The overall goal of the dissertation research is to provide insights into the fundamental structure-composition-function relationship in lumbar intervertebral discs. The research develops and validates a novel multiscale multiphasic structure-based framework for modeling the intervertebral disc and soft fiber-reinforced biological tissues with accuracy, robustness, and translatability, which helps elucidate important stress-bearing mechanisms in both healthy and degenerated disc tissues. The proposed modeling framework and the subsequent model outcomes could have broad scientific and clinical implications related to the development of in vitro testing protocols with improved effectiveness, robustness, and clinical relevance, the design of novel tissue-engineered structures, and the evaluation of subfailure and failure behaviors in healthy and pathological tissues. Ultimately, the hope is that the modeling framework presented and validated in the current work can serve as a foundation for developing and validating future intervertebral disc and fiber-reinforced biological tissue models with patient-specific geometries, morphologies, and pathologies, and the resulting models can be used to improve clinical outcomes of low back pain treatments and, in turn, contribute to the broad effort of addressing this global health concern.

This dissertation comprises a series of separate, but related finite element modeling studies that focus on the development, validation, and application of the proposed models. The goals of these studies are to obtain an accurate, robust, and translatable finite element modeling framework to investigate multiscale and multiphasic disc mechanics, including, but are not limited to, joint stiffness and the stress-bearing contribution of the interstitial fluid at the joint scale, annulus fibrosus (AF) uniaxial tensile mechanics at the tissue scale, and AF stress transmission mechanisms and fiber-matrix interactions at the subtissue scale, under various physiologically relevant boundary and loading conditions in both healthy and degenerated tissues.

The primary results highlighted the accuracy, robustness, and translatability of the modeling framework proposed in the dissertation. Model predictions closely matched experimental measurements across the joint, tissue, and subtissue scales under various boundary and loading conditions with different specimen geometries. Joint- and tissue-scale model outcomes emphasized the significant stress-bearing role of the disc interstitial fluid content (i.e., the tissue water content accounted for up to ~60% of the joint’s stress-bearing capability in healthy discs), highlighting the necessity of multiphasic modeling. Tissue- and subtissue-scale model outcomes provided comprehensive explanations for the hard-to-interpret geometry dependence widely observed in AF tensile mechanics research and directly measured AF fiber stretch that were impossible to characterize during in situ and in vitro testing, highlighting the benefits of directly describing subtissue-level structures using the multiscale structure-based modeling approach.

Model outcomes also highlighted the importance of designing study-specific testing protocols based on individual research objectives. Particularly, physiologically representative specimen geometry, boundary condition, and loading condition should be applied if the measurements are intended to be interpreted in the context of clinical relevance, and vice versa. For example, in this dissertation, model outcomes across the joint, tissue, and subtissue scales helped identify the non-physiologically representative instantaneous center of rotation as a main issue for current herniation testing protocols, highlighting that the finite element models proposed in the current research could serve as a powerful yet effective complementary tool when designing testing protocols for resource- and time-intensive experiments.

In conclusion, a novel multiscale multiphasic structure-based framework is developed and validated for modeling the intervertebral disc; the resulting finite element models are proven accurate, robust, and translatable. The proposed modeling framework provides an effective tool for directly investigating the multiscale disc mechanics, especially at the subtissue scale, with degeneration, disease, and injury. The modeling framework with the subsequent model outcomes has the potential to help lay the foundation for future experimental-computational combined research that aims to comprehend disc and soft tissue failure mechanisms, providing a powerful tool that complements clinical diagnoses and treatments for low back pain.

Lower back pain is the leading cause of physical disability worldwide. In the United States, annual costs associated with lower back pain exceed $100 billion, as 70%-80% of Americans experience debilitating back pain at least once in their lifespan, limiting quality of life and ability to work. Disc degeneration is a major incurable cause of back pain often brought on or exacerbated by excessive loading of the spine. To enable the development of treatments for disc degeneration, more physiological relevant models which include the harsh mechanical environment of the human disc are needed. The dissertation research focused on the Annulus-on-a-Chip (AoC) design, fabrication, and testing of primary cells experimentally and computationally to replicate harsh strains in the annulus fibrosis of the human disc. Strains proved to be controllable, multidirectional, and uniform with magnitudes ranging from -10% in compression to 12% in tension in the axial, radial, and circumferential directions. The dissertation is the first of its kind to replicate complex mechanical loading on a microscale. The Annulus-on-a-Chip was designed to be reconfigurable for other uses such as the modeling of cardiovascular vessels, lymphatic vessels, and the cervix.

Due to the COVID-19 pandemic, the dissertation includes design for pandemic response to help rapidly address the inadequate supply of personal protective equipment (PPE). During the pandemic, shortages of PPE in rural and low-income healthcare settings were thrust into an international bidding war for N95 respirators due to global supply chain disruptions. To extend stockpiles of N95 respirators, benchtop devices for treating N95 respirators with Ultraviolet-C (UVC) germicidal light uniformly, rapidly, and inexpensively were developed and tested. Design iterations improved user safety, efficacy, and process flow, resulting in a set of open-source designs.

Finally, the lessons learned while targeting improvements to societal healthcare through engineering design of the AoC and pandemic response devices led to the ideating, proposing, and implementing of the College of Engineering Business Minor for Engineering PhDs. Intended to complement the strengths specific to PhDs at UC Berkeley, the Engineering Business Minor was designed to significantly support the many students looking to make an impact with their research.

The intervertebral disc has a complex fibrocartilaginous structure, comprised of a jel-like nucleus pulposus (NP) surrounded by the annulus fibrosus (AF) and is sandwiched between cartilaginous (CEPs) and bony endplates. Collagen fibers in AF orient in a cross-ply pattern and fiber angle to the horizontal plane decreases from 43 degree in the inner AF to 28 degree in the outer AF. NP, AF, and CEP are comprised primarily of water, proteoglycans (GAGs), and collagen fibers. A high GAG content gives these tissues an excellent capacity to absorb water resulting in an increase in tissue volume and swelling. in vivo, disc undergoes axial compression, torsion, flexion, extension, and lateral bending. Fluid flows out of the disc during the day and flows back at night exhibiting viscous effects.

Disc malfunctions including herniation and degeneration are the main contributors to low back pain. Disc herniation occurs as NP extrudes through a damaged region of the AF, compressing the spinal nerves and causing neurologic dysfunction. Painful herniations are treated with nucleotomy to remove the herniated material. Disc degeneration is noted by alterations in tissue structure and composition. These changes alter stress distributions between NP and AF, resulting in altered disc joint mechanics during loading and unloaded recovery.

Although the disc structural mechanics has been extensively studied, there are still a lot of unknowns from the literature. During my Ph.D., I studied the effects of fiber orientation, NP size and position, and nucleotomy on disc mechanics. A finite element model of the human lumbar disc based on averaged disc geometry was developed and validated. Then the validated model was modified to do parameter studies. Simulation results showed: (1) Discs with collagen fibers oriented closer to the horizontal plane experienced a decrease in AF stresses, NP pressure, and torsional stiffness. (2) NP size had a significant impact on compressive stiffness, intradiscal pressure, and principal strain. The location of NP centroid within the disc space had a significant impact on the magnitude and distribution of intradiscal pressure in flexion and extension. (3) The effects of nucleotomy on disc mechanics differed between single and more complex loading modalities.

Under single loading conditions, disc joint stiffness decreased with nucleotomy. However, more complex loading conditions resulted in an increase in bending stiffness (25 - 40%), suggesting that the disc is more resistant to bending after nucleotomy. Simulation results indicate that fiber orientation, NP size, and NP location are important factors for developing accurate computational models to study the mechanical behavior of native, injured, or degenerated discs and for creating a tissue-engineered disc. The discrepancy between single- and dual-loading conditions highlights the importance of evaluating disc joint mechanics under conditions that more closely represent in situ loading, which will be important for elucidating mechanisms for disc joint failure.

While multiple studies have reported disc tissues swelling, however, the effects of fiber network, fiber stiffness, GAG distribution, and boundary condition on disc swelling are not clear. Besides the relationships between disc tissue swelling and residual stress/strain/pressure formation are missing from the literature. To answer these questions, I developed finite element models for the intact disc joint and tissue subcomponents, including NP with AF and ex situ tissue explants (NP and CEP tissue cubes, AF rings, and rectangular AF samples based on uniaxial test specimens). Fiber orientation, fiber stiffness, and GAG content were varied to study the effects on tissue swelling and residual strain formation. Variations in GAG content and distribution replicated the healthy and degenerated discs. Simulation results showed: (1) Fiber angle, fiber architecture, and the number of lamellae in single fiber-family structures altered tissue swelling capacity, fiber deformation, and tissue rotation. (2) The kidney-bean shape played an important role in forming residual stress and strain in native AF (compressive stress and strain in the circumferential direction in the inner AF and tensile in the outer). These stretch and stress were comparable to experimental observations. GAG loss in the inner AF, as observed with degeneration, decreased circumferential direction stress by over 65%. (3) Boundary conditions created by surrounding tissues resulted in a relative decrease in swelling capacity by 40% in the NP and 25% in the AF and cartilaginous endplate forming a uniform stretch distribution in the AF. Our model predicted a decrease in equilibrium NP pressure from 0.21 MPa in a healthy disc to 0.03 MPa in the severely degenerated disc, agreeing with data in the literature. Early degeneration decreased the circumferential-direction residual deformation by over 60% and flipped the radial-direction stretch from compressive ~0.95 to tensile ~1.05, which may lead to apoptosis accelerating further degeneration. Degeneration also greatly altered AF residual stress/stretch and fiber stretch in the posterior region, which may cause disc failure. Findings from these studies demonstrate the need to include the native fiber network in computational models to accurately simulate tissue-swelling behavior and the need to replicate NP swelling capacity in engineered discs to prevent degradation of the inner AF.

Water content in nucleus pulposus (NP) and annulus fibrosus (AF) decrease greatly with aging and degeneration (over 10%) resulting in altered disc joint mechanics. Water content is also a key parameter in disc computational models to simulate swelling behavior as well as nutrition transportation. Therefore, accurately measuring disc water content is important to develop accurate patient-specific disc model and to detect disc early degeneration.

Using quantitative magnetic resonance imaging (MRI) to measure disc water content is a promising approach, as signal intensity depends on the single proton density within the tissue and the approach is non-invasive. However, MRI signal intensity is also dependent on scan-parameters, the concentration of free water molecules, and collagen fiber content and architecture. Therefore, how accurately MRI can quantify NP and AF water content is unclear. In this research, experiments were conducted to compare MR based water content measurement with traditional biochemical measurement (lyophilization). Experimental results showed that normalizing NP spin density by mass density provided an excellent agreement between MR measured water content and water content measured through lyophilization. However, normalizing spin density by mass density underestimated AF water content. This discrepancy is likely due to a higher concentration of bound water molecules in the AF, compared to the NP, where tightly bounded water molecules have too short T2 values to be detected in MR imaging.

Back pain is a widespread economic and public health concern, affecting around 70% of the population and incurring annual costs over $100 billion in the US alone. Back pain is frequently associated with degenerative changes to intervertebral discs, including altered biochemical composition, rheology, and mechanics. However, due to the interdependent cascade of degenerative changes occurring in vivo, the relative contribution of individual tissue constituents to disc failure remains unclear. Elucidating the fundamental structure-function relations that drive tissue failure aids in the prevention of avoidable injuries, guides the design of protective therapies and tissue repair strategies, and facilitates the development of advanced computational models that may help predict tissue injury.This dissertation details the development, validation, and implementation an experimental framework to elucidate fundamental tissue-level structure function relations between degeneration- and disease-mediated biochemical changes and annulus fibrosus (AF) failure mechanics. Chapter 2 reports on the development and validation of a novel method for repeatable failure testing of soft tissues with fibers oriented off-axis from the applied loading, such as AF specimens tested in the circumferential-radial or circumferential-axial orientations. With minor subsequent modification, the method described in Chapter 2 serves as the basis for the reliable characterization of AF tensile failure mechanics in subsequent chapters. Chapter 3 describes the effects of enzymatic proteoglycan degradation and concomitant water loss on AF tensile failure mechanics in the circumferential-radial direction at low and high loading rates. Chapter 4 provides a brief empirical analysis of the relative contribution of the three main AF biochemical constituents to the tensile failure mechanics of AF tissue from a cross-sectional population of human donors The use of 0.15M phosphate-buffered saline in Chapters 3 and 4 resulted in hyper-physiologic tissue water contents, which are known to alter the tissue mechanical response. Thus, Chapter 5 provides a more robust method to target and maintain AF hydration levels, mechanics, and composition at fresh-tissue levels during in vitro testing. Chapter 6 utilizes these methods to provide discrete and continuous descriptions of the role of advanced-glycation end products in AF sub-failure, failure, and post-failure tensile mechanics at quasi-static and dynamic loading rates. Finally, Chapter 7 addresses the limitations of the current work and suggests possible directions for future investigations that might build on this dissertation work.

The primary function of the intervertebral disc is to support large, multi-directional loads acting on the spine. The intervertebral disc has a heterogeneous structure, comprised of a gel-like nucleus pulposus (NP) and the annulus fibrosus (AF). The AF has a highly organized structure consisting of collagen fibers oriented in a criss-cross pattern in the alternating layers. Despite differences in composition and structure, water is the primary biochemical constituent of both tissues, accounting for greater than 65% of tissue’s wet weight. The water content of the intervertebral disc fluctuates throughout the day as the magnitude of compressive stress acting on the spine varies with changes in body posture, muscle activity, and external loads. The disc loses water during the day and absorbs water at night when loads are reduced.

Due to the avascular nature of the intervertebral disc, cell viability and metabolism rely on the exchange of nutrients and metabolic by-products via diffusion under biochemical gradients and fluid flow modulated by diurnal loading patterns. Hence, investigating fluid flow kinematics under simulated physiological loading conditions is important for understanding healthy disc function and mechanobiology. However, there is a lack of knowledge of fluid flow behavior and recovery mechanics during low loading conditions when disc absorbs water and increases its height. Hence, this dissertation aims to fill in this gap in the literature by evaluating the time-dependent recovery mechanics and fluid flow kinematics of the healthy intervertebral disc during low loading conditions that simulate bed-rest. To achieve this, this study tested bovine bone-disc-bone motion segments under a series of creep and recovery loading conditions. Results showed that time-dependent disc recovery behavior has contributions from both inherent fluid-independent viscoelasticity and fluid-dependent poroelasticity. Intrinsic viscoelastic effects are present at short time scales, providing partial recovery of disc height within minutes of unloading before poroelastic effects come into play. Poroelastic fluid flow dominates recovery at long time scales and is largely driven by the osmotic differential between tissue and its surrounding environment.

In vitro biomechanical tests on disc joints monitor changes in disc height to understand the direction, magnitude, and rate of fluid flow through the disc. However, these studies report displacements for the entire bone-disc-bone joint without the ability to identify the region-specific changes during swelling due to fluid flow. To improve our understanding of the complex fluid redistribution within the disc, the second part of this work characterized the time-dependent swelling behavior of the intervertebral disc ex situ. The first experiment monitored time-dependent changes in tissue mass to compare differences in the swelling capacities of the NP and AF explants under free swelling conditions. NP explants experienced a higher swelling rate and equilibrium swelling capacity than AF explants. Specifically, there was a 200% increase in the NP tissue mass and a 70% increase in the AF tissue mass under free swelling conditions. The second experiment used an optical, non-contact measurement method to evaluate the distribution of swelling-induced strains throughout intact discs and AF rings. Axial deformations were fixed to prevent out-of-plane motion during swelling. The first group consisted of AF rings in contact with saline at the outer periphery and the center of the annular ring. The second group included AF rings in contact with saline solution only at the outer periphery. The third group included intact discs in contact with saline at the outer periphery. Tissue swelling due to fluid flow was observed to be a slow process that strongly depends on tissue-specific biochemical properties and physical boundary constraints. For AF rings, negative circumferential strains were observed in the inner AF, while positive circumferential strains were observed in the outer AF. However, restricting fluid flow only to the outer periphery during swelling reduced the swelling capacity of the inner AF. The largest absolute radial strain was observed to be in the outer AF for Group 1 and the outer AF for Group 2. The swelling capacity of the NP was largely reduced when swelling was restricted to occur only in the radial direction or constrained by the surrounding AF. Results from intact discs showed that NP pressurization during swelling reduces peak radial strains in the AF and results in uniform strain distribution throughout the AF.

Together these findings provide a better understanding of intervertebral disc mechanics and function, particularly during low loading periods when disc absorbs water and increases its volume due to swelling. In conclusion, fluid flow is a slow, time-dependent process that depends on many factors, including biochemical properties, external osmotic pressure, loading history, and boundary constraints.

The dissertation research focused on exploring relationships between composition, structure, and mechanical properties in hydrogels used for tissue engineering application. Specifically, these series of separate but related studies focused on agarose-based gels and co-gels, looking at how different concentrations of agarose, alginate, and collagen affected their ability to serve as a tissue-engineering scaffold with appropriate manufacturability, compressive mechanical properties, and extra-cellular matrix production of embedded cells. These relationships between composition and structure add to the growing literature of tissue-engineering scaffolds, and help researchers move closer towards functional repair of damaged tissues. The main results of this work identified agarose-alginate co-gels as a suitable candidate for bioprinting tissue engineering scaffolds. Later, it was observed that crosslinking agarose-alginate gels changes the short-term recovery behavior under unconfined compression, and increases elastic mechanical properties. This dissertation work also observed that methods used to quantify collagen content from commercial collagen type I gels vary by species source, and that combining these collagen gels in an agarose-based cell-embedded scaffolds produces a minimal, dose-dependent effect on matrix production and compressive mechanics. In short, the dissertation has expanded on the known literature of agarose co-gel mechanics under different loading scenarios. It is my hope that researchers will use the relationships between matrix production, initial gel content, and compressive and shear mechanics to continue improving the functionality of tissue engineered constructs.

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