The mechanics of PLGA nanofiber scaffolds with biomimetic gradients in mineral for tendon-to-bone repair.

Attachment of dissimilar materials is prone to failure due to stress concentrations that can arise their interface. A compositionally or structurally graded transition can dissipate these stress concentrations and thereby toughen an attachment. The interface between compliant tendon and stiff bone utilizes a monotonic change in hydroxylapatite mineral ("mineral") content to produce a gradient in mechanical properties and mitigate stress concentrations. Previous efforts to mimic the natural tendon-to-bone attachment have included electrospun nanofibrous polymer scaffolds with gradients in mineral. Mineralization of the nanofiber scaffolds has typically been achieved using simulated body fluid (SBF). Depending on the specific formulation of SBF, mineral morphologies ranged from densely packed small crystals to platelike crystal florets. Although this mineralization of scaffolds produced increases in modulus, the peak modulus achieved remained significantly below that of bone. Missing from these prior empirical approaches was insight into the effect of mineral morphology on scaffold mechanics and on the potential for the approach to ultimately achieve moduli approaching that of bone. Here, we applied two mineralization methods to generate scaffolds with spatial gradations in mineral content, and developed methods to quantify the stiffening effects and evaluate them in the context of theoretical bounds. We asked whether either of the mineralization methods we developed holds potential to achieve adequate stiffening of the scaffold, and tested the hypothesis that the smoother, denser mineral coating could attain more potent stiffening effects. Testing this hypothesis required development of and comparison to homogenization bounds, and development of techniques to estimate mineral volume fractions and spatial gradations in modulus. For both mineralization strategies, energy dispersive X-ray analysis demonstrated the formation of linear gradients in mineral concentration along the length of the scaffolds, and Raman spectroscopic analysis revealed that the mineral produced was hydroxylapatite. Mechanical testing showed that the stiffness gradient using the new method was significantly steeper. By analyzing the scaffolds using micromechanical modeling techniques and extrapolating from our experimental results, we present evidence that the new mineralization protocol has the potential to achieve levels of stiffness adequate to contribute to enhanced repair of tendon-to-bone attachments.

The role of mechanics in actin stress fiber kinetics.

The dynamic responses of actin stress fibers within a cell's cytoskeleton are central to the development and maintenance of healthy tissues and organs. Disturbances to these underlie a broad range of pathologies. Because of the importance of these responses, extensive experiments have been conducted in vitro to characterize actin cytoskeleton dynamics of cells cultured upon two-dimensional substrata, and the first experiments have been conducted for cells within three-dimensional tissue models. Three mathematical models exist for predicting the dynamic behaviors observed. Surprisingly, despite differing viewpoints on how actin stress fibers are stabilized or destabilized, all of these models are predictive of a broad range of available experimental data. Coarsely, the models of Kaunas and co-workers adopt a strategy whereby mechanical stretch can hasten the depolymerization actin stress fibers that turn over constantly, while the models of Desphande and co-workers adopt a strategy whereby mechanical stress is required to activate the formation of stress fibers and subsequently stabilize them. In three-dimensional culture, elements of both approaches appear necessary to predict observed phenomena, as embodied by the model of Lee et al. After providing a critical review of existing models, we propose lines of experimentation that might be able to test the different principles underlying their kinetic laws.

A mechanism for effective cell-seeding in rigid, microporous substrates.

Seeding cells into porous ceramic substrates has been shown to improve outcomes in surgical repair of large bone defects, but the physics underlying cellular ingress into such scaffolds remains elusive. This paper demonstrates capillary forces as a novel, yet simple, self-loading or self-seeding mechanism for rigid, microporous substrates. Capillary forces were found to draw cells through a microporous network with interconnections smaller than the diameter of the cells in suspension. Work here emphasizes CaP-based bone scaffolds containing both macroporosity (>100µm) and microporosity (5-50µm); these have been shown to improve bone formation in vivo as compared to their macroporous counterparts and also performed better than microporous scaffolds containing BMP-2 by some measures of bone regeneration. We hypothesize that capillary force driven self-seeding in both macro- and micropores may underlie this improvement, and present a mathematical model and experiments that support this hypothesis. The cell localization and penetration depth within these two-dimensional substrates in vitro depends upon both the cell type (size and stiffness) and the capillary forces generated by the microstructure. Additional experiments showing that cell penetration depth in vitro depends on cell size and stiffness suggest that microporosity could be tailored to optimize cell infiltration in a cell-specific way. Endogenous cells are also drawn into the microporous network in vivo. Results have important implications for design of scaffolds for the healing of large bone defects, and for controlled release of drugs in vivo.

Muscle loading is necessary for the formation of a functional tendon enthesis.

Muscle forces are essential for skeletal patterning during development. Eliminating muscle forces, e.g., through paralysis, leads to bone and joint deformities. Botulinum toxin (BtxA)-induced paralysis of mouse rotator cuffs throughout postnatal development closely mimics neonatal brachial plexus palsy, a significant clinical condition in infants. In these mice, the tendon-to-bone attachment (i.e., the tendon enthesis) presents defects in mineral accumulation and fibrocartilage formation, presumably impairing the function of the tissue. The objective of the current study was to investigate the functional consequences of muscle unloading using BtxA on the developing supraspinatus tendon enthesis. We found that the maximum endurable load and stiffness of the supraspinatus tendon attachment decreased after four and eight weeks of post-natal BtxA-muscle unloading relative to controls. Tendon cross-sectional area was not significantly reduced by BtxA-unloading, while, strength, modulus, and toughness were decreased in the BtxA-unloaded group compared to controls, indicating a decrease in tissue quality. Polarized-light microscopy and Raman microprobe analysis were used to determine collagen fiber alignment and mineral characteristics, respectively, in the tendon enthesis that might contribute to the reduced biomechanical performance in BtxA-unloaded shoulders. Collagen fiber alignment was significantly reduced in BtxA-unloaded shoulders. The mineral-to-matrix ratio in mineralized fibrocartilage was not affected by loading. However, the crystallographic atomic order of the hydroxylapatite phase (a measure of crystallinity) was reduced and the amount of carbonate (substituting for phosphate) in the hydroxylapatite crystals was increased. Taken together, these micrometer-scale structural and compositional changes partly explain the observed decreases in the mechanical functionality of the tendon enthesis in the absence of muscle loading.

Elastic characterization of transversely isotropic soft materials by dynamic shear and asymmetric indentation.

The mechanical characterization of soft anisotropic materials is a fundamental challenge because of difficulties in applying mechanical loads to soft matter and the need to combine information from multiple tests. A method to characterize the linear elastic properties of transversely isotropic soft materials is proposed, based on the combination of dynamic shear testing (DST) and asymmetric indentation. The procedure was demonstrated by characterizing a nearly incompressible transversely isotropic soft material. A soft gel with controlled anisotropy was obtained by polymerizing a mixture of fibrinogen and thrombin solutions in a high field magnet (B = 11.7 T); fibrils in the resulting gel were predominantly aligned parallel to the magnetic field. Aligned fibrin gels were subject to dynamic (20-40 Hz) shear deformation in two orthogonal directions. The shear storage modulus was 1.08 ± 0. 42 kPa (mean ± std. dev.) for shear in a plane parallel to the dominant fiber direction, and 0.58 ± 0.21 kPa for shear in the plane of isotropy. Gels were indented by a rectangular tip of a large aspect ratio, aligned either parallel or perpendicular to the normal to the plane of transverse isotropy. Aligned fibrin gels appeared stiffer when indented with the long axis of a rectangular tip perpendicular to the dominant fiber direction. Three-dimensional numerical simulations of asymmetric indentation were used to determine the relationship between direction-dependent differences in indentation stiffness and material parameters. This approach enables the estimation of a complete set of parameters for an incompressible, transversely isotropic, linear elastic material.

Bi-material attachment through a compliant interfacial system at the tendon-to-bone insertion site.

The attachment of tendon to bone, one of the greatest interfacial material mismatches in nature, presents an anomaly from the perspective of interfacial engineering. Deleterious stress concentrations arising at bi-material interfaces can be reduced in engineering practice by smooth interpolation of composition, microstructure, and mechanical properties. However, following normal development, the rotator cuff tendon-to-bone "insertion site" presents an interfacial zone that is more compliant than either tendon or bone. This compliant zone is not regenerated following healing, and its absence may account for the poor outcomes observed following both natural and post-surgical healing of insertion sites such as those at the rotator cuff of the shoulder. Here, we present results of numerical simulations which provide a rationale for such a seemingly illogical yet effective interfacial system. Through numerical optimization of a mathematical model of an insertion site, we show that stress concentrations can be reduced by a biomimetic grading of material properties. Our results suggest a new approach to functional grading for minimization of stress concentrations at interfaces.

Relative brain displacement and deformation during constrained mild frontal head impact.

This study describes the measurement of fields of relative displacement between the brain and the skull in vivo by tagged magnetic resonance imaging and digital image analysis. Motion of the brain relative to the skull occurs during normal activity, but if the head undergoes high accelerations, the resulting large and rapid deformation of neuronal and axonal tissue can lead to long-term disability or death. Mathematical modelling and computer simulation of acceleration-induced traumatic brain injury promise to illuminate the mechanisms of axonal and neuronal pathology, but numerical studies require knowledge of boundary conditions at the brain-skull interface, material properties and experimental data for validation. The current study provides a dense set of displacement measurements in the human brain during mild frontal skull impact constrained to the sagittal plane. Although head motion is dominated by translation, these data show that the brain rotates relative to the skull. For these mild events, characterized by linear decelerations near 1.5g (g = 9.81 m s⁻²) and angular accelerations of 120-140 rad s⁻², relative brain-skull displacements of 2-3 mm are typical; regions of smaller displacements reflect the tethering effects of brain-skull connections. Strain fields exhibit significant areas with maximal principal strains of 5 per cent or greater. These displacement and strain fields illuminate the skull-brain boundary conditions, and can be used to validate simulations of brain biomechanics.

The development and morphogenesis of the tendon-to-bone insertion - what development can teach us about healing -.

The attachment of dissimilar materials is a major challenge because of the high levels of stress that develop at such interfaces. An effective solution to this problem develops at the attachment of tendon (a compliant "soft tissue") to bone (a stiff "hard tissue"). This tissue, the "enthesis", transitions from tendon to bone through gradations in structure, composition, and mechanical properties. These gradations are not regenerated during tendon-to-bone healing, leading to a high incidence of failure after surgical repair. Understanding the development of the enthesis may allow scientists to develop treatments that regenerate the natural tendon-to-bone insertion. Recent work has demonstrated that both biologic and mechanical factors drive the development and morphogenesis of the enthesis. A cascade of biologic signals similar to those seen in the growth plate promotes mineralization of cartilage on the bony end of the enthesis and the formation of fibrocartilage on the tendon end of the enthesis. Mechanical loading is also necessary for the development of the enthesis. Removal of muscle load impairs the formation of bone, fibrocartilage, and tendon at the developing enthesis. This paper reviews recent work on the development of the enthesis, with an emphasis on the roles of biologic and mechanical factors.

Magnetic Resonance Measurement of Transient Shear Wave Propagation in a Viscoelastic Gel Cylinder.

A magnetic resonance measurement technique was developed to characterize the transient mechanical response of a gel cylinder subjected to angular acceleration. The technique employs tagged magnetic resonance imaging (MRI) synchronized to periodic impact excitation of a bulk specimen. The tagged MRI sequence provides, non-invasively, an array of distributed displacement and strain measurements with high spatial (here, 5 mm) and temporal (6 ms) resolution. The technique was validated on a cylindrical gelatin sample. Measured dynamic strain fields were compared to strain fields predicted using (1) a closed-form solution and (2) finite element simulation of shear waves in a three-parameter "standard" linear viscoelastic cylinder subjected to similar initial and boundary conditions. Material parameters used in the analyses were estimated from measurements made on the gelatin in a standard rheometer. The experimental results support the utility of tagged MRI for dynamic, non-invasive assays such as measurement of shear waves in brain tissue during angular acceleration of the skull. When applied in the inverse sense, the technique has potential for characterization of the mechanical behavior of gel biomaterials.

Deformation of the human brain induced by mild acceleration.

Rapid deformation of brain matter caused by skull acceleration is most likely the cause of concussion, as well as more severe traumatic brain injury (TBI). The inability to measure deformation directly has led to disagreement and confusion about the biomechanics of concussion and TBI. In the present study, brain deformation in human volunteers was measured directly during mild, but rapid, deceleration of the head (20-30 m/sec2 peak, approximately 40 msec duration), using an imaging technique originally developed to measure cardiac deformation. Magnetic resonance image sequences with imposed "tag" lines were obtained at high frame rates by repeating the deceleration and acquiring a subset of image data each repetition. Displacements of points on tag lines were used to estimate the Lagrangian strain tensor field. Qualitative (visual) and quantitative (strain) results illustrate clearly the deformation of brain matter due to occipital deceleration. Strains of 0.02-0.05 were typical during these events (0.05 strain corresponds roughly to a 5% change in the dimension of a local tissue element). Notably, compression in frontal regions and stretching in posterior regions were observed. The motion of the brain appears constrained by structures at the frontal base of the skull; it must pull away from such constraints before it can compress against the occipital bone. This mechanism is consistent with observations of contrecoup injury in occipital impact.

Measurement of strain in physical models of brain injury: a method based on HARP analysis of tagged magnetic resonance images (MRI).

Two-dimensional (2-D) strain fields were estimated non-invasively in two simple experimental models of closed-head brain injury. In the first experimental model, shear deformation of a gel was induced by angular acceleration of its spherical container In the second model the brain of a euthanized rat pup was deformed by indentation of its skull. Tagged magnetic resonance images (MRI) were obtained by gated image acquisition during repeated motion. Harmonic phase (HARP) images corresponding to the spectral peaks of the original tagged MRI were obtained, following procedures proposed by Osman, McVeigh and Prince. Two methods of HARP strain analysis were applied, one based on the displacement of tag line intersections, and the other based on the gradient of harmonic phase. Strain analysis procedures were also validated on simulated images of deformed grids. Results show that it is possible to visualize deformation and to quantify strain efficiently in animal models of closed head injury.