources, e.g. genome sequence and protein–DNA interaction data, clearly supports the network inference process. This review focuses on promising modelling approaches that use such diverse types of molecular biological information. In particular, approaches are discussed that enable the modelling of the dynamics of gene regulatory systems. The review provides an overview of common modelling schemes and learning algorithms and outlines current challenges in GRN modelling.     

Towards mechanistic models of plant organ growth

Modelling and simulation are increasingly used as tools in the study of plant growth and developmental processes. By formulating experimentally obtained knowledge as a system of interacting mathematical equations, it becomes feasible for biologists to gain a mechanistic understanding of the complex behaviour of biological systems. In this review, the modelling tools that are currently available and the progress that has been made to model plant development, based on experimental knowledge, are described. In terms of implementation, it is argued that, for the modelling of plant organ growth, the cellular level should form the cornerstone. It integrates the output of molecular regulatory networks to two processes, cell division and cell expansion, that drive growth and development of the organ. In turn, these cellular processes are controlled at the molecular level by hormone signalling. Therefore, combining a cellular modelling framework with regulatory modules for the regulation of cell division, expansion, and hormone signalling could form the basis of a functional organ growth simulation model. The current state of progress towards this aim is that the regulation of the cell cycle and hormone transport have been modelled extensively and these modules could be integrated. However, much less progress has been made on the modelling of cell expansion, which urgently needs to be addressed. A limitation of the current generation models is that they are largely qualitative. The possibilities to characterize existing and future models more quantitatively will be discussed. Together with experimental methods to measure crucial model parameters, these modelling techniques provide a basis to develop a Systems Biology approach to gain a fundamental insight into the relationship between gene function and whole organ behaviour.     

Statistical finite element method for real-time tissue mechanics analysis

The finite element (FE) method can accurately calculate tissue deformation. However, its low speed renders it ineffective for many biomedical applications involving real-time data processing. To accelerate FE analysis, we introduce a novel tissue mechanics simulation technique. This technique is suitable for real-time estimation of tissue deformation of specific organs, which is required in computer-aided diagnostic or therapeutic procedures. In this method, principal component analysis is used to describe each organ shape and its corresponding FE field for a pool of patients by a small number of weight factors. A mapping function is developed to relate the parameters of organ shape to their FE field counterpart. We show that irrespective of the complexity of the tissue's constitutive law or its loading conditions, the proposed technique is highly accurate and fast in estimating the FE field. Average deformation errors of less than 2% demonstrate the accuracy of the proposed technique.     

In vivo characterization of mechanical tissue properties of internal organs using endoscopic microscopy and inverse finite element analysis

Knowledge about mechanical tissue properties is required for functional modelling and simulating of tissue and organ responses to external mechanical stress. To get the right properties especially for functional modelling of organs, tissue properties have to be determined in vivo. There are only few described methods for characterization of internal organ's tissue mechanics that can be applied in vivo. We introduce and evaluate a method to determine mechanical tissue properties, especially those of lung tissue, endoscopically. Inverse finite element analysis (utilizing a Neo-Hookean model for hyperelastic materials) and image processing algorithms are used to determine the shear modulus of a soft tissue. The resulting values for shear moduli were normally distributed. The shear modulus of the artificial tissue sample was determined with a relative error of 0.47% compared to the value obtained by uniaxial tensile test.     

Identifying a minimal rheological configuration: a tool for effective and efficient constitutive modeling of soft tissues

We describe a modeling methodology intended as a preliminary step in the identification of appropriate constitutive frameworks for the time-dependent response of biological tissues. The modeling approach comprises a customizable rheological network of viscous and elastic elements governed by user-defined 1D constitutive relationships. The model parameters are identified by iterative nonlinear optimization, minimizing the error between experimental and model-predicted structural (load-displacement) tissue response under a specific mode of deformation. We demonstrate the use of this methodology by determining the minimal rheological arrangement, constitutive relationships, and model parameters for the structural response of various soft tissues, including ex vivo perfused porcine liver in indentation, ex vivo porcine brain cortical tissue in indentation, and ex vivo human cervical tissue in unconfined compression. Our results indicate that the identified rheological configurations provide good agreement with experimental data, including multiple constant strain rate load/unload tests and stress relaxation tests. Our experience suggests that the described modeling framework is an efficient tool for exploring a wide array of constitutive relationships and rheological arrangements, which can subsequently serve as a basis for 3D constitutive model development and finite-element implementations. The proposed approach can also be employed as a self-contained tool to obtain simplified 1D phenomenological models of the structural response of biological tissue to single-axis manipulations for applications in haptic technologies.     

Homology modelling and spectroscopy, a never-ending love story

Homology modelling is normally the technique of choice when experimental structure data are not available but three-dimensional coordinates are needed, for example, to aid with detailed interpretation of results of spectroscopic studies. Herein, the state of the art of homology modelling will be described in the light of a series of recent developments, and an overview will be given of the problems and opportunities encountered in this field. The major topic, the accuracy and precision of homology models, will be discussed extensively due to its influence on the reliability of conclusions drawn from the combination of homology models and spectroscopic data. Three real-world examples will illustrate how both homology modelling and spectroscopy can be beneficial for (bio)medical research.     

Bottom up proteomics data analysis strategies to explore protein modifications and genomic variants

The quest to understand biological systems requires further attention of the scientific community to the challenges faced in proteomics. In fact the complexity of the proteome reaches uncountable orders of magnitude. This means that significant technical and data‐analytic innovations will be needed for the full understanding of biology. Current state of art MS is probably our best choice for studying protein complexity and exploring new ways to use MS and MS derived data should be given higher priority. We present here a brief overview of visualization and statistical analysis strategies for quantitative peptide values on an individual protein basis. These analysis strategies can help pinpoint protein modifications, splice, and genomic variants of biological relevance. We demonstrate the application of these data analysis strategies using a bottom‐up proteomics dataset obtained in a drug profiling experiment. Furthermore, we have also observed that the presented methods are useful for studying peptide distributions from clinical samples from a large number of individuals. We expect that the presented data analysis strategy will be useful in the future to define functional protein variants in biological model systems and disease studies. Therefore robust software implementing these strategies is urgently needed.     

Analytical strategies for phosphoproteomics

Protein phosphorylation is a key regulator of cellular signaling pathways. It is involved in most cellular events in which the complex interplay between protein kinases and protein phosphatases strictly controls biological processes such as proliferation, differentiation, and apoptosis. Defective or altered signaling pathways often result in abnormalities leading to various diseases, emphasizing the importance of understanding protein phosphorylation. Phosphorylation is a transient modification, and phosphoproteins are often very low abundant. Consequently, phosphoproteome analysis requires highly sensitive and specific strategies. Today, most phosphoproteomic studies are conducted by mass spectrometric strategies in combination with phospho‐specific enrichment methods. This review presents an overview of different analytical strategies for the characterization of phosphoproteins. Emphasis will be on the affinity methods utilized specifically for phosphoprotein and phosphopeptide enrichment prior to MS analysis, and on recent applications of these methods in cell biological applications.     

Self-expanding stent modelling and radial force accuracy

Computational simulations using finite element analysis are a tool commonly used to analyse stent designs, deployment geometries and interactions between stent struts and arterial tissue. Such studies require large computational models and efforts are often made to simplify models in order to reduce computational time while maintaining reasonable accuracy. The objective of the study is focused on computational modelling and specifically aims to investigate how different methods of modelling stent–artery interactions can affect the results, computational time taken and computational size of the model. Various different models, each with increasing levels of complexity, are used to simulate this analysis, representing the many assumptions and simplifications used in other similar studies in order to determine what level of simplification will still allow for an accurate representation of stent radial force and resulting stress concentrations on the inner lining of the vessel during self-expanding stent deployment. The main conclusions of the study are that methods used in stent crimping impact on the resulting predicted radial force of the stent; that accurate representation of stent–artery interactions can only be made when modelling the full length of the stent due to the incorporation of end effects; and that modelling self-contact of the stent struts greatly impacts on the resulting stress concentrations within the stent, but that the effect of this on the unloading behaviour and resulting radial force of the stent is negligible.     

Structural modelling of the cardiovascular system

Computational modelling of the cardiovascular system offers much promise, but represents a truly interdisciplinary challenge, requiring knowledge of physiology, mechanics of materials, fluid dynamics and biochemistry. This paper aims to provide a summary of the recent advances in cardiovascular structural modelling, including the numerical methods, main constitutive models and modelling procedures developed to represent cardiovascular structures and pathologies across a broad range of length and timescales; serving as an accessible point of reference to newcomers to the field. The class of so-called hyperelastic materials provides the theoretical foundation for the modelling of how these materials deform under load, and so an overview of these models is provided; comparing classical to application-specific phenomenological models. The physiology is split into components and pathologies of the cardiovascular system and linked back to constitutive modelling developments, identifying current state of the art in modelling procedures from both clinical and engineering sources. Models which have originally been derived for one application and scale are shown to be used for an increasing range and for similar applications. The trend for such approaches is discussed in the context of increasing availability of high performance computing resources, where in some cases computer hardware can impact the choice of modelling approach used.     

Digital image correlation and finite element modelling as a method to determine mechanical properties of human soft tissue in vivo

The mechanical properties of human soft tissue are crucial for impact biomechanics, rehabilitation engineering, and surgical simulation. Validation of these constitutive models using human data remains challenging and often requires the use of non-invasive imaging and inverse finite element (FE) analysis. Post-processing data from imaging methods such as tagged magnetic resonance imaging (MRI) can be challenging. Digital image correlation (DIC), however, is a relatively straightforward imaging method. DIC has been used in the past to study the planar and superficial properties of soft tissue and excised soft tissue layers. However, DIC has not been used to non-invasive study of the bulk properties of human soft tissue in vivo. Thus, the goal of this study was to assess the use of DIC in combination with FE modelling to determine the bulk material properties of human soft tissue. Indentation experiments were performed on a silicone gel soft tissue phantom. A two camera DIC setup was then used to record the 3D surface deformation. The experiment was then simulated using a FE model. The gel was modelled as Neo-Hookean hyperelastic, and the material parameters were determined by minimising the error between the experimental and FE data. The iterative FE analysis determined material parameters (μ=1.80 kPa, K=2999 kPa) that were in close agreement with parameters derived independently from regression to uniaxial compression tests (μ=1.71 kPa, K=2857 kPa). Furthermore the FE model was capable of reproducing the experimental indentor force as well as the surface deformation found (R²=0.81). It was therefore concluded that a two camera DIC configuration combined with FE modelling can be used to determine the bulk mechanical properties of materials that can be represented using hyperelastic Neo-Hookean constitutive laws.     

Validation protocol of models for centre of mass estimation.

The estimation of the body centre-of-mass (COM) position requires the modelling of the human body as a system of rigid segments and the measurement of the position of related external anatomical landmarks. Many models for COM position estimation have been proposed with different levels of complexity and, in some cases, specific protocols have been used for model accuracy evaluation. In this paper, we propose a general method for the quantitative assessment of any COM model in relation to a determined set of movements. It consists of an experimental protocol and of a set of comparative indices, which quantify the congruence among the estimated kinematic variables and their expected values. The general applicability of the method is specifically addressed to models' comparison, aiming to support the user in the process of choice and validation of the most suitable model for her/his purposes. In this frame, the results of the analytical comparison among two kinematic models with different levels of complexity are reported.     

GPU-based real-time soft tissue deformation with cutting and haptic feedback

This article describes a series of contributions in the field of real-time simulation of soft tissue biomechanics. These contributions address various requirements for interactive simulation of complex surgical procedures. In particular, this article presents results in the areas of soft tissue deformation, contact modelling, simulation of cutting, and haptic rendering, which are all relevant to a variety of medical interventions. The contributions described in this article share a common underlying model of deformation and rely on GPU implementations to significantly improve computation times. This consistency in the modelling technique and computational approach ensures coherent results as well as efficient, robust and flexible solutions.     

On the effects of residual stress in microindentation tests of soft tissue structures

Microindentation methods are commonly used to determine material properties of soft tissues at the cell or even sub-cellular level. In determining properties from force-displacement (FD) data, it is often assumed that the tissue is initially a stress-free, homogeneous, linear elastic half-space. Residual stress, however, can strongly influence such results. In this paper, we present a new microindentation method for determining both elastic properties and residual stress in soft tissues that, to a first approximation, can be regarded as a pre-stressed layer embedded in or adhered to an underlying relatively soft, elastic foundation. The effects of residual stress are shown using two linear elastic models that approximate specific biological structures. The first model is an axially loaded beam on a relatively soft, elastic foundation (i.e., stress-fiber embedded in cytoplasm), while the second is a radially loaded plate on a foundation (e.g., cell membrane or epithelium). To illustrate our method, we use a nonlinear finite element (FE) model and experimental FD and surface contour data to find elastic properties and residual stress in the early embryonic chick heart, which, in the region near the indenter tip, is approximated as an isotropic circular plate under tension on a foundation. It is shown that the deformation of the surface in a microindentation test can be used along with FD data to estimate material properties, as well as residual stress, in soft tissue structures that can be regarded as a plate under tension on an elastic foundation. This method may not be as useful, however, for structures that behave as a beam on a foundation.     

An eFTD-VP framework for efficiently generating patient-specific anatomically detailed facial soft tissue FE mesh for craniomaxillofacial surgery simulation

Accurate surgical planning and prediction of craniomaxillofacial surgery outcome requires simulation of soft tissue changes following osteotomy. This can only be achieved by using an anatomically detailed facial soft tissue model. The current state-of-the-art of model generation is not appropriate to clinical applications due to the time-intensive nature of manual segmentation and volumetric mesh generation. The conventional patient-specific finite element (FE) mesh generation methods are to deform a template FE mesh to match the shape of a patient based on registration. However, these methods commonly produce element distortion. Additionally, the mesh density for patients depends on that of the template model. It could not be adjusted to conduct mesh density sensitivity analysis. In this study, we propose a new framework of patient-specific facial soft tissue FE mesh generation. The goal of the developed method is to efficiently generate a high-quality patient-specific hexahedral FE mesh with adjustable mesh density while preserving the accuracy in anatomical structure correspondence. Our FE mesh is generated by eFace template deformation followed by volumetric parametrization. First, the patient-specific anatomically detailed facial soft tissue model (including skin, mucosa, and muscles) is generated by deforming an eFace template model. The adaptation of the eFace template model is achieved by using a hybrid landmark-based morphing and dense surface fitting approach followed by a thin-plate spline interpolation. Then, high-quality hexahedral mesh is constructed by using volumetric parameterization. The user can control the resolution of hexahedron mesh to best reflect clinicians’ need. Our approach was validated using 30 patient models and 4 visible human datasets. The generated patient-specific FE mesh showed high surface matching accuracy, element quality, and internal structure matching accuracy. They can be directly and effectively used for clinical simulation of facial soft tissue change.