An inverse method for predicting tissue-level mechanics from cellular mechanical input

Validation of a Biomechanical Injury and Disease Assessment Platform Applying an Inertial-Based Biosensor and Axis Vector Computation

Inertial kinetics and kinematics have substantial influences on human biomechanical function. A new algorithm for Inertial Measurement Unit (IMU)-based motion tracking is presented in this work. The primary aims of this paper are to combine recent developments in improved biosensor technology with mainstream motion-tracking hardware to measure the overall performance of human movement based on joint axis-angle representations of limb rotation. This work describes an alternative approach to representing three-dimensional rotations using a normalized vector around which an identified joint angle defines the overall rotation, rather than a traditional Euler angle approach. Furthermore, IMUs allow for the direct measurement of joint angular velocities, offering the opportunity to increase the accuracy of instantaneous axis of rotation estimations. Although the axis-angle representation requires vector quotient algebra (quaternions) to define rotation, this approach may be preferred for many graphics, vision, and virtual reality software applications. The analytical method was validated with laboratory data gathered from an infant dummy leg's flexion and extension knee movements and applied to a living subject's upper limb movement. The results showed that the novel approach could reasonably handle a simple case and provide a detailed analysis of axis-angle migration. The described algorithm could play a notable role in the biomechanical analysis of human joints and offers a harbinger of IMU-based biosensors that may detect pathological patterns of joint disease and injury.

COMPUTATION OF THE DYNAMIC COMPRESSION EFFECTS IN SPINE DISCS USING INTEGRAL METHODS

The computational modeling using integral methods of dynamic loading and its effects on the nutrients transport in spine discs is addressed in this work. The numerical simulation and analysis was carried out using the Boundary Element Method (BEM) and a 3D model (axisymmetric) of the disc. The boundary model was discretized using linear interpolated elements and a multi-region approach. Concentration and production of three nutrients as lactate, oxygen and glucose were obtained. The maximum lactate concentration was observed very close to the interface between the nucleus and the inner annulus. A relatively simple model discretized with 130 boundary elements yielded very similar results to these coming from more complex FEM-based models. The numerical efforts in the domain and boundary discretizations were optimized using the BEM. Our results are in good agreement with those obtained using with finite element-based models. As expected, the dynamic loading increased the oxygen–glucose consumption and the lactate production, thus leading to a poor oxygen–glucose concentration at the nucleus of the disc. All of that is a favorable environment for a disc degeneration mechanism to be developed.

Programming Mechanical and Physicochemical Properties of 3D Hydrogel Cellular Microcultures via Direct Ink Writing

3D hydrogel scaffolds are widely used in cellular microcultures and tissue engineering. Using direct ink writing, microperiodic poly(2-hydroxyethyl-methacrylate) (pHEMA) scaffolds are created that are then printed, cured, and modified by absorbing 30 kDa protein poly-l-lysine (PLL) to render them biocompliant in model NIH/3T3 fibroblast and MC3T3-E1 preosteoblast cell cultures. Spatial light interference microscopy (SLIM) live cell imaging studies are carried out to quantify cellular motilities for each cell type, substrate, and surface treatment of interest. 3D scaffold mechanics is investigated using atomic force microscopy (AFM), while their absorption kinetics are determined by confocal fluorescence microscopy (CFM) for a series of hydrated hydrogel films prepared from prepolymers with different homopolymer-to-monomer (Mr ) ratios. The observations reveal that the inks with higher Mr values yield relatively more open-mesh gels due to a lower degree of entanglement. The biocompatibility of printed hydrogel scaffolds can be controlled by both PLL content and hydrogel mesh properties.

The stationary configuration of the knee

BACKGROUND

Ligaments and cartilage contact contribute to the mechanical constraints in the knee joints. However, the precise influence of these structural components on joint movement, especially when the joint constraints are computed using inverse dynamics solutions, is not clear.

METHODS

We present a mechanical characterization of the connections between the infinitesimal twist of the tibia and the femur due to restraining forces in the specific tissue components that are engaged and responsible for such motion. These components include the anterior cruciate, posterior cruciate, medial collateral, and lateral collateral ligaments and cartilage contact surfaces in the medial and lateral compartments. Their influence on the bony rotation about the instantaneous screw axis is governed by restraining forces along the constraints explored using the principle of reciprocity.

RESULTS

Published kinetic and kinematic joint data (American Society of Mechanical Engineers Grand Challenge Competition to Predict In Vivo Knee Loads) are applied to define knee joint function for verification using an available instrumented knee data set. We found that the line of the ground reaction force (GRF) vector is very close to the axis of the knee joint. It aligns the knee joint with the GRF such that the reaction torques are eliminated. The reaction to the GRF will then be carried by the structural components of the knee instead.

CONCLUSIONS

The use of this reciprocal system introduces a new dimension of foot loading to the knee axis alignment. This insight shows that locating knee functional axes is equivalent to the static alignment measurement. This method can be used for the optimal design of braces and orthoses for conservative treatment of knee osteoarthritis.

Tracking Knee Joint Functional Axes through Tikhonov Filtering and Plűcker Coordinates

Researchers have reported several compensation methods to estimate bone and joint position from a cluster of skin-mounted markers as influenced by Soft Tissue Artifacts (STA). Tikhonov Regularization Filtering (TRF) as a means to estimate Instantaneous Screw Axes (ISA) was introduced here as a means to reduce the displacement of a rigid body to its simplest geometric form. Recent studies have suggested that the ISA of the knee, i.e., Knee Functional Axes (KFA), might be closely connected to the estimation of constraint forces such as those due to medial and lateral connective tissues. The estimations of ISAs were known to be highly sensitive to noisy data, which may be mathematically ill-posed, requiring smoothing such as that conducted by regularization. The main contribution in this work was to establish the reciprocal connection between the KFA and Ground Reaction Forces (GRF) as a means to estimate joint constraint forces. Presented results compare the computational performance with published kinetic and kinematic joint data generated from an instrumented total knee replacement. Implications of these preliminary findings with respect to dynamic alignment as a functional anatomic metric are discussed.

Cytoskeletal strains in modeled optohydrodynamically stressed healthy and diseased biological cells

Controlled external chemomechanical stimuli have been shown to influence cellular and tissue regeneration/degeneration, especially with regards to distinct disease sequelae or health maintenance. Recently, a unique three-dimensional stress state was mathematically derived to describe the experimental stresses applied to isolated living cells suspended in an optohydrodynamic trap (optical tweezers combined with microfluidics). These formulae were previously developed in two and three dimensions from the fundamental equations describing creeping flows past a suspended sphere. The objective of the current study is to determine the full-field cellular strain response due to the applied three-dimensional stress environment through a multiphysics computational simulation. In this investigation, the multiscale cytoskeletal structures are modeled as homogeneous, isotropic, and linearly elastic. The resulting computational biophysics can be directly compared with experimental strain measurements, other modeling interpretations of cellular mechanics including the liquid drop theory, and biokinetic models of biomolecule dynamics. The described multiphysics computational framework will facilitate more realistic cytoskeletal model interpretations, whose intracellular structures can be distinctly defined, including the cellular membrane substructures, nucleus, and organelles.

Volumetric stress-strain analysis of optohydrodynamically suspended biological cells

Ongoing investigations are exploring the biomechanical properties of isolated and suspended biological cells in pursuit of understanding single-cell mechanobiology. An optical tweezer with minimal applied laser power has positioned biologic cells at the geometric center of a microfluidic cross-junction, creating a novel optohydrodynamic trap. The resulting fluid flow environment facilitates unique multiaxial loading of single cells with site-specific normal and shear stresses resulting in a physical albeit extensional state. A recent two-dimensional analysis has explored the cytoskeletal strain response due to these fluid-induced stresses [Wilson and Kohles, 2010, "Two-Dimensional Modeling of Nanomechanical Stresses-Strains in Healthy and Diseased Single-Cells During Microfluidic Manipulation," J Nanotechnol Eng Med, 1(2), p. 021005]. Results described a microfluidic environment having controlled nanometer and piconewton resolution. In this present study, computational fluid dynamics combined with multiphysics modeling has further characterized the applied fluid stress environment and the solid cellular strain response in three dimensions to accompany experimental cell stimulation. A volumetric stress-strain analysis was applied to representative living cell biomechanical data. The presented normal and shear stress surface maps will guide future microfluidic experiments as well as provide a framework for characterizing cytoskeletal structure influencing the stress to strain response.

The natural frequency of the foot-surface cushion during the stance phase of running

Researchers have reported on the stiffness of running in holistic terms, i.e. for the structures that are undergoing deformation as a whole rather than in terms of specific locations. This study aimed to estimate both the natural frequency and the viscous damping coefficient of the human foot-surface cushion, during the period between the heel strike and the mid-stance phase of running, using a purposely developed one degree-of-freedom inverted pendulum state space model of the leg. The model, which was validated via a comparison of measured and estimated ground reaction forces, incorporated a novel use of linearized and extended Kalman filter estimators. Investigation of the effect of variation of the natural frequency and/or the damping of the cushioning mechanism during running, using the said model, revealed the natural frequency of running on said foot-surface cushion, during the stance phase, to lie between 5 and 11 Hz. The "extended Kalman filter (EKF)" approach, that was used here for the first time to directly apply measured ground forces, may be widely applicable to the identification process of combined estimation of both unknown physiological state and mechanical characteristics of the environment in an inverse dynamic model.

Relationships between degradability of silk scaffolds and osteogenesis

Bone repairs represent a major focus in orthopedic medicine with biomaterials as a critical aspect of the regenerative process. However, only a limited set of biomaterials are utilized today and few studies relate biomaterial scaffold design to degradation rate and new bone formation. Matching biomaterial remodeling rate towards new bone formation is important in terms of the overall rate and quality of bone regeneration outcomes. We report on the osteogenesis and metabolism of human bone marrow derived mesenchymal stem cells (hMSCs) in 3D silk scaffolds. The scaffolds were prepared with two different degradation rates in order to study relationships between matrix degradation, cell metabolism and bone tissue formation in vitro. SEM, histology, chemical assays, real-time PCR and metabolic analyses were assessed to investigate these relationships. More extensively mineralized ECM formed in the scaffolds designed to degrade more rapidly, based on SEM, von Kossa and type I collagen staining and calcium content. Measures of osteogenic ECM were significantly higher in the more rapidly degrading scaffolds than in the more slowly degrading scaffolds over 56 days of study in vitro. Metabolic analysis, including glucose and lactate levels, confirmed the degradation rate differences with the two types of scaffolds, with the more rapidly degrading scaffolds supporting higher levels of glucose consumption and lactate synthesis by the hMSCs upon osteogenesis, in comparison to the more slowly degrading scaffolds. The results demonstrate that scaffold degradation rates directly impact the metabolism of hMSCs, and in turn the rate of osteogenesis. An understanding of the interplay between cellular metabolism and scaffold degradability should aid in the more rational design of scaffolds for bone regeneration needs both in vitro and in vivo.

A Distinct Catabolic to Anabolic Threshold Due to Single-Cell Static Nanomechanical Stimulation in a Cartilage Biokinetics Model

Understanding physicochemical interactions during biokinetic regulation will be critical for the creation of relevant nanotechnology supporting cellular and molecular engineering. The impact of nanoscale influences in medicine and biology can be explored in detail through mathematical models as an in silico testbed. In a recent single-cell biomechanical analysis, the cytoskeletal strain response due to fluid-induced stresses was characterized (Wilson, Z. D., and Kohles, S. S., 2010, "Two-Dimensional Modeling of Nanomechanical Strains in Healthy and Diseased Single-Cells During Microfluidic Stress Applications," J. Nanotech. Eng. Med., 1(2), p. 021005). Results described a microfluidic environment having controlled nanometer and piconewton resolution for explorations of multiscale mechanobiology. In the present study, we constructed a mathematical model exploring the nanoscale biomolecular response to that controlled microenvironment. We introduce mechanical stimuli and scaling factor terms as specific input values for regulating a cartilage molecule synthesis. Iterative model results for this initial multiscale static load application have identified a transition threshold load level from which the mechanical input causes a shift from a catabolic state to an anabolic state. Modeled molecule homeostatic levels appear to be dependent upon the mechanical stimulus as reflected experimentally. This work provides a specific mathematical framework from which to explore biokinetic regulation. Further incorporation of nanomechanical stresses and strains into biokinetic models will ultimately lead to refined mechanotransduction relationships at the cellular and molecular levels.

Cinemechanometry (CMM): A method to determine the forces that drive morphogenetic movements from time-lapse images

Although cell-level mechanical forces are crucial to tissue self-organization in contexts ranging from embryo development to cancer metastases to regenerative engineering, the absence of methods to map them over time has been a major obstacle to new understanding. Here, we present a technique for constructing detailed, dynamic maps of the forces driving morphogenetic events from time-lapse images. Forces in the cell are considered to be separable into unknown active driving forces and known passive forces, where actomyosin systems and microtubules contribute primarily to the first group and intermediate filaments and cytoplasm to the latter. A finite-element procedure is used to estimate the field of forces that must be applied to the passive components to produce their observed incremental deformations. This field is assumed to be generated by active forces resolved along user-defined line segments whose location, often along cell edges, is informed by the underlying biology. The magnitudes and signs of these forces are determined by a mathematical inverse method. The efficacy of the approach is demonstrated using noisy synthetic data from a cross section of a generic invagination and from a planar aggregate that involves two cell types, edge forces that vary with time and a neighbor change.

Two-Dimensional Modeling of Nanomechanical Strains in Healthy and Diseased Single-Cells During Microfluidic Stress Applications

Investigations in cellular and molecular engineering have explored the impact of nanotechnology and the potential for monitoring and control of human diseases. In a recent analysis, the dynamic fluid-induced stresses were characterized during microfluidic applications of an instrument with nanometer and picoNewton resolution as developed for single-cell biomechanics (Kohles, S. S., Nève, N., Zimmerman, J. D., and Tretheway, D. C., 2009, "Stress Analysis of Microfluidic Environments Designed for Isolated Biological Cell Investigations," ASME J. Biomech. Eng., 131(12), p. 121006). The results described the limited stress levels available in laminar, creeping-flow environments, as well as the qualitative cellular strain response to such stress applications. In this study, we present a two-dimensional computational model exploring the physical application of normal and shear stress profiles (with 0.1, 1.0, and 10.0 Pa peak amplitudes) potentially available within uniform and extensional flow states. The corresponding cellular strains and strain patterns were determined within cells modeled with healthy and diseased mechanical properties (5.0-0.1 kPa moduli, respectively). Strain energy density results integrated over the volume of the planar section indicated a strong mechanical sensitivity involving cells with disease-like properties. In addition, ex vivo microfluidic environments creating in vivo stress states would require freestream flow velocities of 2-7 mm/s. Knowledge of the nanomechanical stresses-strains necessary to illicit a biologic response in the cytoskeleton and cellular membrane will ultimately lead to refined mechanotransduction relationships.