Daniel Nadal Cortes - Academia.edu (original) (raw)

Papers by Daniel Nadal Cortes

ASME 2012 Summer Bioengineering Conference, Parts A and B, 2012

Tissue modeling requires an appropriate stress-strain constitutive relationship and a correspondi... more Tissue modeling requires an appropriate stress-strain constitutive relationship and a corresponding set of material properties. It is often the goal of experimental studies to determine these material properties. Uniaxial tension experiments are simple in experimental approach and the interpretation of results is straightforward, prompting its use in several studies. However, the freely contracting lateral edges observed in this loading modality do not mimic the in situ conditions of many fiber-reinforced soft tissues and the unconstrained fibers may also create errors.Copyright © 2012 by ASME

ASME 2011 Summer Bioengineering Conference, Parts A and B, 2011

ABSTRACT Intervertebral disc degeneration is characterized by a progressive cascade of structural... more ABSTRACT Intervertebral disc degeneration is characterized by a progressive cascade of structural, biochemical and biomechanical changes affecting the annulus fibrosus (AF), nucleus pulposus (NP) and end plates (EP). These changes are considered to contribute to the onset of back pain. It has been shown that mechanical properties of the AF and NP change significantly with degeneration [1,2]. Therefore, mechanical properties have the potential to serve as a biomarker for diagnosis of disc degeneration. Currently, disc degeneration is diagnosed based on the detection of structural and compositional changes using MRI, X-ray, discography and other imaging techniques. These methods, however, do not measure directly the mechanical properties of the extracellular matrix of the disc. Magnetic Resonance Elastography (MRE) is a technique that has been used to measure in vivo mechanical properties of soft tissue by applying a mechanical vibration and measuring displacements with a motion-sensitized MRI pulse sequence [3]. The mechanical properties (e.g., the shear modulus) are calculated from the displacement field using an inverse method. Since the applied displacements are in the order of few microns, fibers may not be stretched enough to remove crimping. Therefore, it is unknown if the anisotropy of the AF due to the contribution of the fibers is detectable using MRE. The objective of this study is twofold: to measure shear properties of AF in different orientations to determine the degree of AF anisotropy observable by MRE, and to identify the contribution of different AF constituents to the measured shear modulus by applying different biochemical treatments.

2012 38th Annual Northeast Bioengineering Conference (NEBEC), 2012

ABSTRACT Protein crosslinking and glycosaminoglycan (GAG) depletion are characteristic of disc de... more ABSTRACT Protein crosslinking and glycosaminoglycan (GAG) depletion are characteristic of disc degeneration. The objective of this study is to analyze the role of these biochemical changes on the mechanics of annulus fibrosus extra-fibrillar matrix (EFM). It was found that GAG depletion decreased ionic contribution, but not the nonionic contribution of the EFM. Additionally, crosslinking increased the stiffness of annulus fibrosus EFM.

Annals of Solid and Structural Mechanics, 2009

A constitutive model to predict the onset and evolution of matrix cracking and the subsequent sti... more A constitutive model to predict the onset and evolution of matrix cracking and the subsequent stiffness reduction is derived analytically. The formulation is valid for symmetric laminates with otherwise arbitrary stacking sequence and matrix cracks in one or two directions. The proposed model calculates the reduction of the mechanical properties of the damaged laminate as function of crack densities. The onset and evolution of matrix cracks are predicted by the model in terms of undamaged lamina properties and the critical strain energy release rates for modes I and II (G IC and G IIC). Therefore, there is not need for postulating damage evolution functions and no need for empirically adjusting the associated material parameters. The model formulation was specialized for the particular case of unidirectional loading. Comparison with experimental data showed an excellent prediction of crack initiation and evolution for a variety of laminate stacking sequences. The combination of constitutive and damage evolution equations formed an integrated, mechanistic damage model with no adjustable parameters.

Volume 2: Biomedical and Biotechnology Engineering, 2007

This work investigates the use of frequency spectrum analysis of waveguide propagation in multi-l... more This work investigates the use of frequency spectrum analysis of waveguide propagation in multi-layered anisotropic piezoelectric transducers. A semi-analytical finite-element analysis (SAFE) is used to model the transducer as a piezoelectric infinite plate. Dispersion curves, group velocities and displacement frequency spectra can be obtained for any multilayered piezoelectric plate. Stress-free boundary conditions were assumed for all analyses. Results for open and closed circuit boundary conditions were analyzed. Zero-Group-Velocity (ZGV) frequencies of high-order waveguide modes were observed to provide multi-resonant displacement frequency spectrum. Comparison of numerical and experimental results shows a good agreement between peak and off-peak values of the displacement spectrum. Results showed that optimization of layered structure may provide an efficient means for generating multi-thickness (ZGV) waveguide modes, thus increasing the bandwidth of harmonic ultrasound transducers for contrast imaging.Copyright © 2007 by ASME

The Intervertebral Disc, 2013

The intervertebral disc is the soft tissue between the vertebral bodies. The disc function is to ... more The intervertebral disc is the soft tissue between the vertebral bodies. The disc function is to transmit multi-directional loads through the spine and to allow relative motion between the vertebral bodies. The intervertebral disc is composed of three distinct tissues: nucleus pulposus, annulus fibrosus, and the cartilaginous endplates. Each of these tissues has a characteristic composition and structure which provide them with unique mechanical properties. The interaction between these tissues enables the intervertebral disc to perform its function. The objective of this chapter is to describe the mechanical behavior of the individual disc tissues and then discuss how they work together in physiological loading scenarios. In addition, the effects of degeneration on the mechanics at the tissue and disc level are described.

ASME 2011 Summer Bioengineering Conference, Parts A and B, 2011

ABSTRACT The human supraspinatus tendon (SST) exhibits strong heterogeneity in fiber alignment an... more ABSTRACT The human supraspinatus tendon (SST) exhibits strong heterogeneity in fiber alignment and material properties [1,2]. The relationship between fiber angle distribution and material properties has been previously described by a structurally based continuum model [3], which provided new quantitative structure-function relationships to explain the observed SST heterogeneity; however, in some locations and testing directions, the model predictions were not consistent with a continuum assumption [3]. More recent analysis of the change in fiber angle during loading showed that samples with less aligned fibers have less affine kinematics in uniaxial tensile loading [4]. That is, in uniaxial tensile testing, where the transverse edges freely contract, the fiber strain did not match the tissue strain. Because the SST is somewhat transversely constrained by surrounding rotator cuff structures in vivo and has distributed fibers to support multidirectional loading, the freely contracting edges of uniaxial tension may not appropriately constrain the tendon. Therefore, the objective of this study was to evaluate SST stress-strain behavior and affine deformation under biaxial tension. Specifically, if behaving as a continuum, we expected that applying a fixed boundary condition in the transverse direction would produce a higher apparent modulus, a smaller toe-region, and more affine fiber realignment than a free boundary condition.

ASME 2010 Summer Bioengineering Conference, Parts A and B, 2010

Collagen fibers and their structural arrangement influence tissue tensile stiffness and strength.... more Collagen fibers and their structural arrangement influence tissue tensile stiffness and strength. While a variety of modeling approaches incorporate collagen fibers explicitly as one of the components, due to the complexity of the fiber organization, aligned fibers are usually considered. In the pioneering work of Lanir [1], a constitutive relation for continuous fiber distributions was proposed, where the strain energy and stresses are obtained by angular integration (AI) of infinitesimal fractions of fibers aligned in a given direction. Lanir’s formulation has been successfully used to describe the mechanical behavior of a variety of tissues. In particular, Ateshian et al. [2] showed that large values of the tensile Poisson’s ratio for articular cartilage in tension and the low values observed in compression can be explained using a continuous angular distribution for the fibers. A disadvantage of the AI formulation is the large number of calculations required to evaluate the strains and stresses. On the other hand, Generalized Structure Tensors (GST) have been proposed to model tissues with continuously distributed collagen fibers [3,4]. These tensors are assumed to represent the three-dimensional distribution of the fibers. Once the tensor has been defined, the strain in the fibers can be readily obtained by multiplication with a strain tensor. The advantage of this approach is the small number of calculations required to obtain the strain energy and stresses of the fibers. As a result, this formulation can be efficiently implemented in numerical algorithms like finite elements. However, this approach is limited, as it is valid only when all of the fibers are in tension and when the fiber distribution is small [5]. A numerical comparison is required to quantify when an angular distribution can be considered acceptably small to justify using this more computationally efficient approach. The objective of this study is to numerically compare the AI and GST formulations to determine the range of values of angular distribution for which the GST approach can be accurately used.Copyright © 2010 by ASME

Mechanics of Materials, 2014

The orientation of collagen fibers plays an important role on the mechanics of connective tissues... more The orientation of collagen fibers plays an important role on the mechanics of connective tissues. Connective tissues have fibers with different orientation distributions. The angular integration formulation used to model the mechanics of fibers with distributed orientation is accurate, but computationally expensive for numerical methods such as finite elements. This study presents a formulation based on pre-integrated Generalized High-Order Structure Tensors (GHOST) which greatly improves the accuracy of the predicted stress. Simplifications of the GHOST formulation for transversely-isotropic and planar fiber distributions are also presented. Additionally, the GHOST and the angular integration formulations are compared for different loading conditions, fiber orientation functions, strain energy functions and degrees of fiber non-linearity. It was found that the GHOST formulation predicted the stress of the fibers with an error lower than 10% for uniaxial and biaxial tension. Fiber non-linearity increased the error of the GHOST formulation; however, the error was reduced to negligible values by considering higher order structure tensors. The GHOST formulation produced lower errors when used with an elliptical fiber density function and a binomial strain energy function. In conclusion, the GHOST formulation is able to accurately predict the stress of fibers with distributed orientation without requiring numerous integral calculations. Consequently, the GHOST formulation may reduce the computational effort needed to analyze the mechanics of fibrous tissues with distributed orientations.

Magnetic Resonance in Medicine, 2013

This study aims to: (1) measure the shear modulus of nucleus pulposus (NP) in intact human verteb... more This study aims to: (1) measure the shear modulus of nucleus pulposus (NP) in intact human vertebra-disc-vertebra segments using a magnetic resonance elastography setup for a 7T whole-body scanner, (2) quantify the effect of disc degeneration on the NP shear modulus measured using magnetic resonance elastography, and (3) compare the NP shear modulus to other magnetic resonance-based biomarkers of dis degeneration. Thirty intact human disc segments were classified as normal, mild, or severely degenerated. The NP shear modulus was measured using a custom-made setup that included a novel inverse method less sensitive to noisy displacements. T2 relaxation time was measured at 7T. The accuracy of these parameters to classify different degrees of degeneration was evaluated using receiver operating characteristic curves. The magnetic resonance elastography measure of shear modulus in the NP was able to differentiate between normal, mild degeneration, and severe degeneration. The T2 relaxation time was able to differentiate between normal and mild degeneration, but it could not distinguish between mild and severe degeneration. This study shows that the NP shear modulus measured using magnetic resonance elastography is sensitive to disc degeneration and has the potential of being used as a clinical tool to quantify the mechanical integrity of the intervertebral disc.

Journal of biomechanical engineering, 2012

The heterogeneous composition and mechanical properties of the supraspinatus tendon offer an oppo... more The heterogeneous composition and mechanical properties of the supraspinatus tendon offer an opportunity for studying the structure-function relationships of fibrous musculoskeletal connective tissues. Previous uniaxial testing has demonstrated a correlation between the collagen fiber angle distribution and tendon mechanics in response to tensile loading both parallel and transverse to the tendon longitudinal axis. However, the planar mechanics of the supraspinatus tendon may be more appropriately characterized through biaxial tensile testing, which avoids the limitation of nonphysiologic traction-free boundary conditions present during uniaxial testing. Combined with a structural constitutive model, biaxial testing can help identify the specific structural mechanisms underlying the tendon's two-dimensional mechanical behavior. Therefore, the objective of this study was to evaluate the contribution of collagen fiber organization to the planar tensile mechanics of the human supr...

Composites Part B: Engineering, 2010

A constitutive model to predict stiffness reduction due to transverse matrix cracking is derived ... more A constitutive model to predict stiffness reduction due to transverse matrix cracking is derived for laminae with arbitrary orientation, subject to in-plane stress, embedded in laminates with symmetric but otherwise arbitrary laminate stacking sequence. The moduli of the damaged laminate are a function of the crack densities in the damaging laminae, which are analyzed one by one. The evolution of crack density in each lamina is derived in terms of the calculated strain energy release rate and predicted as function of the applied load using a fracture mechanics approach. Unlike plasticity-inspired formulations, the proposed model does not postulate damage evolution functions and thus there is no need for additional experimental data to adjust material parameters. All that it is needed are the elastic moduli and critical energy release rates for the laminae. The reduction of lamina stiffness is an integral part of the model, allowing for stress redistribution among laminae. Comparisons with experimental data and some results from the literature are presented.

Biomechanics and Modeling in Mechanobiology, 2011

Structural constitutive modeling approaches are often based on the assumption of affine fiber kin... more Structural constitutive modeling approaches are often based on the assumption of affine fiber kinematics, even though this assumption has rarely been evaluated experimentally. We are interested in applying mathematical models to understand the mechanisms responsible for the inhomogeneous, anisotropic, and non-linear properties of human supraspinatus tendon (SST); however, the relationship between macroscopic and fiber-level deformation in this tendon remains unknown and current methods for making this assessment are inadequate. Therefore, the purpose of this study was to develop an improved method for quantitatively assessing agreement between two distributions and to examine the affine assumption in SST by comparing experimental fiber alignment to affine model predictions using this analysis approach. Measured fiber angle values of SST samples in uniaxial tensile tests were compared with predictions of affine fiber deformation using modified projection plots, which provide a method for qualitative and quantitative comparisons of two distributions. The projection plot metrics of offset and range, which were developed in this study, are of particular benefit by providing a quantitative representation of agreement that can be subjected to statistical comparisons. For SST, offset and range values varied by tendon location and test orientation, with more affine deformation evidenced for tendon regions of higher alignment. Results suggest that non-affine fiber behavior is dependent on specific

Biomechanics and Modeling in Mechanobiology, 2010

Modeling of connective tissues often includes collagen fibers explicitly as one of the components... more Modeling of connective tissues often includes collagen fibers explicitly as one of the components. These fibers can be oriented in many directions; therefore, several studies have considered statistical distributions to describe the fiber arrangement. One approach to formulate a constitutive framework for distributed fibers is to express the mechanical parameters, such as strain energy and stresses, in terms of angular integrals. These integrals represent the addition of the contribution of infinitesimal fractions of fibers oriented in a given direction. This approach leads to accurate results; however, it requires lengthy calculations. Recently, the use of generalized structure tensors has been proposed to represent the angular distribution in the constitutive equations of the fibers. Although this formulation is much simpler and fewer calculations are required, such structure tensors can only be used when all the fibers are in tension and the angular distribution is small. However, the amount of error introduced in these cases of non-tensile fiber loading and large angular distributions have not been quantified. Therefore, the objective of this study is to determine the range of values of angular distribution for which acceptable differences (less than 10%) between these two formulations are obtained. It was found, analytically and numerically, that both formulations are equivalent for planar distributions under equal-biaxial stretch. The comparison also showed, for other loading conditions, that the differences decrease when the fiber distribution is very small. Differences of less than 10% were usually obtained when the fiber distribution was very low (κ ≈ 0.03; κ ranges between 0 and 1/3, for aligned and isotropic distributed fibers, respectively). This range of angular distribution

2012 38th Annual Northeast Bioengineering Conference (NEBEC), 2012

ABSTRACT Intervertebral disc degeneration is a cell-mediated process that results in the disrupti... more ABSTRACT Intervertebral disc degeneration is a cell-mediated process that results in the disruption of its function. These changes are difficult to overturn; consequently, early diagnosis is key for the success of any treatment. Clinically, disc degeneration is diagnosed by analyzing morphological changes characteristic of moderate to advanced stages of degeneration. Therefore, there is a need of a reliable biomarker to characterize the compositional and structural integrity of the disc in early stages of degeneration. In this study, shear modulus is proposed as a new biomarker for disc degeneration and a non-invasive method to measure this mechanical property is presented.

ASME 2012 Summer Bioengineering Conference, Parts A and B, 2012

Tissue modeling requires an appropriate stress-strain constitutive relationship and a correspondi... more Tissue modeling requires an appropriate stress-strain constitutive relationship and a corresponding set of material properties. It is often the goal of experimental studies to determine these material properties. Uniaxial tension experiments are simple in experimental approach and the interpretation of results is straightforward, prompting its use in several studies. However, the freely contracting lateral edges observed in this loading modality do not mimic the in situ conditions of many fiber-reinforced soft tissues and the unconstrained fibers may also create errors.Copyright © 2012 by ASME

ASME 2011 Summer Bioengineering Conference, Parts A and B, 2011

ABSTRACT Intervertebral disc degeneration is characterized by a progressive cascade of structural... more ABSTRACT Intervertebral disc degeneration is characterized by a progressive cascade of structural, biochemical and biomechanical changes affecting the annulus fibrosus (AF), nucleus pulposus (NP) and end plates (EP). These changes are considered to contribute to the onset of back pain. It has been shown that mechanical properties of the AF and NP change significantly with degeneration [1,2]. Therefore, mechanical properties have the potential to serve as a biomarker for diagnosis of disc degeneration. Currently, disc degeneration is diagnosed based on the detection of structural and compositional changes using MRI, X-ray, discography and other imaging techniques. These methods, however, do not measure directly the mechanical properties of the extracellular matrix of the disc. Magnetic Resonance Elastography (MRE) is a technique that has been used to measure in vivo mechanical properties of soft tissue by applying a mechanical vibration and measuring displacements with a motion-sensitized MRI pulse sequence [3]. The mechanical properties (e.g., the shear modulus) are calculated from the displacement field using an inverse method. Since the applied displacements are in the order of few microns, fibers may not be stretched enough to remove crimping. Therefore, it is unknown if the anisotropy of the AF due to the contribution of the fibers is detectable using MRE. The objective of this study is twofold: to measure shear properties of AF in different orientations to determine the degree of AF anisotropy observable by MRE, and to identify the contribution of different AF constituents to the measured shear modulus by applying different biochemical treatments.

2012 38th Annual Northeast Bioengineering Conference (NEBEC), 2012

ABSTRACT Protein crosslinking and glycosaminoglycan (GAG) depletion are characteristic of disc de... more ABSTRACT Protein crosslinking and glycosaminoglycan (GAG) depletion are characteristic of disc degeneration. The objective of this study is to analyze the role of these biochemical changes on the mechanics of annulus fibrosus extra-fibrillar matrix (EFM). It was found that GAG depletion decreased ionic contribution, but not the nonionic contribution of the EFM. Additionally, crosslinking increased the stiffness of annulus fibrosus EFM.

Annals of Solid and Structural Mechanics, 2009

A constitutive model to predict the onset and evolution of matrix cracking and the subsequent sti... more A constitutive model to predict the onset and evolution of matrix cracking and the subsequent stiffness reduction is derived analytically. The formulation is valid for symmetric laminates with otherwise arbitrary stacking sequence and matrix cracks in one or two directions. The proposed model calculates the reduction of the mechanical properties of the damaged laminate as function of crack densities. The onset and evolution of matrix cracks are predicted by the model in terms of undamaged lamina properties and the critical strain energy release rates for modes I and II (G IC and G IIC). Therefore, there is not need for postulating damage evolution functions and no need for empirically adjusting the associated material parameters. The model formulation was specialized for the particular case of unidirectional loading. Comparison with experimental data showed an excellent prediction of crack initiation and evolution for a variety of laminate stacking sequences. The combination of constitutive and damage evolution equations formed an integrated, mechanistic damage model with no adjustable parameters.

Volume 2: Biomedical and Biotechnology Engineering, 2007

This work investigates the use of frequency spectrum analysis of waveguide propagation in multi-l... more This work investigates the use of frequency spectrum analysis of waveguide propagation in multi-layered anisotropic piezoelectric transducers. A semi-analytical finite-element analysis (SAFE) is used to model the transducer as a piezoelectric infinite plate. Dispersion curves, group velocities and displacement frequency spectra can be obtained for any multilayered piezoelectric plate. Stress-free boundary conditions were assumed for all analyses. Results for open and closed circuit boundary conditions were analyzed. Zero-Group-Velocity (ZGV) frequencies of high-order waveguide modes were observed to provide multi-resonant displacement frequency spectrum. Comparison of numerical and experimental results shows a good agreement between peak and off-peak values of the displacement spectrum. Results showed that optimization of layered structure may provide an efficient means for generating multi-thickness (ZGV) waveguide modes, thus increasing the bandwidth of harmonic ultrasound transducers for contrast imaging.Copyright © 2007 by ASME

The Intervertebral Disc, 2013

The intervertebral disc is the soft tissue between the vertebral bodies. The disc function is to ... more The intervertebral disc is the soft tissue between the vertebral bodies. The disc function is to transmit multi-directional loads through the spine and to allow relative motion between the vertebral bodies. The intervertebral disc is composed of three distinct tissues: nucleus pulposus, annulus fibrosus, and the cartilaginous endplates. Each of these tissues has a characteristic composition and structure which provide them with unique mechanical properties. The interaction between these tissues enables the intervertebral disc to perform its function. The objective of this chapter is to describe the mechanical behavior of the individual disc tissues and then discuss how they work together in physiological loading scenarios. In addition, the effects of degeneration on the mechanics at the tissue and disc level are described.

ASME 2011 Summer Bioengineering Conference, Parts A and B, 2011

ABSTRACT The human supraspinatus tendon (SST) exhibits strong heterogeneity in fiber alignment an... more ABSTRACT The human supraspinatus tendon (SST) exhibits strong heterogeneity in fiber alignment and material properties [1,2]. The relationship between fiber angle distribution and material properties has been previously described by a structurally based continuum model [3], which provided new quantitative structure-function relationships to explain the observed SST heterogeneity; however, in some locations and testing directions, the model predictions were not consistent with a continuum assumption [3]. More recent analysis of the change in fiber angle during loading showed that samples with less aligned fibers have less affine kinematics in uniaxial tensile loading [4]. That is, in uniaxial tensile testing, where the transverse edges freely contract, the fiber strain did not match the tissue strain. Because the SST is somewhat transversely constrained by surrounding rotator cuff structures in vivo and has distributed fibers to support multidirectional loading, the freely contracting edges of uniaxial tension may not appropriately constrain the tendon. Therefore, the objective of this study was to evaluate SST stress-strain behavior and affine deformation under biaxial tension. Specifically, if behaving as a continuum, we expected that applying a fixed boundary condition in the transverse direction would produce a higher apparent modulus, a smaller toe-region, and more affine fiber realignment than a free boundary condition.

ASME 2010 Summer Bioengineering Conference, Parts A and B, 2010

Collagen fibers and their structural arrangement influence tissue tensile stiffness and strength.... more Collagen fibers and their structural arrangement influence tissue tensile stiffness and strength. While a variety of modeling approaches incorporate collagen fibers explicitly as one of the components, due to the complexity of the fiber organization, aligned fibers are usually considered. In the pioneering work of Lanir [1], a constitutive relation for continuous fiber distributions was proposed, where the strain energy and stresses are obtained by angular integration (AI) of infinitesimal fractions of fibers aligned in a given direction. Lanir’s formulation has been successfully used to describe the mechanical behavior of a variety of tissues. In particular, Ateshian et al. [2] showed that large values of the tensile Poisson’s ratio for articular cartilage in tension and the low values observed in compression can be explained using a continuous angular distribution for the fibers. A disadvantage of the AI formulation is the large number of calculations required to evaluate the strains and stresses. On the other hand, Generalized Structure Tensors (GST) have been proposed to model tissues with continuously distributed collagen fibers [3,4]. These tensors are assumed to represent the three-dimensional distribution of the fibers. Once the tensor has been defined, the strain in the fibers can be readily obtained by multiplication with a strain tensor. The advantage of this approach is the small number of calculations required to obtain the strain energy and stresses of the fibers. As a result, this formulation can be efficiently implemented in numerical algorithms like finite elements. However, this approach is limited, as it is valid only when all of the fibers are in tension and when the fiber distribution is small [5]. A numerical comparison is required to quantify when an angular distribution can be considered acceptably small to justify using this more computationally efficient approach. The objective of this study is to numerically compare the AI and GST formulations to determine the range of values of angular distribution for which the GST approach can be accurately used.Copyright © 2010 by ASME

Mechanics of Materials, 2014

The orientation of collagen fibers plays an important role on the mechanics of connective tissues... more The orientation of collagen fibers plays an important role on the mechanics of connective tissues. Connective tissues have fibers with different orientation distributions. The angular integration formulation used to model the mechanics of fibers with distributed orientation is accurate, but computationally expensive for numerical methods such as finite elements. This study presents a formulation based on pre-integrated Generalized High-Order Structure Tensors (GHOST) which greatly improves the accuracy of the predicted stress. Simplifications of the GHOST formulation for transversely-isotropic and planar fiber distributions are also presented. Additionally, the GHOST and the angular integration formulations are compared for different loading conditions, fiber orientation functions, strain energy functions and degrees of fiber non-linearity. It was found that the GHOST formulation predicted the stress of the fibers with an error lower than 10% for uniaxial and biaxial tension. Fiber non-linearity increased the error of the GHOST formulation; however, the error was reduced to negligible values by considering higher order structure tensors. The GHOST formulation produced lower errors when used with an elliptical fiber density function and a binomial strain energy function. In conclusion, the GHOST formulation is able to accurately predict the stress of fibers with distributed orientation without requiring numerous integral calculations. Consequently, the GHOST formulation may reduce the computational effort needed to analyze the mechanics of fibrous tissues with distributed orientations.

Magnetic Resonance in Medicine, 2013

This study aims to: (1) measure the shear modulus of nucleus pulposus (NP) in intact human verteb... more This study aims to: (1) measure the shear modulus of nucleus pulposus (NP) in intact human vertebra-disc-vertebra segments using a magnetic resonance elastography setup for a 7T whole-body scanner, (2) quantify the effect of disc degeneration on the NP shear modulus measured using magnetic resonance elastography, and (3) compare the NP shear modulus to other magnetic resonance-based biomarkers of dis degeneration. Thirty intact human disc segments were classified as normal, mild, or severely degenerated. The NP shear modulus was measured using a custom-made setup that included a novel inverse method less sensitive to noisy displacements. T2 relaxation time was measured at 7T. The accuracy of these parameters to classify different degrees of degeneration was evaluated using receiver operating characteristic curves. The magnetic resonance elastography measure of shear modulus in the NP was able to differentiate between normal, mild degeneration, and severe degeneration. The T2 relaxation time was able to differentiate between normal and mild degeneration, but it could not distinguish between mild and severe degeneration. This study shows that the NP shear modulus measured using magnetic resonance elastography is sensitive to disc degeneration and has the potential of being used as a clinical tool to quantify the mechanical integrity of the intervertebral disc.

Journal of biomechanical engineering, 2012

The heterogeneous composition and mechanical properties of the supraspinatus tendon offer an oppo... more The heterogeneous composition and mechanical properties of the supraspinatus tendon offer an opportunity for studying the structure-function relationships of fibrous musculoskeletal connective tissues. Previous uniaxial testing has demonstrated a correlation between the collagen fiber angle distribution and tendon mechanics in response to tensile loading both parallel and transverse to the tendon longitudinal axis. However, the planar mechanics of the supraspinatus tendon may be more appropriately characterized through biaxial tensile testing, which avoids the limitation of nonphysiologic traction-free boundary conditions present during uniaxial testing. Combined with a structural constitutive model, biaxial testing can help identify the specific structural mechanisms underlying the tendon's two-dimensional mechanical behavior. Therefore, the objective of this study was to evaluate the contribution of collagen fiber organization to the planar tensile mechanics of the human supr...

Composites Part B: Engineering, 2010

A constitutive model to predict stiffness reduction due to transverse matrix cracking is derived ... more A constitutive model to predict stiffness reduction due to transverse matrix cracking is derived for laminae with arbitrary orientation, subject to in-plane stress, embedded in laminates with symmetric but otherwise arbitrary laminate stacking sequence. The moduli of the damaged laminate are a function of the crack densities in the damaging laminae, which are analyzed one by one. The evolution of crack density in each lamina is derived in terms of the calculated strain energy release rate and predicted as function of the applied load using a fracture mechanics approach. Unlike plasticity-inspired formulations, the proposed model does not postulate damage evolution functions and thus there is no need for additional experimental data to adjust material parameters. All that it is needed are the elastic moduli and critical energy release rates for the laminae. The reduction of lamina stiffness is an integral part of the model, allowing for stress redistribution among laminae. Comparisons with experimental data and some results from the literature are presented.

Biomechanics and Modeling in Mechanobiology, 2011

Structural constitutive modeling approaches are often based on the assumption of affine fiber kin... more Structural constitutive modeling approaches are often based on the assumption of affine fiber kinematics, even though this assumption has rarely been evaluated experimentally. We are interested in applying mathematical models to understand the mechanisms responsible for the inhomogeneous, anisotropic, and non-linear properties of human supraspinatus tendon (SST); however, the relationship between macroscopic and fiber-level deformation in this tendon remains unknown and current methods for making this assessment are inadequate. Therefore, the purpose of this study was to develop an improved method for quantitatively assessing agreement between two distributions and to examine the affine assumption in SST by comparing experimental fiber alignment to affine model predictions using this analysis approach. Measured fiber angle values of SST samples in uniaxial tensile tests were compared with predictions of affine fiber deformation using modified projection plots, which provide a method for qualitative and quantitative comparisons of two distributions. The projection plot metrics of offset and range, which were developed in this study, are of particular benefit by providing a quantitative representation of agreement that can be subjected to statistical comparisons. For SST, offset and range values varied by tendon location and test orientation, with more affine deformation evidenced for tendon regions of higher alignment. Results suggest that non-affine fiber behavior is dependent on specific

Biomechanics and Modeling in Mechanobiology, 2010

Modeling of connective tissues often includes collagen fibers explicitly as one of the components... more Modeling of connective tissues often includes collagen fibers explicitly as one of the components. These fibers can be oriented in many directions; therefore, several studies have considered statistical distributions to describe the fiber arrangement. One approach to formulate a constitutive framework for distributed fibers is to express the mechanical parameters, such as strain energy and stresses, in terms of angular integrals. These integrals represent the addition of the contribution of infinitesimal fractions of fibers oriented in a given direction. This approach leads to accurate results; however, it requires lengthy calculations. Recently, the use of generalized structure tensors has been proposed to represent the angular distribution in the constitutive equations of the fibers. Although this formulation is much simpler and fewer calculations are required, such structure tensors can only be used when all the fibers are in tension and the angular distribution is small. However, the amount of error introduced in these cases of non-tensile fiber loading and large angular distributions have not been quantified. Therefore, the objective of this study is to determine the range of values of angular distribution for which acceptable differences (less than 10%) between these two formulations are obtained. It was found, analytically and numerically, that both formulations are equivalent for planar distributions under equal-biaxial stretch. The comparison also showed, for other loading conditions, that the differences decrease when the fiber distribution is very small. Differences of less than 10% were usually obtained when the fiber distribution was very low (κ ≈ 0.03; κ ranges between 0 and 1/3, for aligned and isotropic distributed fibers, respectively). This range of angular distribution

2012 38th Annual Northeast Bioengineering Conference (NEBEC), 2012

ABSTRACT Intervertebral disc degeneration is a cell-mediated process that results in the disrupti... more ABSTRACT Intervertebral disc degeneration is a cell-mediated process that results in the disruption of its function. These changes are difficult to overturn; consequently, early diagnosis is key for the success of any treatment. Clinically, disc degeneration is diagnosed by analyzing morphological changes characteristic of moderate to advanced stages of degeneration. Therefore, there is a need of a reliable biomarker to characterize the compositional and structural integrity of the disc in early stages of degeneration. In this study, shear modulus is proposed as a new biomarker for disc degeneration and a non-invasive method to measure this mechanical property is presented.