Kevin M. Moerman

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 (micro=1.80kPa, K=2999kPa) that were in close agreement with parameters derived independently from regression to uniaxial compression tests (micro=1.71kPa, K=2857kPa). Furthermore the FE model was capable of reproducing the experimental indentor force as well as the surface deformation found (R(2)=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.

A Structural Model of Passive Skeletal Muscle shows Two Reinforcement Processes in Resisting Deformation

Passive skeletal muscle derives its structural response from the combination of the titin filaments in the muscle fibres, the collagen fibres in the connective tissue and incompressibility due to the high fluid content. Experiments have shown that skeletal muscle tissue presents a highly asymmetrical three-dimensional behaviour when passively loaded in tension or compression, but structural models predicting this are not available. The objective of this paper is to develop a mathematical model to study the internal mechanisms which resist externally applied deformation in skeletal muscle bulk. One cylindrical muscle fibre surrounded by connective tissue was considered. The collagenous fibres of the endomysium and perimysium were grouped and modelled as tension-only oriented wavy helices wrapped around the muscle fibre. The titin filaments are represented as non-linear tension-only springs. The model calculates the force developed by the titin molecules and the collagen network when the muscle fibre undergoes an isochoric along-fibre stretch. The model was evaluated using a range of literature based input parameters and compared to the experimental fibre-direction stress-stretch data available. Results show the fibre direction non-linearity and tension/compression asymmetry are partially captured by this structural model. The titin filament load dominates at low tensile stretches, but for higher stretches the collagen network was responsible for most of the stiffness. The oblique and initially wavy collagen fibres account for the non-linear tensile response since, as the collagen fibres are being recruited, they straighten and re-orient. The main contribution of the model is that it shows that the overall compression/tension response is strongly influenced by a pressure term induced by the radial component of collagen fibre stretch acting on the incompressible muscle fibre. Thus for along-fibre tension or compression the model predicts that the collagen network contributes to overall muscle stiffness through two different mechanisms: (1) a longitudinal force directly opposing tension and (2) a pressure force on the muscle fibres resulting in an indirect longitudinal load. Although the model presented considers only a single muscle fibre and evaluation is limited to along-fibre loading, this is the first model to propose these two internal mechanisms for resisting externally applied deformation of skeletal muscle tissue.

Uniaxial and biaxial mechanical properties of porcine linea alba

Incisional hernia is a severe complication post-laparoscopic/laparotomy surgery that is commonly associated with the linea alba. However, the few studies on the mechanical properties of the linea alba in the literature appear contradictory, possible due to challenges with the physical dimensions of samples and variations in protocol. This study focuses on the tensile mechanical characterisation of the porcine linea alba, as determined by uniaxial and equi-load biaxial testing using image-based strain measurement methods. Results show that the linea alba demonstrated a non-linear elastic, anisotropic behaviour which is often observed in biological soft tissues. The transverse direction (parallel to fibres) was found to be approximately eight times stiffer than the longitudinal (cross-fibre) direction under both uniaxial and equi-load biaxial loading. The equi-load biaxial tensile tests revealed that contraction could occur in the transverse direction despite increasing load, probably due to the anisotropy of the tissue. Optical surface marker tracking and digital image correlation methods were found to greatly improve the accuracy of stretch measurement, resulting in a 75% change in the apparent stiffness compared to using strain derived from machine cross-head displacement. Additionally, a finite element model of the experiments using a combination of an Ogden and fibre exponential power law model for the linea alba was implemented to quantify the effect of clamping and tissue dimensions (which are suboptimal for tensile testing) on the results. The preliminary model results were used to apply a correction factor to the uniaxial experimental data prior to inverse optimisation to derive best fit material parameters for the fibre reinforced Ogden model. Application of the model to the equi-load biaxial case showed some differences compared to the experimental data, suggesting a more complex anisotropic model may be necessary to capture biaxial behaviour. These results provide an improved assessment of the mechanical properties of the porcine linea alba for wound closure and other studies.

A novel MRI compatible soft tissue indentor and fibre Bragg grating force sensor

MRI is an ideal method for non-invasive soft tissue mechanical properties investigation. This requires mechanical excitation of the bodys tissues and measurement of the corresponding boundary conditions such as soft tissue deformation inside the MRI environment. However, this is technically difficult since load application and measurement of boundary conditions requires MRI compatible actuators and sensors. This paper describes a novel MRI compatible computer controlled soft tissue indentor and optical Fibre Bragg Grating (FBG) force sensor. The high acquisition rate (100Hz) force sensor was calibrated for forces up to 15N and demonstrated a maximum error of 0.043N. Performance and MRI compatibility of the devices was verified using indentation tests on a silicone gel phantom and the upper arm of a volunteer. The computer controlled indentor provided a highly repeatable tissue deformation. Since the indentor and force sensor are composed of non-ferromagnetic materials, they are MRI compatible and no artefacts or temporal SNR reductions were observed. In a phantom study the mean and standard deviation of the temporal SNR levels without the indentor present were 500.18 and 207.08, respectively. With the indentor present the mean and standard deviation were 501.95 and 200.45, respectively. This computer controlled MRI compatible soft tissue indentation system with an integrated force sensor has a broad range of applications and will be used in the future for the non-invasive analysis of the mechanical properties of skeletal muscle tissue.

Validation of Continuously Tagged MRI for the Measurement of Dynamic 3D Skeletal Muscle Tissue Deformation

PURPOSE Typically spatial modulation of the magnetization (SPAMM) tagged magnetic resonance imaging (MRI) requires many repeated motion cycles limiting the applicability to highly repeatable tissue motions only. This paper describes the validation of a novel SPAMM tagged MRI and post-processing framework for the measurement of complex and dynamic 3D soft tissue deformation following just three motion cycles. Techniques are applied to indentation induced deformation measurement of the upper arm and a silicone gel phantom. METHODS A SPAMM tagged MRI methodology is presented allowing continuous (3.3-3.6 Hz) sampling of 3D dynamic soft tissue deformation using non segmented 3D acquisitions. The 3D deformation is reconstructed by the combination of three mutually orthogonal tagging directions, thus requiring only three repeated motion cycles. In addition a fully automatic post-processing framework is presented employing Gabor scale-space and filter-bank analysis for tag extrema segmentation and triangulated surface fitting aided by Gabor filter bank derived surface normals. Deformation is derived following tracking of tag surface triplet triangle intersections. The dynamic deformation measurements were validated using indentation tests (∼20 mm deep at 12 mm/s) on a silicone gel soft tissue phantom containing contrasting markers which provide a reference measure of deformation. In addition, the techniques were evaluated in vivo for dynamic skeletal muscle tissue deformation measurement during indentation of the biceps region of the upper arm in a volunteer. RESULTS For the phantom and volunteer tag point location precision were 44 and 92 μm, respectively resulting in individual displacements precisions of 61 and 91 μm, respectively. For both the phantom and volunteer data cumulative displacement measurement accuracy could be evaluated and the difference between initial and final locations showed a mean and standard deviation of 0.44 and 0.59 mm for the phantom and 0.40 and 0.73 mm for the human data. Finally accuracy of (cumulative) displacement was evaluated using marker tracking in the silicone gel phantom. Differences between true and predicted marker locations showed a mean of 0.35 mm and a standard deviation of 0.63 mm. CONCLUSIONS A novel SPAMM tagged MRI and fully automatic post-processing framework for the measurement of complex 3D dynamic soft tissue deformation following just three repeated motion cycles was presented. The techniques demonstrate dynamic measurement of complex 3D soft tissue deformation at subvoxel accuracy and precision and were validated for 3.3-3.6 Hz sampling of deformation speeds up to 12 mm/s.

Validation of SPAMM tagged MRI based measurement of 3D soft tissue deformation.

PURPOSE This study presents and validates a novel (non-ECG-triggered) MRI sequence based on spatial modulation of the magnetization (SPAMM) to noninvasively measure 3D (quasistatic) soft tissue deformations using only six acquisitions (three static and three indentations). In the current SPAMM tagged MRI approaches, data are typically constructed from many repeated motion cycles. This has so far restricted its application to the measurement of highly repeatable and periodic movements (e.g., cardiac deformation). In biomechanical applications where soft tissue deformation is artificially induced, often by indentation, significant repeatability constraints exist, and for clinical applications, discomfort and health issues generally preclude a large number of repetitions. METHODS A novel (non-ECG-triggered) SPAMM tagged MRI sequence is presented, whereby a single 1-1 (first order) SPAMM set is acquired following a 3D transient field echo acquisition. Full 3D deformation measurement is achieved through the combination of only six acquisitions (three static and three motion cycles). The 3D deformation measurements were validated using quasistatic indentation tests and marker tracking in a silicone gel soft tissue phantom. In addition, the techniques ability to measure 3D soft tissue deformation in vivo was evaluated using indentation of the biceps region of the upper arm in a volunteer. RESULTS Following comparison to marker tracking in the silicone gel phantom, the SPAMM tagged MRI based displacement measurement demonstrated subvoxel accuracy with a mean displacement difference of 72 microm and a standard deviation of 289 microm. In addition, precision of displacement magnitude was evaluated for both the phantom and the volunteer data. The standard deviations of the displacement magnitude with respect to the average displacement magnitude were 75 and 169 microm for the phantom and volunteer data, respectively. CONCLUSIONS The subvoxel accuracy and precision demonstrated in the phantom in combination with the precision comparison between the phantom and the volunteer data provide confidence in the methods presented for measurement of soft tissue deformation in vivo. To the authors knowledge, since only six acquisitions are required, the presented methodology is the fastest SPAMM tagged MRI method currently available for the noninvasive measurement of quasistatic 3D soft tissue deformation.

Control of tension-compression asymmetry in Ogden hyperelasticity with application to soft tissue modelling.

This paper discusses tension-compression asymmetry properties of Ogden hyperelastic formulations. It is shown that if all negative or all positive Ogden coefficients are used, tension-compression asymmetry occurs the degree of which cannot be separately controlled from the degree of non-linearity. A simple hybrid form is therefore proposed providing separate control over the tension-compression asymmetry. It is demonstrated how this form relates to a newly introduced generalised strain tensor class which encompasses both the tension-compression asymmetric Seth-Hill strain class and the tension-compression symmetric Bažant strain class. If the control parameter is set to q=0.5 a tension-compression symmetric form involving Bažant strains is obtained with the property Ψ(λ1,λ2,λ3)=Ψ(1λ1,1λ2,1λ3). The symmetric form may be desirable for the definition of ground matrix contributions in soft tissue modelling allowing all deviation from the symmetry to stem solely from fibrous reinforcement. Such an application is also presented demonstrating the use of the proposed formulation in the modelling of the non-linear elastic and transversely isotropic behaviour of skeletal muscle tissue in compression (the model implementation and fitting procedure have been made freely available). The presented hyperelastic formulations may aid researchers in independently controlling the degree of tension-compression asymmetry from the degree of non-linearity, and in the case of anisotropic materials may assist in determining the role played by, either the ground matrix, or the fibrous reinforcing structures, in generating asymmetry.

Multi-material 3-D viscoelastic model of a transtibial residuum from in-vivo indentation and MRI data

Although the socket is critical in a prosthetic system for a person with limb amputation, the methods of its design are largely artisanal. A roadblock for a repeatable and quantitative socket design process is the lack of predictive and patient specific biomechanical models of the residuum. This study presents the evaluation of such a model using a combined experimental-numerical approach. The model geometry and tissue boundaries are derived from magnetic resonance imaging (MRI). The soft tissue non-linear elastic and viscoelastic mechanical behavior was evaluated using inverse finite element analysis (FEA) of in-vivo indentation experiments. A custom designed robotic in-vivo indentation system was used to provide a rich experimental data set of force versus time at 18 sites across a limb. During FEA, the tissues were represented by two layers, namely the skin-adipose layer and an underlying muscle-soft tissue complex. The non-linear elastic behavior was modeled using 2nd order Ogden hyperelastic formulations, and viscoelasticity was modeled using the quasi-linear theory of viscoelasticity. To determine the material parameters for each tissue, an inverse FEA based optimization routine was used that minimizes the combined mean of the squared force differences between the numerical and experimental force-time curves for indentations at 4 distinct anatomical regions on the residuum. The optimization provided the following material parameters for the skin-adipose layer: [c=5.22kPam=4.79γ=3.57MPaτ=0.32s] and for the muscle-soft tissue complex [c=5.20kPam=4.78γ=3.47MPaτ=0.34s]. These parameters were evaluated to predict the force-time curves for the remaining 14 anatomical locations. The mean percentage error (mean absolute error/ maximum experimental force) for these predictions was 7±3%. The mean percentage error at the 4 sites used for the optimization was 4%.

Passive skeletal muscle response to impact loading: experimental testing and inverse modelling.

Appropriate mechanical representation of passive muscle tissue is crucial for human body impact modelling. In this paper the experimental and modelling results of compressive loading of freshly slaughtered porcine muscle samples using a drop-tower testing rig are reported. Fibre and cross-fibre compression tests at strain rates varying from 11,600%/s to 37,800%/s were performed. Experimental results show a nonlinear stress-stretch relationship as well as a clear rate dependency of the stress. The mean (standard deviation) engineering stress in the fibre direction at a stretch of 0.7 was 22.47 kPa (5.34 kPa) at a strain rate of 22,000%/s and 38.11k Pa (5.41 kPa) at a strain rate of 37,800%/s. For the cross-fibre direction, the engineering stresses were 5.95 kPa (1.12 kPa) at a strain rate of 11,600%/s, 25.52 kPa (5.12 kPa) at a strain rate of 22,000%/s and 43.66 kPa (6.62 kPa) at a strain rate of 37,800%/s. Significant local strain variations were observed, as well as an average mass loss of 8% due to fluid exudation, highlighting the difficulties in these kinds of tests. The inverse analysis shows for the first time that the mechanical response in terms of both applied load and tissue deformation for each of the strain rates can be captured using a 1st order Ogden hyperelastic material law extended with a three-term quasilinear viscoelastic (QVL) expansion to model viscoelastic effects. An optimisation procedure was used to derive optimal material parameters for which the error in the predicted boundary condition force at maximum compression was less than 3% for all three rates of testing (11,600%/s, 22,000%/s and 37,800%/s). This model may be appropriate for whole body impact modelling at these rates.

Evaluation of a validation method for MR imaging-based motion tracking using image simulation

Magnetic Resonance (MR) imaging-based motion and deformation tracking techniques combined with finite element (FE) analysis are a powerful method for soft tissue constitutive model parameter identification. However, deriving deformation data from MR images is complex and generally requires validation. In this paper a validation method is presented based on a silicone gel phantom containing contrasting spherical markers. Tracking of these markers provides a direct measure of deformation. Validation of in vivo medical imaging techniques is often challenging due to the lack of appropriate reference data and the validation method may lack an appropriate reference. This paper evaluates a validation method using simulated MR image data. This provided an appropriate reference and allowed different error sources to be studied independently and allowed evaluation of the method for various signal-to-noise ratios (SNRs). The geometric bias error was between 0– voxels while the noisy magnitude MR image simulations demonstrated errors under 0.1161 voxels (SNR: 5–35).