Lyle F. Mockros

A mathematical analysis for indentation tests of articular cartilage

Abstract A mathematical model is developed for indentation tests of articular cartilage. The cartilage, normally bonded to the subchondral bone, is modeled as an infinite elastic layer bonded to a rigid half space, and the indenter is assumed to be a rigid axisymmetric punch. The problem is formulated as a mixed boundary value problem of the theory of elasticity and solutions are obtained for the indentation of the layer by the plane end of a rigid circular cylinder and by a rigid sphere. Subject to detailed verification with independent tests, the present solutions are suggested as useful for the determination of the elastic shear modulus of intact cartilage.

Structural origins of fibrin clot rheology

The origins of clot rheological behavior associated with network morphology and factor XIIIa-induced cross-linking were studied in fibrin clots. Network morphology was manipulated by varying the concentrations of fibrinogen, thrombin, and calcium ion, and cross-linking was controlled by a synthetic, active-center inhibitor of FXIIIa. Quantitative measurements of network features (fiber lengths, fiber diameters, and fiber and branching densities) were made by analyzing computerized three-dimensional models constructed from stereo pairs of scanning electron micrographs. Large fiber diameters and lengths were established only when branching was minimal, and increases in fiber length were generally associated with increases in fiber diameter. Junctions at which three fibers joined were the dominant branchpoint type. Viscoelastic properties of the clots were measured with a rheometer and were correlated with structural features of the networks. At constant fibrinogen but varying thrombin and calcium concentrations, maximal rigidities were established in samples (both cross-linked and noncross-linked) which displayed a balance between large fiber sizes and great branching. Clot rigidity was also enhanced by increasing fiber and branchpoint densities at greater fibrinogen concentrations. Network morphology is only minimally altered by the FXIIIa-catalyzed cross-linking reaction, which seems to augment clot rigidity most likely by the stiffening of existing fibers.

Indentation tests of human articular cartilage

Abstract The short-time shear and bulk moduli of articular cartilage were determined experimentally using torsional shear and uniaxial confined compression tests. These results are compared to the values of shear moduli predicted by using data from indenter tests and the theoretical solution for the identation of a rigid punch pressed into an elastic layer bonded to a rigid halfspace. To verify the effectiveness of predicting moduli from indenter tests, control experiments were performed on polyurethane rubber. Although they accurately predict the elastic properties for rubber, the nonlinearity, anisotropy and non-homogeneity of articular cartilage make indenter tests less appropriate for use with cartilage. The predicted and measured values correlate but with considerable dispersion. The short-time shear modulus of articular cartilage, including both healthy and diseased samples, were found to vary over the range 4–35 × 105 N/m2 and the short-time bulk modulus over the range 9–170 × 106 N/m2. The means of tissue storage was found to have a major effect on the measured mechanical properties.

Shear-induced activation of platelets

Platelet-rich plasma was subjected to shear in Poiseuille flows through tubes, i.d. = 305, 406 and 508 μm. Bulk-average shear stresses were 300, 750 and 1000 dynes/cm2 and the average residence times were 25–1650 ms. These shears for these residence times did not produce cell lysis but did activate the platelets so that their response to exogenous ADP were reduced and platelet factor 3 was released. Also, thromboelastographic measurements indicated shear-induced hypercoagulability. Allowing samples to stand 30–60 mins after being sheared revealed some of the indicated activation was reversible. Adding the anticoagutant heparin to sheared samples produced an anomalous response. The quantitative results were independent of tube surface-volume ratio, but were dependent on both level of shear stress and on residence time.

Use of a mathematical model to predict oxygen transfer rates in hollow fiber membrane oxygenators.

&NA; A semi‐empirical theoretical model of oxygen transfer is used to predict the rates of oxygen transfer to blood in hollow fiber membrane oxygenators over a wide range of inlet conditions. The predicted oxygen transfer rates are based on performance of the devices with water, which is more cost effective and easier to handle than blood for in vitro evaluations. Water experiments were conducted at three different flow rates to evaluate oxygen transfer performance in three commercially available membrane oxygenators. Data obtained from these experiments were used in a computer model to predict the rate of oxygen transfer to bovine blood at specified inlet conditions. Blood experiments were conducted at three different flow rates at a wide variety of inlet conditions, including different pH levels, hemoglobin concentrations, and oxyhemoglobin saturations for the three types of oxygenators. The measured and predicted oxygen transfer rates are closely correlated, which suggests that we have an accurate, reliable method for predicting oxygen transfer in hollow fiber membrane lungs. ASAIO Journal 1994; 40:990‐996.

Development of an implantable artificial lung : Challenges and progress

Unlike dialysis, which functions as a bridge to renal transplantation, or a ventricular assist device, which serves as a bridge to cardiac transplantation, no suitable bridge to lung transplantation exists. Our goal is to design and build an ambulatory artificial lung that can be perfused entirely by the right ventricle and completely support the metabolic O2 and CO2 requirements of an adult. Such a device could realize a substantial clinical impact as a bridge to lung transplantation, as a support device immediately post-lung transplant, and as a rescue and/or supplement to mechanical ventilation during the treatment of severe respiratory failure. Research on the artificial lung has focused on the design, mode of attachment to the pulmonary circulation, and intracorporeal versus paracorporeal placement of the device.

Hemodynamic effects of attachment modes and device design of a thoracic artificial lung.

A thoracic artificial lung (TAL) was designed to treat respiratory insufficiency, acting as a temporary assist device in acute cases or as a bridge to transplant in chronic cases. We developed a computational model of the pulmonary circulatory system with the TAL inserted. The model was employed to investigate the effects of parameter values and flow distributions on power generated by the right ventricle, pulsatility in the pulmonary system, inlet flow to the left atrium, and input impedance. The ratio of right ventricle (RV) power to cardiac output ranges between 0.05 and 0.10 W/(L/min) from implantation configurations of low impedance to those of high impedance, with a control value of 0.04 W/(L/min). Addition of an inlet compliance to the TAL reduces right heart power (RHP) and impedance. A compliant TAL housing reduces flow pulsatility in the fiber bundle, thus affecting oxygen transfer rates. An elevated bundle resistance reduces flow pulsatility in the bundle, but at the expense of increased right heart power. The hybrid implantation mode, with inflow to the TAL from the proximal pulmonary artery (PA), outflow branches to the distal PA and the left atrium (LA), a band around the PA between the two anastomoses, and a band around the outlet graft to the LA, is the best compromise between hemodynamic performance and preservation of some portion of the nonpulmonary functions of the natural lungs.

Pressure and flow in the systemic arterial system

Abstract The dynamic characteristics of the proximal arterial system are studied by solving the nonlinear momentum and mass conservation equations for pressure and flow. The equations are solved for a model systemic arterial system that includes the aorta, common iliacs, and the internal and external iliac arteries. The model includes geometric and elastic taper of the aorta, nonlinearly elastic arteries, side flows, and a complex distal impedance. The model pressure wave shape, inlet and outlet impedance, wave travel, and apparent wave velocity compare favorably with the values measured on humans. Calculations indicate that: (i) reflections are the major factor determining the shape and distal amplification of the pressure wave in the arterial tree; (ii) although important in attenuating the proximal transmission of reflecting waves, geometric taper is not the major cause of the distal pressure wave amplification; (iii) the dicrotic wave is a result of peripheral reflection and is not due to the sudden change in flow at the end of systole; (iv) the elastic taper and nonlinearity of the wall elasticity are of minor significance in determining the flow and pressure profiles; and (v) in spite of numerous nonlinearities, the system behaves in a somewhat linear fashion for the lower frequency components.

The Stokes-flow drag on prolate and oblate spheroids during axial translatory accelerations

Stokess linearized equations of motion are used to calculate the flow field generated by a spheroid executing axial translatory oscillations in an infinite, otherwise still, incompressible, viscous fluid. The flow field, expressed in terms of spheroidal wave functions of order one, is used to develop general expressions for the drag on oscillating prolate and oblate spheroids. Formulae for the approximate drag, useful in making calculations, are obtained for small values of an oscillation parameter. These formulae reduce to the Stokes result in the limit when the spheroid becomes a sphere and the steady-state drag for a spheroid as the frequency of oscillation becomes zero. The fluid forces on spheroids of various shapes are compared graphically. The approximate formulae for the drag are integrated over all frequencies to obtain formulae for the drag on spheroids executing general axial translatory accelerations. The fluid resistance on the spheroid is expressed as the sum of an added mass effect, a steady-state drag and an effect due to the history of the motion. A table of added mass, viscous and history coefficients is given.

Hemodynamic and gas transfer properties of a compliant thoracic artificial lung

A compliant thoracic artificial lung (TAL) has been developed for acute respiratory failure or as a bridge to transplantation. The development goal was to increase TAL compliance, lower TAL impedance, and improve right ventricular function during use. Prototypes were tested in vitro and in vivo in eight pigs between 67 and 79 kg to determine hemodynamic and gas transfer properties. The in vitro compliance was 16.2 ± 4.4 ml/mm Hg at pressures < 7.8 mm Hg and 4.3 ± 1.1 ml/mm Hg above 7.8 mm Hg. In vivo, this compliance significantly reduced blood flow pulsatility from 1.7 at the inlet to 0.36 at the outlet. Device resistance was 1.9 and 1.8 mm Hg/(L/min) at a flow rate of 4 L/min in vitro and in vivo, respectively. Approximately 75% of the resistance was at the inlet and outlet. In vivo TAL O2 and CO2 transfer rates were 188 and 186 ml/min, respectively, at 4 L/min of blood and gas flow, and average outlet O2 saturations exceeded 98% for average flow rates up to and including the maximum tested, 5.3 L/min. The new design has a markedly improved compliance and excellent gas transfer but also possesses inlet and outlet resistances that must be reduced in future designs.