Unloaded Configuration Research Articles

Effects of Incremental Changes to Frame Mass on Manual Wheelchair Propulsion Cost.

The objective of this study was to assess the effects of small, incremental additions to wheelchair frame mass (0 kg, +2 kg, and +4 kg) on the mechanical propulsion characteristics in both straight and curvilinear maneuvers. A robotic propulsion system was used to propel a manual wheelchair over a smooth tiled surface following rectilinear ("Straight") and curvilinear ("Slalom") trajectories. Three unique loading conditions were tested. Propulsion costs and system rolling resistance estimations were empirically collected using the robotic wheelchair tester. Propulsion cost values were equivalent across all loading conditions over the Slalom trajectory. In the Straight trajectory, adding 2 kg on the axle had equivalent propulsion cost to the unloaded configuration. Adding 4 kg on axle was comparable, but not equivalent, to the unloaded configuration with small (≤4.1%) increases in propulsion cost. This study demonstrates that small (0-4 kg) changes to the frame mass have no meaningful impacts on the propulsion characteristics of the manual wheelchair system. Differences in propulsion cost and rolling resistance were detectable but contextually insignificant.

MR-based quantitative measurement of human soft tissue internal strains for pressure ulcer prevention.

Pressure ulcers are a severe disease affecting patients that are bedridden or in a wheelchair bound for long periods of time. These wounds can develop in the deep layers of the skin of specific parts of the body, mostly on heels or sacrum, making them hard to detect in their early stages. Strain levels have been identified as a direct danger indicator for triggering pressure ulcers. Prevention could be possible with the implementation of subject-specific Finite Element (FE) models. However, generation and validation of such FE models is a complex task, and the current implemented techniques offer only a partial solution of the entire problem considering only external displacements and pressures, or cadaveric samples. In this paper, we propose an in vivo solution based on the 3D non-rigid registration between two Magnetic Resonance (MR) images, one in an unloaded configuration and the other deformed by means of a plate or an indenter. From the results of the image registration, the displacement field and subsequent strain maps for the soft tissues were computed. An extensive study, considering different cases (on heel pad and sacrum regions) was performed to evaluate the reproducibility and accuracy of the results obtained with this methodology. The implemented technique can give insight for several applications. It adds a useful tool for better understanding the propagation of deformations in the heel soft tissues that could generate pressure ulcers. This methodology can be used to obtain data on the material properties of the soft tissues to define constitutive laws for FE simulations and finally it offers a promising technique for validating FE models.

Robust and efficient fixed-point algorithm for the inverse elastostatic problem to identify myocardial passive material parameters and the unloaded reference configuration

Image-based computational models of the heart represent a powerful tool to shed new light on the mechanisms underlying physiological and pathological conditions in cardiac function and to improve diagnosis and therapy planning. However, in order to enable the clinical translation of such models, it is crucial to develop personalized models that are able to reproduce the physiological reality of a given patient. There have been numerous contributions in experimental and computational biomechanics to characterize the passive behavior of the myocardium. However, most of these studies suffer from severe limitations and are not applicable to high-resolution geometries. In this work, we present a novel methodology to perform an automated identification of in vivo properties of passive cardiac biomechanics. The highly-efficient algorithm fits material parameters against the shape of a patient-specific approximation of the end-diastolic pressure-volume relation (EDPVR). Simultaneously, an unloaded reference configuration is generated, where a novel line search strategy to improve convergence and robustness is implemented. Only clinical image data or previously generated meshes at one time point during diastole and one measured data point of the EDPVR are required as an input. The proposed method can be straightforwardly coupled to existing finite element (FE) software packages and is applicable to different constitutive laws and FE formulations. Sensitivity analysis demonstrates that the algorithm is robust with respect to initial input parameters.

A quasi-static poromechanical model of the lungs.

The lung vital function of providing oxygen to the body heavily relies on its mechanical behavior and the interaction with its complex environment. In particular, the large compliance and the porosity of the pulmonary tissue are critical for lung inflation and air inhalation, and the diaphragm, the pleura, the rib cage and intercostal muscles all play a role in delivering and controlling the breathing driving forces. In this paper, we introduce a novel poromechanical model of the lungs. The constitutive law is derived within a general poromechanics theory via the formulation of lung-specific assumptions, leading to a hyperelastic potential reproducing the volume response of the pulmonary mixture to a change of pressure. Moreover, physiological boundary conditions are formulated to account for the interaction of the lungs with their surroundings, including a following pressure and bilateral frictionless contact. A strategy is established to estimate the unloaded configuration from a given loaded state, with a particular focus on ensuring a positive porosity. Finally, we illustrate through several realistic examples the relevance of our model and its potential clinical applications.

A new approach to calculating fiber fields in 2D vessel cross sections using conformal maps.

An arterial vessel has three layers, namely, the intima, the media and the adventitia. Each of these layers is modeled to have two families of strain-stiffening collagen fibers that are transversely helical. In an unloaded configuration, these fibers are coiled up. In the case of a pressurized lumen, these fibers stretch and start to resist further outward expansion. As the fibers elongate, they stiffen, affecting the mechanical response. Having a mathematical model of vessel expansion is crucial in cardiovascular applications such as predicting stenosis and simulating hemodynamics. Thus, to study the mechanics of the vessel wall under loading, it is important to calculate the fiber configurations in the unloaded configuration. The aim of this paper is to introduce a new technique of using conformal maps to numerically calculate the fiber field in a general arterial cross-section. The technique relies on finding a rational approximation of the conformal map. First, points on the physical cross section are mapped to points on a reference annulus using a rational approximation of the forward conformal map. Next, we find the angular unit vectors at the mapped points, and finally a rational approximation of the inverse conformal map is used to map the angular unit vectors back to vectors on the physical cross section. We have used MATLAB software packages to achieve these goals.

Some Issues on Crystal Plasticity Models Formulation: Motion Decomposition and Constitutive Law Variants

In this paper, kinematic relations and constitutive laws in crystal plasticity are analyzed in the context of geometric nonlinearity description and fulfillment of thermodynamic requirements in the case of elastic deformation. We consider the most popular relations: in finite form, written in terms of the unloaded configuration, and in rate form, written in terms of the current configuration. The presence of a corotational derivative in the relations formulated in terms of the current configuration testifies to the fact that the model is based on the decomposition of motion into the deformation motion and the rigid motion of a moving coordinate system, and precisely the stress rate with respect to this coordinate system is associated with the strain rate. We also examine the relations of the mesolevel model with an explicit separation of a moving coordinate system and the elastic distortion of crystallites relative to it in the deformation gradient. These relations are compared with the above formulations, which makes it possible to determine how close they are. The results of the performed analytical calculations show the equivalence or similarity (in the sense of the response determined under the same influences) of the formulation and are supported by the results of numerical calculation. It is shown that the formulation based on the decomposition of motion with an explicit separation of the moving coordinate system motion provides a theoretical framework for the transition to a similar formulation in rate form written in terms of the current configuration. The formulation of this kind is preferable for the numerical solution of boundary value problems (in a case when the current configuration and, consequently, contact boundaries, are not known a priori) used to model the technological treatment processes.

Seeing Beyond Morphology-Standardized Stress MRI to Assess Human Knee Joint Instability.

While providing the reference imaging modality for joint pathologies, MRI is focused on morphology and static configurations, thereby not fully exploiting the modality’s diagnostic capabilities. This study aimed to assess the diagnostic value of stress MRI combining imaging and loading in differentiating partial versus complete anterior cruciate ligament (ACL)-injury. Ten human cadaveric knee joint specimens were subjected to serial imaging using a 3.0T MRI scanner and a custom-made pressure-controlled loading device. Emulating the anterior-drawer test, joints were imaged before and after arthroscopic partial and complete ACL transection in the unloaded and loaded configurations using morphologic sequences. Following manual segmentations and registration of anatomic landmarks, two 3D vectors were computed between anatomic landmarks and registered coordinates. Loading-induced changes were quantified as vector lengths, angles, and projections on the x-, y-, and z-axis, related to the intact unloaded configuration, and referenced to manual measurements. Vector lengths and projections significantly increased with loading and increasing ACL injury and indicated multidimensional changes. Manual measurements confirmed gradually increasing anterior tibial translation. Beyond imaging of ligament structure and functionality, stress MRI techniques can quantify joint stability to differentiate partial and complete ACL injury and, possibly, compare surgical procedures and monitor treatment outcomes.

Mathematical Modelling of Residual-Stress Based Volumetric Growth in Soft Matter

Growth in nature is associated with the development of residual stresses and is in general heterogeneous and anisotropic at all scales. Residual stress in an unloaded configuration of a growing material provides direct evidence of the mechanical regulation of heterogeneity and anisotropy of growth. The present study explores a model of stress-mediated growth based on the unloaded configuration that considers either the residual stress or the deformation gradient relative to the unloaded configuration as a growth variable. This makes it possible to analyze stress-mediated growth without the need to invoke the existence of a fictitious stress-free grown configuration. Furthermore, applications based on the proposed theoretical framework relate directly to practical experimental scenarios involving the “opening-angle” in arteries as a measure of residual stress. An initial illustration of the theory is then provided by considering the growth of a spherically symmetric thick-walled shell subjected to the incompressibility constraint.

The effect of residual stress on the stability of a circular cylindrical tube

Residual stresses in an unloaded configuration of an elastic material have a significant influence on the response of the material from that configuration, but the effect of residual stress on the stability of the material, whether loaded or unloaded, has only been addressed to a limited extent. In this paper we consider the level of residual stress that can be supported in a thick-walled circular cylindrical tube of non-linearly elastic material without loss of stability when subjected to fixed axial stretch and either internal or external pressure. In particular, we consider the tube to have radial and circumferential residual stresses, with a simple form of elastic constitutive law that accommodates the residual stress, and incremental deformations restricted to the cross section of the tube. Results are described for a tube subject to a level of (internal or external) pressure characterized by the internal azimuthal stretch. Subject to restrictions imposed by the strong ellipticity condition, the emergence of bifurcated solutions is detailed for their dependence on the level of residual stress and mode number.

Elastic–plastic deformation decomposition algorithm for metal clusters at the atomic scale

This study proposes a new elastic–plastic deformation decomposition algorithm for metal clusters to calculate micro-nanoscale elastic and plastic deformation gradients. In the macroscopic plasticity theory, the intermediate configuration is usually constructed by the dissection–unloading method. Because an atomic cluster is equivalent to a small element on a macroscopic object, our decomposition algorithm regards the unloaded configuration as the intermediate configuration for atomic clusters. This algorithm uses a new unloading method to obtain the unloaded configuration. This micro-nanoscale unloading method is constructed based on the principle of minimum potential energy and the embedded-atom method. Moreover, this method rigidly fixes atoms around dislocations during unloading. Therefore, the unloading process will not cause new plastic flow. Once the intermediate configuration is obtained, elastic and plastic deformation gradients are calculated by the interpolation method. Numerical examples of Cu nanowire stretching and bending show that the new decomposition algorithm can accurately and rapidly conduct the elastic–plastic decomposition of the total deformation. This algorithm provides a computational basis for multiscale coupling analysis of mechanical behavior of metal materials from the micro-nanoscale to the macroscale.

The identification of the unloaded configuration of breast tissue with unknown non-homogenous stiffness parameters using surface measured data in deformed configuration

Large deformation analysis of the breast is known as a useful approach for locating the tumor and treatment strategies of breast cancer, for which knowing the breast stiffness parameters and unloaded configuration is crucial to obtain reliable results. In this study, an iterative inverse finite element algorithm is developed to identify the unloaded configuration of the breast while its stiffness constants are unknown and its internal structure is assumed to be non-homogeneous. The position vector of surface points in the deformed configuration of the breast is employed to obtain the unknowns of the inverse problem. An objective function based on the difference between the position vector of the calculated and measured deformed configurations is defined. Thereafter, the objective function is minimized using a gradient-based method. The sensitivity analysis for material parameters is performed using an analytic direct differentiation approach. Through several numerical examples, the effectiveness of the proposed inverse method for identifying the unloaded configuration of a uniform, a computational breast phantom with a single inclusion as well as a computational breast phantom with randomly distributed stiffness, is demonstrated. The effects of the number of load cases, measurement error, and initial guesses on the results of the inverse problem are investigated, as well. It is observed that the unloaded configuration of the computational breast phantom with a single inclusion or heterogeneous breast tissues can be accurately found by considering an equivalent homogenous material for the tissue.

A nonlinear rotation-free shell formulation with prestressing for vascular biomechanics

We implement a nonlinear rotation-free shell formulation capable of handling large deformations for applications in vascular biomechanics. The formulation employs a previously reported shell element that calculates both the membrane and bending behavior via displacement degrees of freedom for a triangular element. The thickness stretch is statically condensed to enforce vessel wall incompressibility via a plane stress condition. Consequently, the formulation allows incorporation of appropriate 3D constitutive material models. We also incorporate external tissue support conditions to model the effect of surrounding tissue. We present theoretical and variational details of the formulation and verify our implementation against axisymmetric results and literature data. We also adapt a previously reported prestress methodology to identify the unloaded configuration corresponding to the medically imaged in vivo vessel geometry. We verify the prestress methodology in an idealized bifurcation model and demonstrate the significance of including prestress. Lastly, we demonstrate the robustness of our formulation via its application to mouse-specific models of arterial mechanics using an experimentally informed four-fiber constitutive model.

Identifying the imaging correlates of cartilage functionality based on quantitative MRI mapping - The collagenase exposure model

Cartilage functionality is determined by tissue structure and composition. If altered, cartilage is predisposed to premature degeneration. This pathomimetical study of early osteoarthritis evaluated the dose-dependant effects of collagenase-induced collagen disintegration and proteoglycan depletion on cartilage functionality as assessed by serial T1, T1ρ, T2, and T2* mapping under loading. 30 human femoral osteochondral samples underwent imaging on a clinical 3.0 T MRI scanner (Achieva, Philips) in the unloaded reference configuration (δ0) and under pressure-controlled quasi-static indentation loading to 15.1 N (δ1) and to 28.6 N (δ2). Imaging was performed before and after exposure to low (LC, 0.5 mg/mL; n = 10) or high concentration (HC, 1.5 mg/mL; n = 10) of collagenase. Untreated samples served as controls (n = 10). Loading responses were determined for the entire sample and the directly loaded (i.e. sub-pistonal) and bilaterally adjacent (i.e. peri‑pistonal) regions, referenced histologically, quantified as relative changes, and analysed using adequate parametric and non-parametric statistical tests. Dose-dependant surface disintegration and tissue loss were reflected by distinctly different pre- and post-exposure response-to-loading patterns. While T1 generally decreased with loading, regardless of collagenase exposure, T1ρ increased significantly after HC exposure (p = 0.008). Loading-induced decreases in T2 were significant after LC exposure (p = 0.006), while changes in T2* were ambiguous. In conclusion, aberrant loading-induced changes in T2 and T1ρ reflect moderate and severe matrix changes, respectively, and indicate the close interrelatedness of matrix changes and functionality in cartilage.

A novel method for the identification of the unloaded configuration of a deformed hyperelastic body

ABSTRACT The unloaded configuration of a body without residual stresses is generally used as the starting point to compute the displacement field but may be unknown for some applications. In this paper, we propose a novel inverse formulation to identify the unloaded configuration of a deformed hyperelastic body using finite element based discretization schemes. The inverse problem consists of finding a domain that is geometrically defined by its boundary such that it deforms in a way consistent with the measurements taken on its deformed configuration. The coordinates of boundary nodes in the deformed configuration can be measured and are assumed to be known for the inverse problem. Since only the coordinates of boundary nodes in the unloaded configuration are updated in each step of the inverse analysis, re-meshing is essential to continue the optimization process. The Akin’s method is employed to map the mesh used for the unloaded configuration in the previous step for the updated one. Both numerical and experimental data sets are used in 2D/3D to demonstrate the effectiveness of the proposed inverse technique. This work could have practical applications in the design of elastomeric parts or to recover the unloaded configuration of soft tissues in vivo.

Identification of in vivo nonlinear anisotropic mechanical properties of ascending thoracic aortic aneurysm from patient-specific CT scans

Accurate identification of in vivo nonlinear, anisotropic mechanical properties of the aortic wall of individual patients remains to be one of the critical challenges in the field of cardiovascular biomechanics. Since only the physiologically loaded states of the aorta are given from in vivo clinical images, inverse approaches, which take into account of the unloaded configuration, are needed for in vivo material parameter identification. Existing inverse methods are computationally expensive, which take days to weeks to complete for a single patient, inhibiting fast feedback for clinicians. Moreover, the current inverse methods have only been evaluated using synthetic data. In this study, we improved our recently developed multi-resolution direct search (MRDS) approach and the computation time cost was reduced to 1~2 hours. Using the improved MRDS approach, we estimated in vivo aortic tissue elastic properties of two ascending thoracic aortic aneurysm (ATAA) patients from pre-operative gated CT scans. For comparison, corresponding surgically-resected aortic wall tissue samples were obtained and subjected to planar biaxial tests. Relatively close matches were achieved for the in vivo-identified and ex vivo-fitted stress-stretch responses. It is hoped that further development of this inverse approach can enable an accurate identification of the in vivo material parameters from in vivo image data.

A relaxed growth modeling framework for controlling growth-induced residual stresses

BackgroundConstitutive models of the mechanical response of soft tissues have been established and are widely accepted, but models of soft tissues remodeling are more controversial. Specifically for growth, one important question arises pertaining to residual stresses: existing growth models inevitably introduce residual stresses, but it is not entirely clear if this is physiological or merely an artifact of the modeling framework. As a consequence, in simulating growth, some authors have chosen to keep growth-induced residual stresses, and others have chosen to remove them. MethodsIn this paper, we introduce a novel “relaxed growth” framework allowing for a fine control of the amount of residual stresses generated during tissue growth. It is a direct extension of the classical framework of the multiplicative decomposition of the transformation gradient, to which an additional sub-transformation is introduced in order to let the original unloaded configuration evolve, hence relieving some residual stresses. We provide multiple illustrations of the framework mechanical response, on time-driven constrained growth as well as the strain-driven growth problem of the artery under internal pressure, including the opening angle experiment. FindingsThe novel relaxed growth modeling framework introduced in this paper allows for a better control of growth-induced residual stresses compared to standard growth models based on the multiplicative decomposition of the transformation gradient. InterpretationGrowth-induced residual stresses should be better handled in soft tissues biomechanical models, especially in patient-specific models of diseased organs that are aimed at augmented diagnosis and treatment optimization.

Influence of heart failure on biomechanical properties during left ventricular passive diastolic filling

ObjectiveHeart failure (HF) results in changes of the function of left ventricular (LV) which can be reflected by the variation of the biomechanical properties, such as fiber stress and strain. Finite element (FE) method is often seen as an effective way to analysis biomechanical properties of the heart. Our requirement is to build an accurate patient‐specific LV FE model and analyze its biomechanical behavior.MethodSix patients from Peking University First Hospital are divided in two groups, infarcted (n=3) and normal (n=3). All these patients are scanned by the magnetic resonance (MR). Three‐dimensional LV geometries are segmented from cardiac MR images at end‐diastolic from their hearts. By developing non‐linear finite element model as well as the algorithm based on the multiplicative decomposition of the deformation gradient tensor, we find the unloaded configuration with zero pressure. To determine regional stress and strain distributions in ventricular myocardium, transversely isotropic constitutive law is taken. To better describe different stiffness of LV with HF, it is divided into three regions, respectively called infarcted region, border zone and remote region. For three patients with HF, the stress scaling coefficient of constitutive law at the infarcted region is defined to be ten times stiffer than two other areas while the stiffness of the whole LV remains the same for three normal patients.ResultsAs can be shown from Fig. 1, fiber stresses of three infracted patients are 8.748±5.733kPa, 9.488±6.566kPa, 6.170±5.622kPa, compared with 2.722±1.596kPa, 1.929±1.122kPa, 1.918±1.175kPa of three normal patients. As can be shown from Fig. 2, fiber strains of three infracted patients are 0.424±0.028, 0.422±0.025, 0.431±0.028, compared with 0.439±0.018, 0.447±0.018, 0.447±0.017 of three normal patients.ConclusionsFiber stresses of infracted group are significantly higher than the normal one while there are no obvious distinctions of the figure of fiber strain between two groups.Support or Funding InformationThis research is supported in part by the Shenzhen Science and Technology Innovation Institution (China) Grant JCYJ20160427170536358 (Y Huo).This abstract is from the Experimental Biology 2019 Meeting. There is no full text article associated with this abstract published in The FASEB Journal.

On the existence of elastic minimizers for initially stressed materials.

A soft solid is said to be initially stressed if it is subjected to a state of internal stress in its unloaded reference configuration. In physical terms, its stored elastic energy may not vanish in the absence of an elastic deformation, being also dependent on the spatial distribution of the underlying material inhomogeneities. Developing a sound mathematical framework to model initially stressed solids in nonlinear elasticity is key for many applications in engineering and biology. This work investigates the links between the existence of elastic minimizers and the constitutive restrictions for initially stressed materials subjected to finite deformations. In particular, we consider a subclass of constitutive responses in which the strain energy density is taken as a scalar-valued function of both the deformation gradient and the initial stress tensor. The main advantage of this approach is that the initial stress tensor belongs to the group of divergence-free symmetric tensors satisfying the boundary conditions in any given reference configuration. However, it is still unclear which physical restrictions must be imposed for the well-posedness of this elastic problem. Assuming that the constitutive response depends on the choice of the reference configuration only through the initial stress tensor, under given conditions we prove the local existence of a relaxed state given by an implicit tensor function of the initial stress distribution. This tensor function is generally not unique, and can be transformed according to the symmetry group of the material at fixed initial stresses. These results allow one to extend Ball's existence theorem of elastic minimizers for the proposed constitutive choice of initially stressed materials. This article is part of the theme issue 'Rivlin's legacy in continuum mechanics and applied mathematics'.

Sensitivity of stress and strain calculations to passive material parameters in cardiac mechanical models using unloaded geometries

Cardiac stress (load) and strain (stretch) are widely studied indicators of cardiac function and outcome, but are difficult or impossible to directly measure in relation to the cardiac microstructure. An alternative approach is to estimate these states using computer methods and image-based measurements, but this still requires knowledge of the tissue material properties and the unloaded state, both of which are difficult to determine. In this work, we tested the sensitivity of these two interdependent unknowns (reference geometry and material parameters) on stress and strain calculations in cardiac tissue. Our study used a finite element model of the human ventricle, with a hyperelastic passive material model, and was driven by a cell model mediated active contraction. We evaluated 21 different published parameter sets for the five parameters of the passive material model, and for each set we optimised the corresponding unloaded geometry and contractility parameter to model a single pressure-volume loop. The resulting mechanics were compared, and calculated systolic stresses were largely insensitive to the chosen parameter set when an unloading algorithm was used. Meanwhile, material strain calculations varied substantially depending on the choice of material parameters. These results indicate that determining the correct material and unloaded configuration may be highly important to understand strain driven processes, but less so for calculating stress estimates.

Compact four‐element SRR‐loaded dual‐band MIMO antenna for WLAN/WiMAX/WiFi/4G‐LTE and 5G applications

A four-element dual-band MIMO configuration consisting of split-ring resonator (SRR)-loaded inverted L-monopole antenna elements is realised. In the proposed antenna, the lower-frequency mode of the unloaded MIMO configuration merges with one SRR-induced antenna resonance. This leads to antenna operation around 2.93 GHz with wide impedance bandwidth (IBW) of 35.21%, encompassing the lower WLAN, worldwide interoperability for microwave access, wireless fidelity, fourth generation (4G)-long-term evolution and sub-6 GHz 5G bands. Furthermore, due to SRR loading, the proposed MIMO antenna exhibits a resonance at 5.68 GHz (IBW 6.86%), covering the upper WLAN band. Minimum inter-element isolation of 14 dB is achieved, in spite of the compact total area ( 0.103 λ 0 2 , λ 0 = highest operating wavelength) and the presence of inter-connected ground plane. Both the working bands exhibit directional radiation patterns with average gain ≈ 4 dBi . Experiments on the fabricated antenna prototype confirm that the simulated and measured S-parameters, radiation patterns (envelope-correlation coefficient, channel capacity loss and total active reflection coefficient) are in good agreement.