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The highly optimized hierarchical structure of trabecular bone is a major contributor to its remarkable mechanical properties. At the micro-scale level, individual plate-like and rod-like trabeculae are interconnected, forming a complex trabecular architecture. It is widely believed that bone strength, an important mechanical characteristic that describes the capability of bone to resist fracture, is largely determined by the tissue-level material properties of these microscopic trabecular elements. However, due to the complicated microstructure and irregular morphology of trabecular bone, a link between the tissue-level and the apparent level mechanics in trabecular bone has never been established. Thus, the goal of this thesis is to examine the tissue-level material properties of trabecular bone and their contribution to apparent-level bone mechanics, and ultimately to improve our fundamental understanding and assessment of bone strength in diseased and healthy patients. At the micro-scale level, plate-like and rod-like trabeculae are distinctly aligned along different orientations on the anatomical axis of the skeleton. Also, the highly organized underlying ultrastructure of bone tissue suggests trabecular bone might possess an anisotropic tissue modulus, i.e. different modulus in the axial and lateral cross-section of a trabecula. In this thesis, we studied this tissue-level anisotropy by examining mechanical properties of individual trabecular plates and rods aligned longitudinally, obliquely, and transversely on the anatomical axis using micro-indentation. We discovered that, despite the different orientations of trabeculae, tissue moduli are higher in the axial direction than in the lateral direction for both plates and rods. We also discovered that plates have a higher tissue modulus than rods, suggesting different degrees of mineralization. Furthermore, the tissue mineral density correlated strongly but distinctly with tissue modulus in the axial and lateral directions, providing descriptions on how spatially heterogeneous mineralization at the tissue level affects the tissue modulus. After characterization of the anisotropic and heterogeneous modulus of trabecular bone at the tissue level, we then sought to investigate its contribution to apparent-level mechanical properties, including apparent Young’s modulus and yield strength. Non-linear FE voxel models incorporating experimentally determined anisotropy and heterogeneity were created from micro-computed tomography (µCT) images of healthy trabecular bone samples. Apparent Young's modulus and yield strength predicted by the models were compared to and correlated with gold standard mechanical testing measurements, as well as to the same FE models without incorporation of anisotropy and/or heterogeneity. We discovered that the anisotropic model prediction was highly correlated and indistinguishable from mechanical testing measurements. However, the prediction power of the model was not enhanced by incorporating anisotropy and heterogeneity (compared to a homogeneous and isotropic model), suggesting that variances in tissue-level material properties contribute minimally to the apparent level bone behaviors in healthy bone. However, the possibility remained that a more substantial contribution could arise in diseased bone, particularly diseases in which tissue-level properties are compromised. Therefore, we studied trabecular bone in two diseased conditions – subchondral bone in human knees affected by osteoarthritis and pelvic bone affected by adolescent idiopathic sclerosis – to see how disease can alter the tissue-level and, consequently, apparent-level bone mechanics. In OA bone, we found a significant decrease in tissue modulus in the subchondral bone under severely damaged cartilage compared to control, which provides an explanation for a minimal increase in apparent stiffness with an almost doubled bone volume fraction. In AIS bone, no differences were found in tissue-level or apparent level Young’s modulus compared to control. However, the mineral density was found to play a distinct role in the modulus of growing bone tissue compared to mature bone.

The present work contains two parts: nanofluids and bioheat transport, both involving multiscales and sharing some common features. The former centers on addressing the three key issues of nanofluids research: (i) what is the macroscale manifestation of microscale physics, (ii) how to optimize microscale physics for the optimal system performance, and (iii) how to effectively manipulate at microscale. The latter develops an analytical theory of bioheat transport that includes: (i) identification and contrast of the two approaches for developing macroscale bioheat models: the mixture-theory (scaling-down) and porous-media (scaling-up) approaches, (ii) rigorous development of first-principle bioheat model with the porous-media approach, (iii) solution-structure theorems of dual-phase-lagging (DPL) bioheat equations, (iv) practical case studies of bioheat transport in skin tissues and during magnetic hyperthermia, and (v) rich effects of interfacial convective heat transfer, blood velocity, blood perfusion and metabolic reaction on blood and tissue macroscale temperature fields. Nanofluids, fluid suspensions of nanostructures, find applications in various fields due to their unique thermal, electronic, magnetic, wetting and optical properties that can be obtained via engineering nanostructures. The present numerical simulation of structure-property correlation for fourteen types of two/three-dimensional nanofluids signifies the importance of nanostructure’s morphology in determining nanofluids’ thermal conductivity. The success of developing high-conductive nanofluids thus depends very much on our understanding and manipulation of the morphology. Nanofluids with conductivity of upper Hashin-Shtrikman bounds can be obtained by manipulating structures into an interconnected configuration that disperses the base fluid and thus significantly enhancing the particle-fluid interfacial energy transport. The numerical simulation also identifies the particle’s radius of gyration and non-dimensional particle-fluid interfacial area as two characteristic parameters for the effect of particles’ geometrical structures on the effective thermal conductivity. Predictive models are developed as well for the thermal conductivity of typical nanofluids. A constructal approach is developed to find the constructal microscopic physics of nanofluids for the optimal system performance. The approach is applied to design nanofluids with any branching level of tree-shaped microstructures for cooling a circular disc with uniform heat generation and central heat sink. The constructal configuration and system thermal resistance have some elegant universal features for both cases of specified aspect ratio of the periphery sectors and given the total number of slabs in the periphery sectors. The numerical simulation on the bubble formation in T-junction microchannels shows: (i) the mixing enhancement inside liquid slugs between microfluidic bubbles, (ii) the preference of T-junctions with small channel width ratio for either producing smaller microfluidic bubbles at a faster speed or enhancing mixing within the liquid phase, and (iii) the existence of a critical value of nondimensional gas pressure for bubble generation. Such a precise understanding of two-phase flow in microchannels is necessary and useful for delivering the promise of microfluidic technology in producing high-quality and microstructure-controllable nanofluids. Both blood and tissue macroscale temperatures satisfy the DPL bioheat equation with an elegant solution structure. Effectiveness and features of the developed solution structure theorems are demonstrated via examining bioheat transport in skin tissues and during magnetic hyperthermia. / published_or_final_version / Mechanical Engineering / Doctoral / Doctor of Philosophy

In this thesis a parameter recovery method for use in ultrasound elasticity imaging is developed. Elasticity imaging is a method for using a series of ultrasound images (and the displacement field between them) to estimate the spatial variation of the stiffness of the tissue being imaged. Currently iterative methods are used to do this: a model of tissue mechanics is assumed and a large number of simulations using varying parameters are compared to the actual displacement field. The aim of this work is to develop a solution method that works back from the known displacement field to determine the tissue properties, reducing the number of simulations that must be performed to one. The parameter recovery method is based on the formulation and direct solution of the 2-d linear elasticity inverse problem using finite element methods. The inverse problem is analyzed mathematically and the existence and uniqueness of solutions is described for varying numbers of displacement fields and appropriate boundary conditions. It is shown to be hyperbolic (and so difficult to solve numerically) and then reformulated as a minimization problem with hyperbolic Euler-Lagrange equations. A finite element solution of the minimization problem is developed and implemented. The results of the finite element implementation are shown to work well in recovering the parameters used in numerical simulations of the linear elasticity forward problem so long as these are continuous. The method is shown to be robust in dealing with small errors in displacement estimation and larger errors in the boundary values of the parameters. The method is also tested on displacement fields calculated from series of real ultrasound images. The validity of modelling the ultrasound elasticity imaging process as a 2-d problem is discussed. The assumption of plane strain is shown not to be valid and methods for extending the parameter recovery method to 3 dimensions once 3-d ultrasound becomes more widely used are described (but not implemented).

Indiana University-Purdue University Indianapolis (IUPUI) / Articular cartilage is subjected to dynamic mechanical loading during normal daily activities. This complex mechanical loading, including cell deformation and interstitial fluid flow, affects chondrocyte mechano-chemical signaling and subsequent cartilage homeostasis and remodeling. Focal adhesion kinase (FAK) and Src are known to be main mechanotransduction proteins, but little is known about the effect of mechanical loading on FAK and Src under its varying magnitudes and types. In this study, we addressed two questions using C28/I2 chondrocytes subjected to the different types and magnitudes of mechanical loading: Does a magnitude of the mechanical loading affect activities of FAK and Src? Does a type of the mechanical loading also affect their activities? Using fluorescence resonance energy transfer (FRET)-based FAK and Src biosensor in live C28/I2 chondrocytes, we monitored the effects of interstitial fluid flow and combined effects of cell deformation/interstitial fluid flow on FAK and Src activities. The results revealed that both FAK and Src activities in C28/I2 chondrocytes were dependent on the different magnitudes of the applied fluid flow. On the other hand, the type of mechanical loading differently affected FAK and Src activities. Although FAK and Src displayed similar activities in response to interstitial fluid flow only, simultaneous application of cell deformation and interstitial fluid flow induced differential FAK and Src activities possibly due to the additive effects of cell deformation and interstitial fluid flow on Src, but not on FAK. Collectively, the data suggest that the intensities and types of mechanical loading are critical in regulating FAK and Src activities in chondrocytes.

Indiana University-Purdue University Indianapolis (IUPUI) / Tendinopathy is a common degenerative pathology that is characterized by activity related pain, focal tendon tenderness, intratendinous imaging changes, and typically results in changes in the histological, mechanical, and molecular properties of the tendon. Tendinopathy is difficult to study in humans, which has contributed to limited knowledge of the pathology, and thus a lack of appropriate treatment options. However, most believe that the pathology is degenerative as a result of a combination of both extrinsic and intrinsic factors. In order to gain understanding of this pathology, animal models are required. Because each tendon is naturally exposed to different conditions, a universal model is not feasible; therefore, an appropriate animal model must be established for each tendon susceptible to degenerative changes. While acceptable models have been developed for several tendons, a reliable model for the Achilles tendon remains elusive. The purpose of this dissertation was to develop an animal model of Achilles tendinopathy by investigating the individual and combined effects of an intrinsic and extrinsic factor on the rodent Achilles tendon. Rats selectively bred for high capacity running and Sprague Dawley rats underwent uphill treadmill running (an extrinsic factor) to mechanically overload the Achilles tendon or served as cage controls. Collagenase (intrinsic factor) was injected into one Achilles tendon in each animal to intrinsically break down the tendon. There were no interactions between uphill running and collagenase injection, indicating that the influence of the two factors was independent. Uphill treadmill running alone failed to produce any pathological changes in the histological or mechanical characteristics of the Achilles tendon, but did modify molecular activity. Intratendinous collagenase injection had negative effects on the histological, mechanical, and molecular properties of the tendon. The results of this dissertation demonstrated that the combined introduction of uphill treadmill running and collagenase injection did not lead to degenerative changes consistent with human Achilles tendinopathy. Intratendiouns collagenase injection negatively influenced the tendon; however, these changes were generally transient and not influenced by mechanical overload. Future studies should consider combinations of other intrinsic and extrinsic factors in an effort to develop an animal model that replicates human Achilles tendinopathy.