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Estimation of the Fracture Toughness of Soft Tissue from Needle Insertion
Abstract
A fracture mechanics approach was employed to develop a model that can predict the penetration force during quasi-static needle
insertion in soft tissue. The model captures a mechanical process where the sharp needle produces a crack that is opened to
accommodate the shaft of the needle. This process involves the interchange of energy between four distinct phenomena: the
work done by the needle, the irreversible work of fracture, the work of friction, and the change in recoverable strain energy.
From measurements made in vivo, porcine liver fracture toughness was estimated from the difference in penetration force between
two consecutive insertions at the same location. The values obtained fall within a reasonable range and confirm the relevance
of a computational model of needle insertion based on fracture mechanics.
... During autoinjection, the needle initially elastically deforms the tissue. When sufficient stress concentrations are achieved, a mode I crack forms and propagates ahead of the needle tip (Shergold and Fleck, 2004;Azar and Hayward, 2008). Finite element models have been employed to describe quasi-static needle insertion (Oldfield et al., 2013;Terzano et al., 2020;Mohammadi et al., 2021;Bojairami et al., 2021). ...
... However, these models do not consider the coupled dynamics of the autoinjector, which affect the needle insertion process. Both autoinjector design parameters and tissue properties determine the injection process (Azar and Hayward, 2008). For example it has been experimentally observed that increasing needle insertion velocities reduces the force required for needle insertion (Mahvash and Dupont, 2009;van Gerwen et al., 2012). ...
... The needle insertion process is modeled as an energy balance problem, where the total work done by the autoinjector on the skin is V. Sree et al. split into deformation of the tissue, crack propagation, and dissipation between the needle and the crack surface due to frictional contact (Shergold and Fleck, 2004;Azar and Hayward, 2008). A detailed description of the model and its validation against experiments is in our recent publication (Sree et al., 2022). ...
Autoinjectors are becoming a primary drug delivery option to the subcutaneous space. These devices need to work robustly and autonomously to maximize drug bio-availability. However, current designs ignore the coupling between autoinjector dynamics and tissue biomechanics. Here we present a Bayesian framework for optimization of autoinjector devices that can account for the coupled autoinjector-tissue biomechanics and uncertainty in tissue mechanical behavior. The framework relies on replacing the high fidelity model of tissue insertion with a Gaussian process (GP). The GP model is accurate yet computationally affordable, enabling a thorough sensitivity analysis that identified tissue properties, which are not part of the autoinjector design space, as important variables for the injection process. Higher fracture toughness decreases the crack depth, while tissue shear modulus has the opposite effect. The sensitivity analysis also shows that drug viscosity and spring force, which are part of the design space, affect the location and timing of drug delivery. Low viscosity could lead to premature delivery, but can be prevented with smaller spring forces, while higher viscosity could prevent premature delivery while demanding larger spring forces and increasing the time of injection. Increasing the spring force guarantees penetration to the desired depth, but it can result in undesirably high accelerations. The Bayesian optimization framework tackles the challenge of designing devices with performance metrics coupled to uncertain tissue properties. This work is important for the design of other medical devices for which optimization in the presence of material behavior uncertainty is needed.
... While not fit to specific data-set, the fracture toughness was obtained from reported values of fracture toughness for skin, which ranges from 0.1 − 10 kJ/m 2 (Purslow 1983;Azar and Hayward 2008). The fracture curves in Fig. 9b are in line with pure shear testing of other collagenous thin tissues such as amniotic membranes (Koh et al. 2019). ...
... Additionally, for the fracture simulations we also considered range of fracture toughness for dermis from the literature (Koh et al. 2019;Purslow 1983;Azar and Hayward 2008). Because we use a Weibull distribution to parameterize fiber waviness, the strategy to model damage used here is to model how the scale parameter of the Weibull distribution changes as a function of deformation. ...
... Our analysis was informed by available data in the literature, e.g. (Kumaraswamy et al. 2017;Azar and Hayward 2008). Thus, the range of parameters is within reasonable ranges based on these sources. ...
The analysis of tissue mechanics in biomedical applications demands nonlinear constitutive models able to capture the energy dissipation mechanisms, such as damage, that occur during tissue deformation. Furthermore, implementation of sophisticated material models in finite element models is essential to improve medical devices and diagnostic tools. Building on previous work toward microstructure-driven models of collagenous tissue, here we show a constitutive model based on fiber orientation and waviness distributions for skin that captures not only the anisotropic strain-stiffening response of this and other collagen-based tissues, but, additionally, accounts for tissue damage directly as a function of changes in the microstructure, in particular changes in the fiber waviness distribution. The implementation of this nonlinear constitutive model as a user subroutine in the popular finite element package Abaqus enables large-scale finite element simulations for biomedical applications. We showcase the performance of the model in fracture simulations during pure shear tests, as well as simulations of needle insertion into skin relevant to auto-injector design.
... Puncturing of soft solids is characterised by complex mechanisms of progressive failure and penetration of a cutting tool into a target material. 1 The analysis and experimental measurement of puncturing and cutting forces are of great interest for a diversified range of engineering applications, including optimisation of high-precision cutting machines in the food industry, 2-4 mechanical characterisation of soft polymers [5][6][7][8] and biological tissues, [9][10][11][12][13] optimisation of surgical tools [14][15][16][17][18] and design of advanced drug delivery systems. 19,20 Research concerning the mechanics of puncturing is particularly active in the realm of soft biological tissues. ...
... On the other hand, by assuming a uniform contact pressure equal to s 0 = E*/2 -which, according to (9), produces a maximum crack flank displacement equal to R -we get ...
The integrity of soft materials against puncturing is of great relevance for their performance because of the high sensitivity to local rupture caused by rigid sharp objects. In this work, the mechanics of puncturing is studied with respect to a sharp-tipped rigid needle with a circular cross section, penetrating a soft target solid. The failure mode associated with puncturing is identified as a mode-I crack propagation, which is analytically described by a two-dimensional model of the target solid, taking place in a plane normal to the penetration axis. It is shown that the force required for the onset of needle penetration is dependent on two energy contributions, that are, the strain energy stored in the target solid and the energy consumed in crack propagation. More specifically, the force is found to be dependent on the fracture toughness of the material, its stiffness and the sharpness of the penetrating tool. The reference case within the framework of small strain elasticity is first investigated, leading to closed-form toughness parameters related to classical linear elastic fracture mechanics. Then, nonlinear finite element analyses for an Ogden hyperelastic material are presented. Supporting the proposed theoretical framework, a series of puncturing experiments on two commercial silicones is presented. The combined experimental-theoretical findings suggest a simple, yet reliable tool to easily handle and assess safety against puncturing of soft materials.
... Deformation-based models come from the observation of forces due to the penetration of the needle into the tissues without considering underlying physics. In the second category, the needle insertion is modeled as a crack that propagates with the help of an energetic approach [21]. ...
... In EBM, the cutting is considered as the consequence of exchanges of energy between the needle and the tissue, causing crack propagation. Early works demonstrated the relevance of this approach [21,38] but only Barnett et al. exploited this approach to predict insertion forces. Yet, this has not been embedded in a training simulator. ...
Purpose of Review
This short review updates an exhaustive one written by Correa et al. in 2019 about haptic training simulation on needle insertion in the medical field.
Recent Findings
Latest works refine well-known models and enhance setups and methods to facilitate generically getting experimental data.
Summary
We provide a complementary focus on device specifications and recent models to render this specific haptic feedback on computer-based simulators. Assessment approaches and the issues encountered when introducing such simulators into curricula are also discussed. FEM-based approaches still do not permit real-time computation but hybrid approaches as proposed by Wittek et al. in 2020 may become a good compromise. Nonetheless, psychophysical studies should be performed to determine the haptic fidelity of the various approaches found in the literature, and embed them efficiently in medical curricula. This would permit to delay the necessary final hands-on training on patients that raises ethical issues.
... They provided force-displacement results for the investigated variation of cohesive parameters as well as a detailed interpretation of different stages of the insertion procedure and the related energy distribution of the cutting process. They stated that the energy required for needle insertion ( W ext ) consists of three main components including strain energy ( U s ), fracture energy ( U G ), and frictional energy ( U f ) [70,76]: ...
Needle insertion into soft biological tissues has been of interest to researchers in the recent decade due to its minimal invasiveness in diagnostic and therapeutic medical procedures. This paper presents a review of the finite-element (FE) modelling of the interaction of needle/microneedles with soft biological tissues or tissue phantoms. The reviewed models laid a solid foundation for developing more efficient novel medical technologies. This paper encompasses FE models for both invasive and non-invasive needle-tissue interactions. The former focuses on tissue and needle deformation without employing any damage mechanism, whereas the latter incorporates algorithms that enable crack propagation with a damage mechanism. Invasive FE models are presented in five categories, namely nodal separation, element failure/deletion, cohesive zone (CZ), arbitrary Lagrangian–Eulerian (ALE), and coupled Eulerian–Lagrangian (CEL) methods. In each section, the most important aspects of modelling, challenges, and novel techniques are presented. Furthermore, the application of FE modelling in real-time haptic devices and a survey on some of the most important studies in this area are presented. At the end of the paper, the importance and strength of the reviewed studies are discussed and the remaining limitations for future studies are highlighted.
... 71 The indication of length of crack for porcine liver is somewhat same as the needle diameter for 22°bevel and greater diameter in the case of 45°bevel was found out by Azar and Hayward. 86 A big needle model having diameter 15 mm and angle of bevel 10°-60°was inserted in three types of plastisol gels was demonstrated by Misra et al. 87 With the increase in angle of bevel there was a decrease of transverse force, which started at 4 N for 10°angle of bevel that is approaching zero at angle of 45°. The consideration of the tip angle effect was done by Naemura 88 and Kataoka et al. 28 though the clear results were not found. ...
The insertion of the surgical needle in soft tissue has involved significant interest in the current time because of its purpose in minimally invasive surgery (MIS) and percutaneous events like biopsies, PCNL, and brachytherapy. This study represents a review of the existing condition of investigation on insertion of a surgical needle in biological living soft tissue material. As observes the issue from numerous phases, like, analysis of the cutting forces modeling (insertion), tissue material deformation, analysis of the needle deflection for the period of the needle insertion, and the robot-controlled insertion procedures. All analysis confirms that the total needle insertion force is the total of dissimilar forces spread sideways the shaft of the insertion needle for example cutting force, stiffness force, and frictional force. Various investigations have analyzed all these kinds of forces during the needle insertion process. The force data in several measures are applied for recognizing the biological tissue materials as the needle is penetrated or for path planning. The deflection of the needle during insertion and tissue material deformation is the main trouble for defined needle placing and efforts have been prepared to model them. Applying existing models numerous insertion methods are established that are discussed in this review.
Needle-tissue interaction deformation model can provide the future interaction deformation prediction which can be used to establish the virtual surgery training platform. The prediction information can be used to assist needle path planning scheme. However, existing models either only model the global coupled deformation without force prediction module or model the local contact mechanism between the needle and tissue. The calculation efficiency of the contact mechanism based model limits its application in needle path planning task. In this paper, a novel full prediction model of 3D needle insertion procedures was proposed. The Kriging model can realize fast calculation of the friction force, which is coupled to the 3D needle-tissue coupled deformation model. The local constraint method is applied to avoid the reconstruction of stiffness matrix in each step. The model can simultaneously predict tissue deformation, needle deflection and the interaction force with an acceptable calculation efficiency. The simulation results demonstrate the accuracy of the Kriging based friction force model. The visual simulation results of needle insertion process was also given in this paper. The simulation calculation speed (with an average run time of 30 s) demonstrates the feasibility of its application to needle path planning schemes.
Biopsy puncture is commonly used to extract the suspected tissue of cancer for cytological diagnosis. However, the low accuracy and poor performance instability of puncture sample can lead to misdiagnosis. For this problem, the technology of vibration assisted was applied in the process of soft tissue puncture in this paper. The influence of process parameters on the puncture performances were investigated and analyzed. The results indicate that the method of vibration assisted has significant advantages on the puncture performances compared with conventional puncture. The fracture toughness is increased with the increase of insertion velocity and vibration frequency. And, the needle deflection is decreased with the increase of vibration frequency. The conclusions prompt the application of vibration assisted puncture technology in clinical practice.
Micromechanical models are developed for the deep penetration of a soft
solid by a flat-bottomed and by a sharp-tipped cylindrical punch. The
soft solid is taken to represent mammalian skin and silicone rubbers,
and is treated as an incompressible, hyperelastic, isotropic solid
described by a one-term Ogden strain energy function. Penetration of the
soft solid by a flat-bottomed punch is by the formation of a mode-II
ring crack that propagates ahead of the penetrator tip. The sharp-tipped
punch penetrates by the formation of a planar mode-I crack at the punch
tip, followed by wedging open of the crack by the advancing punch. For
both modes of punch advance the steady-state penetration load is
calculated by equating the work done in advancing the punch to the sum
of the fracture work and the strain energy stored in the solid. For the
case of a sharp penetrator, this calculation is performed by considering
the opening of a plane-strain crack by a wedge using a finite-element
approach. Analytical methods suffice for the flat-bottomed punch. In
both models the crack dimensions are such that the load on the punch is
minimized. For both geometries of punch tip, the predicted penetration
pressure increases with diminishing punch radius, and with increasing
toughness and strain-hardening capacity of solid. The penetration
pressure for a flat-bottomed punch is two to three times greater than
that for a sharp-tipped punch (assuming that the mode-I and mode-II
toughnesses are equal), in agreement with experimental observations
reported in a companion paper.
Cutting a deformable body may be viewed as an in- terchange between three forms of energy: the elas- tic energy stored in the deformed body, the work done by a sharp tool as it moves against it, and the irreversible work spent in creating a fracture. Other dissipative phenomena such as friction can optionally also be considered. The force applied can be found by evaluating the work done by a tool which is sufficiently sharp to cause local de- formation only. To evaluate this work, we propose a computational model that reduces cutting to the existence of three modes of interaction: deforma- tion, rupture, and cutting, each of which considers the exchange between two forms of energy. During deformation, the work done by a tool is recover- able. During rupture, this work is zero. During cutting, it is equal to the irreversible work spent by fracture formation. The work spent in separat- ing the sample is a function of its fracture tough- ness and of the area of a crack extension. It is in principle necessary to compute the deformation caused by a sharp tool in order to recover the force. This is in general an unsolved problem. However, for the case of a sharp interaction, measurements from tests performed on samples used in conjunc- tion with analytical approximations to the contact problem, make it possible to propose a model which is applicable to haptic rendering. The technique is then compared to experimental results which con- firms the model hypotheses. An implementation of the model that yields realistic results is also de- scribed.
Percutaneous procedures are among the developing minimally invasive techniques to treat cancerous diseases of the digestive system. They require a very accurate targeting of the organs, achieved by the combination of tactile sensing and medical imaging. In this paper, we study the forces involved during in vivo percutaneous procedures for the development of a force feedback needle insertion robotic system as well as the development of a realistic simulation device. The paper presents different conditions (manual and robotic insertions) and different organs (liver and kidney). Finally, we review some bio-mechanical models of the literature in the light of our measurements.
This paper addresses the characteristic response of soft tissue to the growth of a cut (cracking) with a scalpel blade. We present our experimental equipment, experiments, and the results for scalpel cutting of soft tissue. The experimentally measured cut-force versus cut-length data was used to determine the soft tissue's resistance to fracture (resistance to crack extension) in scalpel cutting. The resistance to fracture (the toughness) of the soft tissue is quantified by the measure R defined as the amount of mechanical work needed to cause a cut (crack) to extend for a unit length in a soft-tissue sample of unit thickness. The equipment, method, and model are applicable for all soft tissue. We used pig liver as soft-tissue samples for our experiments
Needle based intervention procedures are a common minimally invasive surgical technique. In many of these procedures, the needle can be considered rigid and the tissue deforms and displaces substantially as the needle is advanced to its target. An energy based, fracture mechanics approach is presented to show that the velocity dependence of tissue properties can reduce tissue motion with increased needle velocities. In-vitro test results on porcine heart samples show that the force required to initiate cutting reduces with increasing needle velocity up to a critical speed, above which, the rate independent cutting force of the underlying tissue becomes the limiting factor. In-vivo tests show increased needle speed results in reduced force and displacement for needle insertion into the heart. Results indicate that automated insertion could substantially improve performance in some applications.
During percutaneous interventions, the haptic perception of transi- tions and ruptures in the tissues is fundamental. In the medical ro- botics context, these events should be conveyed to a remote telema- nipulating practitioner or should be taken into account in a robotic control scheme. However, this problem is extremely complex given the nature and the variety of tissues involved in percutaneous procedures. In this article, in vivo percutaneous experiments associated with an online model estimation of the interaction between tissues and a sur- gical needle are presented for the first time. The estimation scheme is then used to provide a robust method to automatically detect the transitions that occur during needle insertion. Finally, the principle of a modified teleoperation scheme that would allow better haptic discrimination of ruptures is proposed and illustrated. KEY WORDS—Medical robots, systems, telerobotics
Thin biological membranes such as skin are highly deformable, nonlinear in behaviour and fracture resistant. As a result of these properties, measuring the resistance to fracture of such materials is difficult. This paper investigates the resistance to fracture of a thin biological membrane, using the example of animal skin. Models of cutting using a fracture approach are examined and a review of the structure and mechanical properties of skin is given. A review of previous work in examining the fracture behaviour of skin is carried out and a strain energy-based failure model for skin is proposed. A method of measuring the fracture resistance of skin in opening mode (mode I) using this failure model is described. Values for the resistance to fracture of skin samples were calculated from experiments to be 2.32 ± 0.40 kj m-2. These results were found to be in good agreement with the literature. The model and experimental technique proposed here may be applied to establish the failure properties of membranes and, in particular, a range of soft tissues under a variety of cutting conditions.
Soft tissues modeling is a very present preoccupation in different scientific fields, from computer simulation to biomechanics or medical robotics. In this article, we consider the interaction of a needle with living tissues, which is a particularly complex modeling problem since it is characterized by inhomogeneity and nonlinearity properties. We propose a robust method to online estimate forces involved in typical percutaneous interventions. The ability to obtain physically consistent models during in vivo insertions is also discussed.
The sharpness of a blade is a key parameter in cutting soft solids, such as biological tissues, foodstuffs or elastomeric materials. It has a first order effect on the effort, and hence energy needed to cut, the quality of the cut surface and the life of the cutting instrument. To date, there is no standard definition, measurement or protocol to quantify blade sharpness. This paper derives a quantitative index of blade sharpness via indentation experiments in which elastomeric materials are cut using both sharp and blunt straight edge blades. It is found that the depth of blade indentation required to initiate a cut or crack in the target material is a function of the condition or sharpness of the blade’s cutting edge, and this property is used to formulate a so-called “blade sharpness index” (BSI). It is shown theoretically that this index is zero for an infinitely sharp blade and increases in a quadratic manner for increasing bluntness. For the blades tested herein, the sharpness index was found to vary between 0.2 for sharp blades and 0.5 for blunt blades, respectively. To examine the suitability of the index in other cutting configurations, experiments are performed using different blade types, target materials and cutting rates and it is found that the index is independent of the target material and cutting rate and thus pertains to the blade only. In the companion Part II to this paper a finite element model is developed to examine the effect of blade geometry on the sharpness index derived herein.