bluuebunny/crossref_metadata_2025 huggingface dataset:
Forward and Backward Running Waves in the Arteries: Analysis Using the Method of Characteristics
Authors: Parker K. H. , Jones C. J. H.
Published: March 2008

The one-dimensional equations of flow in the elastic arteries are hyperbolic and admit nonlinear, wavelike solutions for the mean velocity, U, and the pressure, P. Neglecting dissipation, the solutions can be written in terms of wavelets defined as differences of the Riemann invariants across characteristics. This analysis shows that the product, dUdP, is positive definite for forward running wavelets and negative definite for backward running wavelets allowing the determination of the net magnitude and direction of propagating wavelets from pressure and velocity measured at a point in the artery. With the linearizing assumption that intersecting wavelets are additive, the forward and backward running wavelets can be separately calculated. This analysis, applied to measurements made in the ascending aorta of man, shows that forward running wavelets dominate during both the acceleration and deceleration phases of blood flow in the aorta. The forward and backward running waves calculated using the linearized analysis are similar to the results of an impedance analysis of the data. Unlike the impedance analysis, however, this is a time domain analysis which can be applied to nonperiodic or transient flow.
A Six-Degree-of-Freedom Acoustic Transducer for Rotation and Translation Measurements Across the Knee
Authors: Quinn T. P. , Mote C. D.
Published: March 2008

An acoustic transducer design to measure the relative translations and rotations across the knee with no mechanical coupling between the tibia and femur is presented. Platforms attached to femoral and tibial tracking fixtures hold acoustic sources and receivers, respectively. The distance from each source to each receiver is measured by the acoustic transit time and the translations and rotations across the knee joint are computed. For rotations less than 30 deg around the expected operating position, the resolution of the transducer is 0.3 deg; for translations less than 1.5 cm around the expected operating position, the resolution is 0.03 cm. Theoretical error analysis using a Monte Carlo method shows that the uncertainty in the measurement depends on the relative position of the sources and receivers. The analysis predicts the worst case resolution of the transducer as 0.09 cm in translation and 0.6 deg in rotation when the receiver platform is translated 8.0 cm parallel to the source platform. The transducer and fixturing system are demonstrated on a cadaver specimen for applied anterior force and applied internal-external rotation. Errors due to (soft tissue) motion of the transducer relative to the bone during in vivo measurements are assessed on the cadaver specimen. For internal-external rotation the error due to soft tissue motion is a maximum of 0.5 cm in translation and 1.8 deg in rotation. For applied anterior force the error due to soft tissue motion is a maximum of 0.16 cm in translation and 2.7 deg in rotation.
Planning Tendon Paths Using an Interactive Graphic Workstation
Authors: Yoon Inmo , Thompson D. E.
Published: March 2008

This study provides a technique to be used for planning tendon paths in thumb reconstruction surgery. All mathematical modeling computations are performed on a VAX 11/750 host computer and the graphic manipulation is carried out by the Evans & Sutherland PS390 color display system. The results of the simulation are stored in a log file, including the rotation angles of the joints and the location of the pulley and the insertion points as a record of the tendon transfer design for a specific hand. The methods are based on the modeling of two separate types of tendon paths that consist of straight line segments and curved segments that follow bone contours. The method further assumes that the path of the tendon will always evolve to a planar curve. By integrating this technique with an existing kinematic model of the hand derived from CT-scans, a clinically relevant method has been developed.
Quantitative Measures for Fracture Healing: An In-Vitro Biomechanical Study
Authors: Foux A. , Black R. C. , Uhthoff H. K.
Published: March 2008

A method is presented to assess the functional capabilities of plated osteotomized canine femora as load bearing structures and to quantify their healing status. In this method the osteotomized bones and their intact contralateral controls are tested in nondestructive bending, in twenty-four planes of loading at 15 degree angular increments. Flexural rigidity (EI), in each of the planes, is determined by using classical beam theory. It has been found that the EI values have the expected elliptical distribution. The 24 EI values, obtained for each bone, are curve fitted by regression analysis and the characteristics of each bone are described by the three parameters defining its ellipse. The parameters of the ellipses of the osteotomized bone and of its contralateral control are used to define four new parameters that may serve as measures for the healing efficiency. One of these serves as an indicator for the fragility of the healed bone and the other three add quantiative information on its mechanical state.
A Microstructural Model for the Anisotropic Drained Stiffness of Articular Cartilage
Authors: Farquhar T. , Dawson P. R. , Torzilli P. A.
Published: March 2008

A constitutive model for articular cartilage is developed to study directional load sharing within the soft biological tissue. Cartilage is idealized as a composite structure whose static mechanical response is dominated by distortion of a sparse fibrous network and by changes in fixed charge density. These histological features of living cartilage are represented in a microstructural analog of the tissue, linking the directionality of mechanical stiffness to the orientation of microstructure. The discretized ‘model tissue’ is used to define a stiffness tensor relating drained stress and strain over a regime of large deformation. The primary goal of this work was to develop a methodology permitting more complete treatment of anisotropy in the stiffness of cartilage. The results demonstrate that simple oriented microscopic behaviors can combine to produce complicated larger scale response. For the illustrative example of a homogeneous specimen subjected to confined compression, the model predicts a nonlinear anisotropic drained response, with inherent uncertainty at cellular size scales.
Theoretical Prediction of Muscle Forces on the Mandible During Bite
Authors: Kang Q. S. , Updike D. P. , Salathe Eric P.
Published: March 2008

We present a mathematical model to determine the contribution of each muscle acting on the mandible in the development of a given bite force. We give special attention to the representation of the widely radiated temporalis and account for the attachment of the external pterygoid to the capsular ligament. An optimization technique based on minimizing the maximum stress occurring in the muscles is used to resolve the statically indeterminant nature of the problem formulated. The theoretically predicted values of the muscle forces are compared to experimental results taken from the literature.
One-Dimensional Steady Inviscid Flow Through a Stenotic Collapsible Tube
Authors: Ku David N. , Zeigler Marvin N. , Downing J. Micah
Published: March 2008

A one-dimensional inviscid solution for flow through a compliant tube with a stenosis is presented. The model is used to represent an artery with an atherosclerotic plaque and to investigate a range of conditions for which arterial collapse may occur. The coupled equations for flow through collapsible tubes are solved using a Runge-Kutta finite difference scheme. Quantitative results are given for specific physiological parameters including inlet and outlet pressure, flow rate, stenosis size, length and stiffness. The results suggest that high-grade stenotic arteries may exhibit collapse with typical physiological pressures. Critical stenoses may cause choking of flow at the throat followed by a transition to supercritical flow with tube collapse downstream. Greater amounts of stenosis produced a linear reduction of flow rate and a shortening of the collapsed region. Changes in stenosis length created proportional changes in the length of collapse. Increasing the stiffness of the stenosis to a value greater than the nominal tube stiffness caused a greater amount of flow limitation and more negative pressures, compared to a stenosis with constant stiffness. These findings assist in understanding the clinical consequences of flow through atherosclerotic arteries.
Red Blood Cell Motion and Hematocrit Distribution in a Deforming Capillary
Authors: Friend M. , Lee J. S.
Published: March 2008

Based on the relation between the red blood cell velocity and the blood velocity of the Fahraeus effect, we analyze the motion of a red blood cell in a deforming capillary to investigate how the ventilatory induced deformation affects the transit of the red blood cell through the pulmonary capillary and changes the hematocrit discharged from the capillary. An analytical solution is also obtained for the case of an infinitesimal deformation. The numerical and analytic solutions demonstrate that the variation in discharge hematocrit is proportional to the change of pulmonary capillary blood volume between the time that the red cell enters and the time that it exits the capillary. We also find that this hematocrit variation could be regarded, in terms of transport, to originate from the mid-section of the capillary.
First-Order Model for the Analysis of Stump Stresses for Below-Knee Amputees
Authors: Winarski D. J. , Pearson J. R.
Published: March 2008

This study extends what had been a purely numerical model that used influence-factor matrices to relate the stump stresses to prosthesis loads for unilateral, below/knee amputees. Previously published influence-factor matrices are now factored into a coefficient matrix times the inverse of a stump geometry matrix. Using actual stump parameters, new information is learned about how the resistive moment of the stump balances the flexion-extension moment of the prosthesis and why certain normal stresses reach a maximum during a specific portion of the stance phase of the prosthesis.
Hematopoiesis on Suspended Nylon Screen-Stromal Cell Microenvironments
Authors: Naughton B. A. , Tjota A. , Sibanda B. , Naughton G. K.
Published: March 2008

A three-dimensional culture system for the growth of primate and rodent bone marrow was developed in our laboratory. This method involves the seeding of stromal cells onto a nylon screen and the inoculation of fresh or cryopreserved bone marrow hematopoietic cells after stromal cell processes had extended across 3 to 4 out of every 5 mesh openings. Stromal cells attach, grow, and secrete matrix proteins which contribute to an intricate microenvironment for the support of multilineage hematopoiesis, which was observed for >270 days in the rat model and for >12 weeks in the human system, as evidenced by flow cytometry analysis and in vitro clonogenic assays. The adherent zones of these suspended nylon screen cultures consisted primarily of immature cells. These cultures could also be used as substrates for cytotoxicity measurements; treatment of rat bone marrow cultures of various ages with cytosine β-D arabinofuranoside, cyclophosphamide, 5-fluorouracil, or methotrexate resulted in a dose-dependent decrease in CFU-C numbers and altered the phenotypic distribution of hematologic cells in the adherent zone. The use of a modification of this method to generate large numbers of active cytolytic cells after >75 days culture of rat bone marrow-derived natural killer cells is described also. Suspended nylon screen bone marrow culture also has potential uses in genetic insertion and graft vs. host disease studies, blood component therapy, the evaluation of ex vivo purging programs, and in marrow expansion for transplantation.
Transplantation of Polymer Encapsulated Neurotransmitter Secreting Cells: Effect of the Encapsulation Technique
Authors: Aebischer P. , Winn S. R. , Tresco P. A. , Jaeger C. B. , Greene L. A.
Published: March 2008

Deficits associated with neurological diseases may be improved by the transplantation within the brain lesioned target structure of polymer encapsulated cells releasing the missing neurotransmitter. Surrounding cells with a permselective membrane of appropriate molecular weight cut-off allows inward diffusion of nutrients and outward diffusion of neurotransmitters, but prevents immunoglobulins or immune cells from reaching the transplant. This technique therefore allows transplantation of postmitotic cells across species. It also permits neural grafting of transformed cell lines since the polymer capsule prevents the formation of tumors by physically sequestering the transplanted tissue. In the present study, we compared the ability of dopaminesecreting cells, encapsulated by 2 different methods, to reverse experimental Parkinson’s disease, a neurodegenerative disease characterized by motor disturbances due to a lack of dopamine within the striatum following degeneration of the dopaminergic nigro-striatal pathway. PC12 cells were loaded in polyelectrolyte-based microcapsules or thermoplastic-based macrocapsules and maintained in vitro or transplanted in a rat experimental Parkinson model for 4 weeks. Chemically-induced depolarization increased the in vitro release of dopamine from macrocapsules over time, while no increase in release was observed from microcapsules. Encapsulated PC12 cells were able to reduce lesion-induced rotational asymmetry in rats for at least 4 weeks, regardless of the encapsulation technique used. With both encapsulation methods, PC12 cell viability was greater in vivo than in vitro which suggests that the striatum releases trophic factors for PC12 cells. More brain tissue damage was observed with microcapsules than macrocapsules, possibly the result of the difficulty of manipulating the more fragile microcapsules. Material resembling alginate was observed in the brain parenchyma surrounding the microcapsules, whereas no structural changes were observed with poly (acrylonitrile vinyl chloride) based capsules 4 weeks post-implantation. This fact raises questions about the in vivo stability of polyelectrolyte-based capsules implanted in the nervous system. We conclude that the implantation of polymer-encapsulated cells may provide a means for long-term delivery of neurotransmitters providing adequate encapsulation technology.
Recent Progress in Bone Induction by Osteogenin and Bone Morphogenetic Proteins: Challenges for Biomechanical and Tissue Engineering
Authors: Reddi A. H. , Cunningham N. S.
Published: March 2008

Implantation of demineralized bone matrix results in local bone induction. Bone induction is a sequential biological chain reaction that consists of chemotaxis and proliferation of mesenchymal cells and differentiation of bone. Osteogenin, a bone morphogenetic protein has been purified and the amino acid sequence determined. Recently a family of bone morphogenetic proteins have been cloned and expressed by recombinant DNA technology. The availability of growth and morphogenetic factors will permit the rational design of new bone. The challenge for the biomechanical engineer is to attain mechanically optimal and functionally adaptive new bone for various skeletal prostheses. We are on the threshold for fabrication of new bone based on sound architectural design principles of tissue engineering based on cellular and molecular biology of growth and differentiation factors.
Experimental Studies on Repair of Large Osteochondral Defects at a High Weight Bearing Area of the Knee Joint: A Tissue Engineering Study
Authors: Mow V. C. , Ratcliffe A. , Rosenwasser M. P. , Buckwalter J. A.
Published: March 2008

There is a vast clinical need for the development of an animal model to study the fundamentals of healing of injured or diseased diarthrodial joints (knee, hip, shoulder, wrist, etc). Current prosthetic replacements do not offer acceptable treatment for injuries and diseases of these joints in young active individuals. New clinical treatment modalities, based on sound biologic principles, are sought for the development of repair or healing tissues engineered to have similar biomechanical properties as normal articular cartilage. In this paper we present a brief review of this need, and propose a grafting procedure which may lead to a successful animal model for studies of long term repair of major osteochondral defects. This grafting procedure uses an autologous periosteum-bone graft or an autologous-synthetic bone replacement graft. We have applied these grafts for in vivo repair of large surgically created defects in the high weight bearing area of the distal femoral condyle of mature New Zealand white rabbits. Further, an interdisciplinary study, including histochemistry, biochemistry (composition and metabolic activities), and biomechanics (biphasic properties), was performed to assess the feasibility of our animal model to generate viable repair tissues. We found our grafting procedure produced, 8 weeks postoperatively, tissues which were very similar to those found in normal articular cartilage. However, our histological studies indicate incomplete bonding between the repair tissue and the adjacent cartilage, and lack of an appropriate superficial zone at the articular surface. These deficiencies may cause long term failure of the repair tissue. Further studies must be undertaken to enhance development of a strong bond and a collagen-rich surface zone. This may require the use of growth factors (e.g., transforming growth factors β) capable of simulating extra collagen production, or the use of serum derived tissue glue for bonding. At present, we are pursuing these studies.
Estimating Three-Dimensional Temperature Fields During Hyperthermia: Studies of the Optimal Regularization Parameter and Time Sampling Period
Authors: Liauh C.-T. , Clegg S. T. , Roemer R. B.
Published: March 2008

During hyperthermia therapy it is desirable to know the entire temperature field in the treatment region. However, accurately inferring this field from the limited number of temperature measurements available is very difficult, and thus state and parameter estimation methods have been used to attempt to solve this inherently ill-posed problem. To compensate for this ill-posedness and to improve the accuracy of this method, Tikhonov regularization of order zero has been used to significantly improve the results of the estimation procedure. It is also shown that the accuracies of the temperature estimates depend upon the value of the regularization parameter, which has an optimal value that is dependent on the perfusion pattern and magnitude. In addition, the transient power-off time sampling period (i.e., the length of time over which transient data is collected and used) influences the accuracy of the estimates, and an optimal sampling period is shown to exist. The effects of additive measurement noise are also investigated, as are the effects of the initial guess of the perfusion values, and the effects of both symmetric and asymmetric blood perfusion patterns. Random perfusion patterns with noisy data are the most difficult cases to evaluate. The cases studied are not a comprehensive set, but continue to show the feasibility of using state and parameter estimation methods to reconstruct the entire temperature field.
Finite Element Stress Analysis of a Push-Out Test Part II: Free Interface With Nonlinear Friction Properties
Authors: Shirazi-Adl A. , Forcione A.
Published: March 2008

In this second part of a two-part paper, nonlinear frictional properties measured at the bone/porous-surfaced metal interface are used to perform the stress analysis of a push-out test assuming free interface. In this case, the friction at the interface is the only mechanism to resist the externally applied load. Similar to the part I, the model is axisymmetric and consists of two cylinders in contact with each other through the interface. Various relative material properties and boundary conditions are simulated in order to examine their effects on the interface stresses and overall push-out resistance. The role of the force-fit and the load direction (push-out versus pull-out) on the results is also investigated. The computed radial and shear stresses are found to markedly vary both with location along the interface and with the testing configuration. The ultimate push-out resistance is also found to significantly alter as the material arrangement and boundary conditions change. The predicted push-out load augments with an increase in the force-fit and diminishes to nil in the absence of a press-fit. For the cases studied here, there is a relative difference of as large as 13 percent between the push-out response and the pull-out response so far as the interface stresses and the maximum resistance are concerned. Therefore, any comparison between the results of push-out (or pull-out) tests performed with different design configurations appears to be invalid.
Theoretical Analysis of an Implantable Force Transducer for Tendon and Ligament Structures
Authors: Xu W. S. , Butler D. L. , Stouffer D. C. , Grood E. S. , Glos D. L.
Published: March 2008

A mathematical model was developed for an implantable force transducer to be inserted within the midsubstance of a ligament or tendon. The model was generated by performing both equilibrium and strain-displacement analyses on a metallic, curved beam structure placed within a parallel-fibered tissue. The analysis permitted the transverse pressure acting between the device and fibers to be calculated along with peak device strain and sensitivity (ratio of strain output to axial tissue force). Transducer pressure and transducer strain were expressed in terms of nondimensionalized design factors. A parametric analysis of the key design factors was then performed. The transverse pressure was shown to vary little for large changes in these factors whereas device strain changed markedly. The analysis was verified by a bench test on an example device. Such a model permits a proposed design to be evaluated without having to conduct costly experiments.
Influence of Bifurcations on Forced Oscillations in an Airway Model
Authors: Bunk D. A. , Federspiel W. J. , Jackson A. C.
Published: March 2008

Forced oscillations is a technique to determine respiratory input impedance from small amplitude sinusoidal pressure excursions introduced at the airway opening. Models used to predict respiratory input impedance typically ignore the direct effect of bifurcations on the flow, and treat airway branches as individual straight tubes placed appropriately in parallel and series. The flow within the individual tubes is assumed equivalent to that which would occur in infinitely long tubes. In this study we examined the influence of bifurcations on impedance for conditions of the forced oscillatory technique. We measured input impedance using forced oscillations in straight tubes and in an anatomically-relevant, four generation physical model of a human airway network. The input impedance measured experimentally compared well to that obtained theoretically using model predictions. The predictive scheme was based on appropriate parallel and series combinations of theoretically computed individual tube impedances, which were computed from solutions to oscillatory flow of a compressible gas in an infinitely long rigid tube. The agreement between experimental measurements and predictions indicates that bifurcations play a relatively minor direct role on the flow impedance for conditions of the forced oscillations technique. These results are explained in terms of the small tidal volumes used, whereby the axial distance traveled by a fluid particle during an oscillation cycle is appreciably smaller than branch segment lengths. Accordingly, only a small fraction of fluid particles travel through the bifurcation region, and the remainder experience an environment approaching flow in an infinite straight tube. The relevance of the study to the prediction of impedances in the human lung during forced oscillations is discussed.
A Lumped Parameter Mathematical Model of the Splanchnic Circulation
Authors: Chu Tai-Ming , Reddy Narender P.
Published: March 2008

A lumped parameter mathematical model to describe the propulsion of blood in the splanchnic circulation was developed by integrating the principles of mechanics and physiology. A set of governing equations by derived by specifically considering the contractility of the portal vein, hepatic vein, liver sinusoids, and of the draining lymphatics. These equations were then simulated on a computer. The present simulation results substantiate previous experimental observations that hepatic venous pressure leads to portal hypertension and increased liver interstitial fluid volume.
The Distribution of Fluid Forces on Model Arterial Endothelium Using Computational Fluid Dynamics
Authors: Satcher R. L. , Bussolari S. R. , Gimbrone M. A. , Dewey C. F.
Published: March 2008

Numerical calculations are used in conjunction with linear perturbation theory to analyze the problem of laminar flow of an incompressible fluid over a wavy surface which approximates a monolayer of vascular endothelial cells. These calculations model flow conditions in an artery very near the vessel wall at any instant in time, providing a description of the velocity field with detail that would be difficult to identify experimentally. The surface pressure and shear stress distributions are qualitatively similar for linear theory and numerical computations. However, the results diverge as the amplitude of surface undulation is increased. The shear stress gradient along the cell model surface is reduced for geometries which correspond to aligned endothelial cells (versus nonaligned geometries).
Effects of Arterial Compliance and Non-Newtonian Rheology on Correlations Between Intimal Thickness and Wall Shear
Authors: Friedman M. H. , Bargeron C. B. , Duncan D. D. , Hutchins G. M. , Mark F. F.
Published: March 2008

A minimally diseased (mean intimal thickness = 56 μm) human aortic bifurcation was replicated in rigid and compliant flow-through casts. Both casts were perfused with physiological flow waves having the same Reynolds and unsteadiness numbers; the pulse pressure in the compliant cast produced radial strains similar to those expected from post-mortem measurements of the compliance of the original tissue. The compliant cast was perfused with a Newtonian fluid and one whose rheology was closer to that of blood. Wall shear rate histories were estimated from near-wall velocities obtained by laser Doppler velocimetry at identical sites in both casts. Intimal thickness was measured at corresponding sites in the original vessel and linear regressions were performed between these thicknesses and several normalized shear rate measures obtained from the histories. The correlations showed a positive slope—that is, the intima was thicker at sites exposed to higher shear rates—consistent with earlier results for relatively healthy vessels, but their significance was often poor. There was no significant effect of either model compliance or fluid rheology on the slopes of the correlations of intimal thickness against any normalized shear rate measure.
Mechanical Properties of the Rabbit Patellar Tendon
Authors: Yamamoto N. , Hayashi K. , Kuriyama H. , Ohno K. , Yasuda K. , Kaneda K.
Published: March 2008

The mechanical and structural properties of the patellar tendon fascicle-bone units of rabbit knees were determined by tensile tests, particularly focusing on their local differences. There were no significant differences in the strains measured by a video dimension analyzer among the proximal, middle, and distal regions of the central portion of tendon. The mechanical properties of the medial portion agreed well with those of the central portion. However, significant differences were observed in the tensile strength between the lateral and the other two portions: the tensile strength of the lateral portion was about 16 percent larger than those in the other portions.
Contact Stress Gradient Detection Limits of Pressensor Film
Authors: Hale J. E. , Brown T. D.
Published: March 2008

Fuji Pressensor film has been widely used for measurement of contact stresses in articular joints. In relatively smooth contact fields, measurement errors are reported to be in the range of approximately 10-15 percent. However, when local incongruities exist, strong contact stress gradients are present. This study investigates the film’s capability to accurately transduce such gradients. Standardized stress distributions were produced by compressing the film between a rigid cylinder and an elastic layer supported by a rigid substrate. Seven different cylinder radii were used to obtain a range of gradient magnitudes. The resulting stains were digitized, and the contact stress gradients assessed by image analysis. Experimentally detected gradients were compared with those predicted analytically. The film’s capability to reliably transduce contact stress gradients was shown to be sufficient for usage in the study of typical local articular incongruities.
Adaptive Control of Above Knee Electro-Hydraulic Prosthesis
Authors: Wang T. K. , Ju M. S. , Tsuei Y. G.
Published: March 2008

Conventional designs of an above-knee prosthesis are based on mechanisms with mechanical properties (such as friction, spring and damping coefficients) that remain constant during changing cadence. These designs are unable to replace natural legs due to the lack of active knee joint control. Since the nonlinear and time-varying dynamic coupling between the thigh and the prosthetic limb is high during swing phase, an adaptive control is employed to control the knee joint motion. Two dimensional simulation indicates that the adaptive controller can improve the appearance of gait pattern. It is adaptable to walking speed and can compensate for the variations of hip moment, hip trajectory and toe-off conditions.
A Mathematical Description of Pressures in Alveolar Pores of Kohn
Authors: Lu De-fu , Stanley Charles , Nunez German , Frazer David
Published: March 2008

Small interalveolar holes within the lung are called pores of Kohn. Some researchers have correlated enlarged pore size with diseases, e.g. emphysema, that are characterized by tissue destruction. Mathematical models of the pressures generated in closed, fluid-filled and open, fluid-lined pores demonstrate that pressures capable of rupturing lung tissue can be developed in a pore due to the surface tension and shape of the air-liquid interface. Pore enlargement accompanied by tissue destruction is presented as a possible mechanism for the disease process observed during aging and the development of emphysema in the lung.
Subcritical Flutter in Collapsible Tube Flow: A Model of Expiratory Flow in the Trachea
Authors: Walsh C. , Sullivan P. A. , Hansen J. S.
Published: March 2008

Using an axisymmetric geometry that retains certain qualitative features of the trachea, we extend one-dimensional modeling of flow in collapsible tubes to include both curved shell effects and, for untethered tubes, wall inertia. A systematic scaling of the finite deformation membrane equations leads to an approximate set which is consistent with the one-dimensional fluid model; axial and normal wall variables are coupled elastically, but only axial inertia is retained. Transverse curvature causes elastic coupling that can give rise to axial wall motion and a flutter instability. The source of instability is the product of a nonzero reference axial curvature with axial tension variation due to axial stretching. The numerical results suggest that this mechanism may be significant even in processes which cannot be assumed one-dimensional.
The Effects of Layer Properties on Shear Disturbance Propagation in Skin
Authors: Pereira J. M. , Mansour J. M. , Davis B. R.
Published: March 2008

The effects of the stratum corneum and dermis on shear wave propagation along the skin surface was investigated using a mathematical model. The skin was modeled as two distinct viscoelastic layers, one representing the stratum corneum and the other representing the dermis. The layers were supported by a semi-infinite viscoelastic half-space representing the subcutaneous fat. Physical and mechanical properties of the materials in the model were determined from the literature and from our own experimental measurements. Although the stratum corneum is very thin (12-15 microns), results showed that it could have a strong effect on the wave propagation due to its high stiffness relative to the dermis. Results of the analysis are discussed with respect to an experimental procedure used to determine age-related changes in mechanical properties of skin.
A Continuum Model of Elephant Trunks
Authors: Wilson J. F. , Mahajan U. , Wainwright S. A. , Croner L. J.
Published: March 2008

A continuum model is presented that relates the trunk parameters of loading, geometry, and muscle structure to the necessary conditions of static equilibrium. Linear theory for stress-strain behavior is used to describe an elephant trunk for an incremental displacement as the animal slowly lifts a weight at the trunk tip. With this analysis and experimental values for the trunk parameters, the apparent trunk stiffness Ea is estimated for the living animal. For an Asian elephant with a maximum compression strain of 33 percent, Ea is of the order of 106 N/m2. The continuum model is quite general and may be applied to similar nonskeletal appendages and bodies of other animals.
Cardiac Mechanics in the Stage-16 Chick Embryo
Authors: Taber L. A. , Keller B. B. , Clark E. B.
Published: March 2008

A theoretical model is presented for the tubular heart of the stage-16 chick embryo (2.3 days of a 21-day incubation period). The model is a thick-walled, pseudoelastic cylindrical shell composed of three isotropic layers: the endocardium, the cardiac jelly, and the myocardium. The analysis is based on a shell theory that accounts for large deformation, material nonlinearity, residual strain, and muscle activation, with material properties inferred from available experimental data. We also measured epicardial strains from recorded motions of microspheres on the primitive right ventricles of stage-16 white Leghorn chick embryos. Relative to end diastole, peak axial and circumferential Lagrange strains occurred near end systole and had similar values. The magnitudes of these strains varied along the longitudinal axis of the heart (-0.16 ± 0.08), being larger near the ends of the primitive right ventricle and smaller near midventricle. The in-plane shear strain was less than 0.05. Comparison of theoretical and experimental strains during the cardiac cycle shows generally good agreement. In addition, the model gives strong stress concentrations in the myocardial layer at end systole.
Estimation of Organ Transport Function: Model-Free Deconvolution by Recursive Quadratic Programming Optimization
Authors: Li Zheng , Lieber Baruch B.
Published: March 2008

A model-free deconvolution method is proposed for evaluating the frequency distribution function of organ transit times. The deconvolution is treated as a nonlinear constrained optimization problem and it is solved by using a modified constrained variable metric approach. The only constraint implemented in the solution is that all the discrete transport function values are not allowed to become negative. The method is tested on model mathematical systems of known analytical transport functions. The tests are performed on systems that included noise in both the input and output functions. The criteria of successful deconvolution are the reconvolution error and, most importantly, the deviation of the computed transport function from the known analytical one. The proposed method is then applied, as a pilot experiment, to biological data obtained from an isolated, perfused rabbit lung preparation contained within a plethysmograph. The results indicate that this type of deconvolution produces stable estimates which faithfully follow the analytical function while negating the need to assume either any functional form for the behavior of the transport function or any educated initial guess of its values.
Non-Newtonian Flow Patterns Associated With an Arterial Stenosis
Authors: Luo X. Y. , Kuang Z. B.
Published: March 2008

A non-Newtonian constitutive equation for blood has been introduced in this paper. Using this equation, blood flow attributes such as velocity profiles, flowrate, pressure gradient, and wall shear stress in both straight and stenotic (constricted) tubes have been examined. Results showed that compared with Newtonian flow at the same flowrate, the non-Newtonian normally features larger pressure gradient, higher wall shear stress, and different velocity profile, especially in stenotic tube. In addition, the non-Newtonian stenotic flow appears to be more stable than Newtonian flow.
In Vivo Measurement of Leukocyte Viscosity During Capillary Plugging
Authors: Warnke K. C. , Skalak T. C.
Published: March 2008

Leukocyte plugging of capillaries in vivo was measured in rat spinotrapezius muscle. The plug durations, leukocyte and capillary dimensions, and arteriolar pressure at the plug sites were applied to the mechanical model of Needham and Hochmuth (1990) to estimate the leukocyte viscosities. The viscosity distribution of 389 cells was lognormal with a median value of 232 Poise. 3.1 percent of the cells were apparently activated and displayed viscosities greater than 3000 Poise. The median viscosity suggests that inactivated leukocytes have a minimal effect on blood flow, but that leukocyte activation may result in significant increases in microvascular flow resistance.
The Variation of Isometric Energy Rates With Muscle Length: A Distribution-Moment Model Analysis
Authors: Rouhaud E. , Zahalak G. I.
Published: March 2008

The Distribution-Moment Model of skeletal muscle, which has been enhanced recently to make possible the calculation of chemical energy release (E˙) and heat production (H˙) rates [1], is applied to isometric muscle. Under steady-state isometric conditions the model predicts a simple relation between the energy rates and the muscle length, namely (E/˙E˙max)=(H/˙H˙max)=[1+Bα(Λ)]/[1+B], where Λ is the ratio of muscle length to the “optimal” length at which maximal isometric tension is produced, and α(Λ) is a function numerically equal to the ratio of the tetanic isometric force to its maximum value. The single dimensionless constant in this relation, B, can be calculated from model parameters characterizing muscle dynamics at the optimum length, and has a value near unity for frog sartorius at 0°C. The predicted behavior is shown to agree reasonably well with experimental measurements of heat production and phosphocreatine (PCr) hydrolysis. The model relates the isometric energy rates to PCr hydrolysis in (1) cross-bridge interactions, and (2) calcium pumping into the sarcoplasmic reticulum.
Pressure Propagation in Pulsatile Flow Through Random Microvascular Networks
Authors: He X. S. , Georgiadis J. G.
Published: March 2008

A microvascular network with random dimensions of vessels is built on the basis of statistical analysis of conjuctival beds reported in the literature. Our objective is to develop a direct method of evaluating the statistics of the pulsatile hydrodynamic field starting from a priori statistics which mimic the large-scale heterogeneity of the network. The model consists of a symmetric diverging-converging dentritic network of ten levels of vessels, each level described by a truncated Gaussian distribution of vessel diameters and lengths. In each vascular segment, the pressure distribution is given by a diffusion equation with random parameters, while the blood flow rate depends linearly on the pressure gradient. The results are presented in terms of the mean value and standard deviation of the pressure and flow rate waveforms at two positions along the network. It is shown that the assumed statistical variation of vessel lengths results in flow rate deviations as high as 50 percent of the mean, while the corresponding effect of vessel diameter variation is much smaller. For a given pressure drop, the statistical variation of lengths increases the mean flow while the effect on the mean pressure distribution is negligible.
Sternal Force-Displacement Relationship During Cardiopulmonary Resuscitation
Authors: Gruben K. G. , Guerci A. D. , Halperin H. R. , Popel A. S. , Tsitlik J. E.
Published: March 2008

A viscoelastic model is presented to describe the dynamic response of the human chest to cyclic loading during manual cardiopulmonary resuscitation (CPR). Sternal force and displacement were measured during 16 clinical resuscitation attempts and during compressions on five CPR training manikins. The model was developed to describe the clinical data and consists of the parallel combination of a spring and dashpot. The human chests’ elastic and damping properties were both augmented with increasing displacement. The manikins’ elastic properties were stiffer and both elastic and damping properties were less dependent on displacement than the humans’.
A Time Delay Controller for Systems With Unknown Dynamics
Authors: Youcef-Toumi Kamal , Ito Osamu
Published: March 2008

This paper focuses on the control of systems with unknown dynamics and deals with the class of systems described by x˙=f(x,t) + h(x,t) + B(x,t)u + d(t) where h(x,t) and d(t) are unknown dynamics and unexpected disturbances, respectively. A new control method, Time Delay Control (TDC), is proposed for such systems. Under the assumption of accessibility to all the state variables and estimates of their delayed derivatives, the TDC is characterized by a simple estimation technique that evaluates a function representing the effect of uncertainties. This is accomplished using time delay. The control system’s structure, stability and design issues are discussed for linear time-invariant and single-input-single-output systems. Finally, the control performance was evaluated through both simulations and experiments. The theoretical and experimental results indicate that this control method shows excellent robustness properties to unknown dynamics and disturbances.
Control of Linear Systems by Output Proportional Plus Derivative Feedback
Authors: Haraldsdottir A. , Kabamba P. T. , Ulsoy A. G.
Published: March 2008

This paper presents a design procedure for linear time invariant systems using output proportional plus derivative feedback. The derivative feedback is shown to improve the controller performance in the presence of parameter variations and disturbance inputs, at the cost of increased noise response. A quadratic performance index, with the addition of terms to penalize disturbance and noise response and eigenvalue and response sensitivity, is used as the basis for a design method. The proposed method is a generalization of one presented previously for the case of perfect state and state derivative feedback. The method is illlustrated on a simple first order example and on the design of a controller for the lateral dynamnics of an L1011 aircraft. The results indicate that improved performance is obtained through the addition of perfect output derivative feedback, however, much of that improvement is lost when approximate differentiation is used.
A Triphasic Theory for the Swelling and Deformation Behaviors of Articular Cartilage
Authors: Lai W. M. , Hou J. S. , Mow V. C.
Published: March 2008

Swelling of articular cartilage depends on its fixed charge density and distribution, the stiffness of its collagen-proteoglycan matrix, and the ion concentrations in the interstitium. A theory for a tertiary mixture has been developed, including the two fluid-solid phases (biphasic), and an ion phase, representing cation and anion of a single salt, to describe the deformation and stress fields for cartilage under chemical and/or mechanical loads. This triphasic theory combines the physico-chemical theory for ionic and polyionic (proteoglycan) solutions with the biphasic theory for cartilage. The present model assumes the fixed charge groups to remain unchanged, and that the counter-ions are the cations of a single salt of the bathing solution. The momentum equation for the neutral salt and for the intersitial water are expressed in terms of their chemical potentials whose gradients are the driving forces for their movements. These chemical potentials depend on fluid pressure p, salt concentration c, solid matrix dilatation e and fixed charge density cF. For a uni-uni valent salt such as NaCl, they are given by μi = μoi + (RT/Mi)ln[γ±2c (c + c F)] and μW = μow + [p − RTφ(2c + cF) + Bwe]/ρTw, where R, T, Mi, γ±, φ, ρTw and Bw are universal gas constant, absolute temperature, molecular weight, mean activity coefficient of salt, osmotic coefficient, true density of water, and a coupling material coefficient, respectively. For infinitesimal strains and material isotropy, the stress-strain relationship for the total mixture stress is σ = − pI − TcI + λs(trE)I + 2μsE, where E is the strain tensor and (λs,μs) are the Lame´ constants of the elastic solid matrix. The chemical-expansion stress (− Tc) derives from the charge-to-charge repulsive forces within the solid matrix. This theory can be applied to both equilibrium and non-equilibrium problems. For equilibrium free swelling problems, the theory yields the well known Donnan equilibrium ion distribution and osmotic pressure equations, along with an analytical expression for the “pre-stress” in the solid matrix. For the confined-compression swelling problem, it predicts that the applied compressive stress is shared by three load support mechanisms: 1) the Donnan osmotic pressure; 2) the chemical-expansion stress; and 3) the solid matrix elastic stress. Numerical calculations have been made, based on a set of equilibrium free-swelling and confined-compression data, to assess the relative contribution of each mechanism to load support. Our results show that all three mechanisms are important in determining the overall compressive stiffness of cartilage.
Ligament-Bone Interaction in a Three-Dimensional Model of the Knee
Authors: Blankevoort L. , Huiskes R.
Published: March 2008

In mathematical knee-joint models, the ligaments are usually represented by straightline elements, connecting the insertions of the femur and tibia. Such a model may not be valid if a ligament is bent in its course over bony surfaces, particularly not if the resulting redirection of the ligament force has a considerable effect on the laxity or motion characteristics of the knee-joint model. In the present study, a model for wrapping of a ligament around bone was incorporated in a three-dimensional mathematical model of the human knee. The bony edge was described by a curved line on which the contact point of the line element representing a ligament bundle was located. Frictionless contact between the ligament bundle and the bone was assumed. This model was applied to the medial collateral ligament (MCL) interacting with the bony edge of the tibia. It was found that, in comparison with the original model without bony interactions, the bony edge redirected the ligament force of the MCL in such a way that it counterbalanced valgus moments on the tibia more effectively. The effect of the bony interaction with the MCL on the internal-external rotation laxity, however, was negligible.