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RESEARCH PAPERS

J Biomech Eng. 1993;115(3):211-217. doi:10.1115/1.2895477.

Robotics technologies have been modified to control and measure both the force and position of synovial joints for the study of joint kinematics. One such system was developed to perform kinematic testing of a human joint. A 6-axis articulated robotic manipulator with 6 degrees of freedom (DOF) of motion was designed and constructed; a mathematical description for joint force and position was devised; and hardware and software to control forces applied to the joint, as well as position of the joint, were developed. The new methodology was utilized to simulate physiological loading conditions and to perform an anterior-posterior (A-P) translation test on a human cadaveric knee. Testing showed that this new system can simulate complex loading conditions and also measure the resulting joint kinematics.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1993;115(3):218-224. doi:10.1115/1.2895478.

A new technique has been devised for measuring the in situ tension in small ligaments. It is based on measuring the tension in an axially loaded flexible cable with pinned endpoints by deflecting the cable laterally and measuring its lateral load and deformation. Studies were performed in which nylon line and bone ligament bone preparations were placed in a materials tester and loaded in axial tension. Axial load as measured by lateral load and deformation was found to agree with the known load to within 8 percent. The method was sensitive to error in determination of ligament length, nonperpendicularity of the laterally applied load to the long axis of the ligament, and when used in situ, impingement of the ligament on a third bone causing bending. A device, consisting of an LVDT mounted to a rigid frame with its core rod connected to a load cell, was developed. The position of the core rod was controlled by a manual screw drive, and a hook on the other end of the core rod was used to deflect the ligament laterally. This device was applied to the study of tensions in five ligaments of the palmar wrist carpus, in seven cadaver specimens. Results showed that the radioscaphocapitate (RSC) and radiolunate (RL) ligaments had significantly greater tensions than the lunotriquetral (LT), the triquetrocapitate (TC), and scaphocapitate (SC) ligaments. For the four positions of the hand tested, neutral, 14 deg radial and 14 deg ulnar deviation, and 28 deg of extension, ligament tensions were found to be unaffected by position. In all positions tested, all ligaments had measurable tension, demonstrating the importance of ligaments in maintaining the integrity of the wrist carpus.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1993;115(3):225-230. doi:10.1115/1.2895479.

Strain was measured along the length of frog (Rana pipiens) gastrocnemius muscle-tendon units (MTU). Maximum muscle tension (P0 ) was measured, and the MTU was passively loaded to P0 . Strain at P0 was measured at eight intervals along the tendon and aponeurosis and was approximately two percent for all regions except the aponeurosis region closest to the muscle fibers where it was about six percent. A computer model predicted sarcomere shortening of up to 0.5 μm due to tendon lengthening which demonstrates that tendons provide a more complex physiological function than simply transmitting muscle force to bones.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1993;115(3):231-238. doi:10.1115/1.2895480.

A mathematical analysis of ocular pneumoplethysmography is presented, based on the physiological, anatomical, and biomechanical properties of the eye. Ocular pneumoplethysmography is a clinical procedure involving elevation of intraocular pressure, by application of a suction cup to the sclera, to a level that exceeds ophthalmic artery systolic pressure. As decay in intraocular pressure is allowed, return of retinal artery pulsations indicates ophthalmic artery systolic pressure. We obtain a quantitative relationship between increase in intraocular pressure and applied vacuum, and compare the theoretical predictions with experiments on rabbits in which a variable descending vacuum was applied to bilateral scleral eyecups. The bilateral intraocular pressures were simultaneously recorded from cannulae in the respective vitreous bodies, and the pressures at which return of ocular pulsations were observed were correlated with the scleral vacuums. Regression lines were calculated for three serial determinations in each animal, with two groups of animals distinguished by the inner diameter of the eyecups used. The theoretical results indicate that the relationship between intraocular pressure increase and applied vacuum is independent of Young’s modulus, and depends primarily on the ratio of the diameter of the vacuum cup to the diameter of the eye.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1993;115(3):239-246. doi:10.1115/1.2895481.

Using one-, two-, and three-dimensional numerical simulation models it is shown that multiple minima solutions exist for some inverse hyperthermia temperature estimation problems. This is a new observation that has important implications for all potential applications of these inverse techniques. The general conditions under which these multiple minima occur are shown to be solely due to the existence of symmetries in the bio-heat transfer model used to solve the inverse problem. General rules for determining the number of these global minimum points in the unknown parameter (perfusion) space are obtained for several geometrically symmetric (with respect to the sensor placement and the inverse case blood perfusion model) one-, two- and three-dimensional problem formulations with multiple perfusion regions when no model mismatch is present. As the amount of this symmetry is successively reduced, all but one of these global minima caused by symmetry become local minima. A general approach for (a) detecting when the inverse algorithm has converged to a local minimum, and (b) for using that knowledge to direct the search algorithm toward the global minimum is presented. A three-dimensional, random perfusion distribution example is given which illustrates the effects of the multiple minima on the performance of a state and parameter estimation algorithm. This algorithm attempts to reconstruct the entire temperature field during simulated hyperthermia treatments based on knowledge of measured temperatures from a limited number of locations.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1993;115(3):247-253. doi:10.1115/1.2895482.

Dual beam microwave heating is known to deposit heat at depth in a medium. Thus transient heating times may be reduced and more even heating may be obtained. Such a system has potential in the treatment of cancer by hyperthermia. A theoretical analysis of this situation is presented here. A simulation has been made of the thermal fields generated in the treatment of malignant tumors using local hyperthermia. The simulation utilizes the alternating direction implicit method which is particularly suited to the solution of the governing equations, and provides rapid convergence in multiple dimensions. The simulation is three dimensional in temperature, with variations occurring through two spatial coordinates and one time coordinate. The simulation can accommodate the transient flow of heat due to conductive heat transfer through tissues such as healthy tissue, malignant tumors, cartilage and bone, convective heat transfer through perfusion in the tissue and flow through the arteries, and heat generation from sources such as microwave beams. Small changes in the thermophysical properties of the tissue, and the blood perfusion rates are shown to exhibit only minor effects on the thermal fields, whereas the power of the heat sources, and the conductive flux are shown to have major effects on the thermal fields. The effects of adjacent physiological structures such as arteries and bones have also been determined. The temperature fields have been found to be weakly dependent on the increased perfusion rates encountered in the arteries except when the perfusion rate in the artery exceeds that in the tissue by at least one order of magnitude. A similar effect is noticed if the tumor is close to a bone. The greater thermal insulation exhibited by the bone restricts the flow of heat into it, and therefore causes the tissue to increase in temperature. Once the transient heating has been employed and the heating proceeds under steady-state conditions, the dual beam microwave applicator must be controlled to avoid overheating. The effect of on/off control and proportional + integral + derivative control is discussed.

Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J Biomech Eng. 1993;115(3):257-261. doi:10.1115/1.2895484.

An improved state and parameter estimation algorithm has been developed which decreases the total computational time required to accurately reconstruct complete hyperthermia temperature fields. Within this improved iterative estimation algorithm, if the change in the unknown perfusion parameters is small a linear approximation scheme is implemented in which the old Jacobian matrix (the sensitivity matrix) is used, instead of recalculating the new Jacobian matrix for the next iteration. In the hyperthermia temperature estimation problem the relationship between the temperature and the blood perfusion based on the bioheat transfer equation is generally nonlinear. However, the temperature can be approximated as a linear function of the blood perfusion over a certain range thus allowing this improved approach to work. Results show that if the temperature is approximated as a linear (or quasi-linear) function of the blood perfusion, the linearizing approach considerably reduces the CPU time required to accurately reconstruct the temperature field. The limiting case of implementing this approach is to calculate the Jacobian matrix for each iteration, which is identical to the approach used in the original nonlinear algorithm. Critical values of determining whether or not there is a need to recalculate the new Jacobian matrix during the iterations are presented for several inverse hyperthermia temperature estimation problems.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1993;115(3):262-270. doi:10.1115/1.2895485.

The respiratory tract of mammals is lined with a layer of mucus, described as viscoelastic semi-solid, above a layer of watery serous fluid. The interaction of these compliant layers with pulmonary airflow plays a major role in lung clearance by two-phase gas-liquid flow and in increased flow resistance in patients with obstructive airway diseases such as cystic fibrosis, chronic bronchitis and asthma. Experiments have shown that such coupled systems of flow-compliant-layers are quite susceptible to sudden shear instabilities, leading to formation of relatively large amplitude waves at the interface. Although these waves enhance the lung clearance by mobilizing the secretions, they increase the flow resistance in airways. The objective of this paper is to understand the basic interaction mechanism between the two media better by studying airflow through a rigid pipe that is lined by a compliant layer. The mathematical model that has been developed for this purpose is capable of explaining some of the published experimental observations. Wave instability theory is applied to the coupled air-mucus system to explore the stability of the interface. The results show that the onset flow speed for the initiation of unstable surface waves, and the resulting wavelength, are both very sensitive to mucus thickness. The model predicts that the instabilities initiate in the form of propagating waves for the elastic mucus where the wave speed is about 40 percent of the flow speed. The wavelength and phase speed to air velocity ratio are shown to increase with increasing mucus thickness. Also, results show that the mucus viscosity causes the onset air velocity to increase and the wave speed to decrease. The predictions of the model for the viscoelastic case are in good qualitative and quantitative agreement with some of the published experimental observations.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1993;115(3):271-277. doi:10.1115/1.2895486.

A theoretical analysis is presented predicting the closure of small airways in the region of the terminal and respiratory bronchioles. The airways are modelled as thin elastic tubes, coated on the inside with a thin viscous liquid lining. This model produces closure by a coupled capillary-elastic instability leading to liquid bridge formation, wall collapse or a combination of both. Nonlinear evolution equations for the film thickness, wall position and surfactant concentration are derived using an extended version of lubrication theory for thin liquid films. The positions of the air-liquid and wall-liquid interfaces and the surfactant concentration are perturbed about uniform states and the stability of these perturbations is examined by solving the governing equations numerically. Solutions show that there is a critical film thickness, dependent on fluid, wall and surfactant properties above which liquid bridges form. The critical film thickness, εc , decreases with increasing mean surface-tension or wall compliance. Surfactant increases εc by as much as 60 percent for physiological conditions, consistent with physiological observations. Airway closure occurs more rapidly with increasing film thickness and wall flexibility. The closure time for a surfactant rich interface can be approximately five times greater than an interface free of surfactant.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1993;115(3):278-285. doi:10.1115/1.2895487.

This report deals with noninvasive imaging of airway geometry based upon information contained in acoustic reflections measured at the mouth. Here we describe a new theoretical approach that enables development of a new miniaturized apparatus. Unlike the single-transducer systems used currently, this new strategy is based upon a two-transducer system that is a variant of that suggested originally by Shroeder (1967). We have developed, implemented, and tested computational algorithms necessary to reconstruct airway dimensions from acoustic reflection data using this two-transducer strategy.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1993;115(3):286-289. doi:10.1115/1.2895488.

Although vasomotor activity in small pulmonary vessels has been studied extensively in the past, using the concept of resistance to flow, information on the distensibility of these vessels is very sparse. In an attempt to reduce this deficit, we adapted a theoretical method developed for small systemic vessels, to estimate distensibility of pulmonary resistance vessels in experimental animals and man. Pressure-flow data from 11 dogs and 10 human subjects (5 control subjects and 5 patients with long-standing left heart failure) were used to calculate distensibility of small pulmonary vessels. The conductance, G, was calculated from these data as the ratio of blood flow to driving pressure. The slope of the relationship between the logarithm of G1/4 and the average distending pressure (ADP) provides a graphic picture of circumferential extensibility, E, defined as percent change in radius for an infinitesimal change in ADP. Results indicate that: (1) the value of E in dogs was 1.85 ± .40 mmHg−1 for the control state, which decreased to 1.45 ± .43 mmHg−1 during norepinephrine administration; however, the decrease in the value was not statistically significant (p = 0.53); (2) the value of E in control human subjects was 3.38 ± .47 mmHg−1 and the value of E in patients with left heart failure was −0.64 ± 0.39 mmHg−1 ; the difference was significant (P = .0001). Moreover, at a given ADP in the range of overlapping pressures, the “average” radius of small pulmonary vessels in patients with left heart failure was smaller than that in the control subjects; and (3) small pulmonary vessels were more distensible than both the small systemic vessels and the large pulmonary arteries.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1993;115(3):290-298. doi:10.1115/1.2895489.

An experimental investigation was conducted in steady flow to examine the fluid dynamics performance of three prosthetic heart valves of 27 mm diameter: Starr-Edwards caged ball valve, Bjork-Shiley convexo-concave tilting disk valve, and St. Vincent tilting disk valve. It was found that the pressure loss across the St. Vincent valve is the least and is, in general, about 70 percent of that of the Starr-Edwards valve. The pressure recovery is completed about 4 diameters downstream. The velocity profiles for the ball valve reveal a large single reversed flow region behind the occluder while those for the tilting disks valves reveal two reversed flow regions immediately behind the occluders. Small regions of stasis are also found near the wall in the minor opening of Bjork-Shiley valve and in the major opening of St. Vincent valve. The maximum wall shear stresses of the three valves at a flow rate of 30 l/min are in the range 30–50 dyn/cm2 which can cause hemolysis of attached red blood cells. The corresponding maximum Reynolds normal stresses are in the range of 1600–3100 dyn/cm2 . The Reynolds normal stresses decay quickly and return approximately to the upstream undisturbed level at about 4 diameters downstream while the wall shear stresses decay at a slower rate. The maximum Reynolds normal stresses occur at about 1 diameter downstream while the maximum wall shear stress is at about 2 diameters downstream. In general, the St. Vincent valve has better performance. A method to compensate for refractive index variations and curvature effect of the sinus region of the aorta root using laser doppler anemometer measurements is also proposed.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1993;115(3):299-305. doi:10.1115/1.2895490.

Experiments were conducted over a range of Reynolds numbers from 50 to 8000 to study the pressure-flow relationship for a single bifurcation in a multi-generation model during steady expiratory flow. Using the energy equation, the measured static pressure drop was decomposed into separate components due to fluid acceleration and viscous energy dissipation. The frictional pressure drop was found to closely approximate that for an equivalent length of curved tube with the same curvature ratio as in the model bifurcation. The sensitivity of these results to changes in airway cross-sectional shape, non-planar configuration, and flow regime (laminar-turbulent) was investigated. In separate experiments using dye visualization and hot-wire anemometry, a transition to turbulent flow was observed at Reynolds numbers between 1000 and 1500. Transition had very little effect on the pressure-flow relation.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1993;115(3):306-315. doi:10.1115/1.2895491.

To understand the role of fluid dynamics in atherogenesis, especially the effect of the flexibility of arteries, a two-dimensional numerical model for blood flow at the aortic bifurcation with linear viscoelastic walls is developed. The arbitrary Lagrangian-Eulerian method is adopted to deal with the moving boundary problem. The wall expansion induces flow reversals or eddies during the decelerating systole while the wall contraction restricts them during the diastole. A flexible bifurcation experiences the shear stresses about 10 percent lower than those of a rigid one.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1993;115(3):316-326. doi:10.1115/1.2895492.

A three-dimensional flow simulation at Repeak = 192 and 580 was made in a smooth reverse curvature model that conformed to the gentle “S” shape from a human left femoral artery angiogram. The objective of this numerical investigation was to find the changes in pressure, shear stress, velocity profile, and particle path occurring in the double-curved arterial vessel. Due to the impingement of blood at the outer wall in the first bend region, the wall shear stress approached 40 dyne/cm2 —a value over twice as large as in the straight upstream segment. Conversely, at the inner wall in the first bend, a low shear stress region was found where the value of the shear stress was consistently smaller than that in the straight section. The initiation of centrifugal effects caused by the first bend could clearly be seen at Repeak = 580, but due to the close proximity of the reverse curvature segment, the momentum effect due to the second bend overshadowed the centrifugal effect. Hence, only near the end of the second bend did the centrifugal effect due to the second bend result in a double-spiral-secondary motion. In addition, the numerically calculated pressure drop data were in agreement with prior experimental values.

Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

Commentary by Dr. Valentin Fuster
J Biomech Eng. 1993;115(3):329-331. doi:10.1115/1.2895494.

Recently, a new microsensor employing low-velocity ultrasonic Lamb waves was developed and demonstrated to be capable of measuring the viscosity of solutions in small volumes. The microsensor, when attached to a temperature-controlled stage, can measure viscosity as a function of temperature. In this investigation, the ultrasonic Lamb-wave oscillator is employed to experimentally measure the viscosity of dimethylsulfoxide (Me2 SO) solutions as a function of temperature. The microsensor and the experimental procedure are described and results for 1M, 3M, and 5M Me2 SO aqueous solutions are presented. Dimethylsulfoxide is a compound commonly employed as a cryoprotectant in cryopreservation, the low-temperature preservation of biological materials. The temperature dependence of viscosity obtained through this study can be used in determining the probability for ice nucleation in biological materials, a parameter of importance during cryopreservation.

Commentary by Dr. Valentin Fuster

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