Allen H. Hoffman

An Experimental Study on the Ultimate Strength of the Adventitia and Media of Human Atherosclerotic Carotid Arteries in Circumferential and Axial Directions

Atherosclerotic plaque may rupture without warning causing heart attack or stroke. Knowledge of the ultimate strength of human atherosclerotic tissues is essential for understanding the rupture mechanism and predicting cardiovascular events. Despite its great importance, experimental data on ultimate strength of human atherosclerotic carotid artery remains very sparse. This study determined the uniaxial tensile strength of human carotid artery sections containing type II and III lesions (AHA classifications). Axial and circumferential oriented adventitia, media and intact specimens (total=73) were prepared from 6 arteries. The ultimate strength in uniaxial tension was taken as the peak stress recorded when the specimen showed the first evidence of failure and the extensibility was taken as the stretch ratio at failure. The mean adventitia strength values calculated using the first Piola-Kirchoff stress were 1996+/-867 and 1802+/-703 kPa in the axial and circumferential directions respectively, while the corresponding values for the media sections were 519+/-270 and 1230+/-533 kPa. The intact specimens showed ultimate strengths similar to media in circumferential direction but were twice as strong as the media in the axial direction. Results also indicated that adventitia, media and intact specimens exhibited similar extensibility at failure, in both the axial and circumferential directions (stretch ratio 1.50+/-0.22). These measurements of the material strength limits for human atherosclerotic carotid arteries could be useful in improving computational models that assess plaque vulnerability.

A method for measuring strains in soft tissue

A finite element based method has been developed for measuring strains in soft tissue. An array of markers is placed on the tissue surface and treated as nodes of a four node isoparametric element. The displacements of the marker centroids are directly measured using a high sensitivity television camera. Finite element method mathematics are then used to calculate the plane strain tensor at any point inside the element. The method has been implemented using non-rectangular elements that are approximately 2 mm on each side.

Ruffini mechanoreceptors in isolated joint capsule: responses correlated with strain energy density.

Mechanoreceptive afferents innervating the posterior capsule of the cat knee joint were recorded in a preparation of isolated capsule. The purpose of the experiments was to identify mechanical states in the capsule that were associated with afferent discharge. The capsule was excised from the knee with its bone attachments intact, so that the geometry of the capsule could be reproduced in vitro. The capsule was deformed, and measurements were made of stresses and strains in the plane of the capsule. Afferent discharge was correlated with each of the components of plane stress, plane strain, and strain energy density (SED). SED, the stored elastic energy at the receptor location, was the only mechanical variable that was consistently positively correlated with afferent discharge. A model of the Ruffini-type receptor is presented that accounts for the sensitivity to SED.

A Finite Element Based Method to Determine the Properties of Planar Soft Tissue

A finite element based method to determine the incremental elastic material properties of planar membranes was developed and evaluated. The method is applicable to tissues that exhibit inhomogeneity, geometric and material nonlinearity, and anisotropy. Markers are placed on the tissue to form a four-node quadrilateral element. The specimen is loaded to an initial reference state, then three incremental loading sets are applied and the nodal displacements recorded. One of these loadings must include shear. These data are used to solve an over-determined system of equations for the tangent stiffness matrix. The method was first verified using analytical data. Next, data obtained from a latex rubber sheet were used to evaluate experimental procedures. Finally, experiments conducted on preconditioned rat skin revealed nonlinear orthotropic behavior. The vector norm comparing the applied and calculated nodal force vectors was used to evaluate the accuracy of the solutions.

The Effect of Diabetes on the Viscoelastic Properties of Rat Knee Ligaments

A series of experiments was performed to determine the effect of diabetes on the viscoelastic properties of knee joint ligaments. The experimental model was collateral ligaments from spontaneously diabetic, hyperglycemic (BBZDP/Wor) rats, and various controls including nondiabetic littermates, insulin treated diabetic rats, and alloxan treated rats. Material properties were measured using a dynamic, uniaxial loading paradigm. Ligaments were subjected to load controlled, sinusoidal tensile testing, using frequencies from 0.1 to 2.0 Hz. The resulting data were used to determine the storage and loss compliances of the ligaments. Storage compliance, which reflects tissue elastic properties, did not differ between groups. Loss compliance, which reflects the viscous component of the tissue response, was increased in the hyperglycemic animals. Thus, hyperglycemic diabetes affects tissue mechanical properties through the viscous rather than the elastic component of the response to dynamic loading. Rats treated with alloxan to induce diabetes did not show an increase in loss compliance.

Calibrating joint capsule mechanoreceptors as in vivo soft tissue load cells

A method has been developed whereby the discharge of mechanically sensitive neurons from the cat knee joint capsule can be calibrated and used as load cells. The neurons are located in the upper edge of the capsule which has been previously modeled as a suspension cable and where the loading has been shown to be one dimensional. The calibration procedure relies upon applying known point loads to the cable and measuring its shape. The biomechanical model is then used to compute the cable tension at the neuron location. Results for 20 neurons showed a strong linear relationship between the tension and the frequency of neuronal discharge (r = 0.96, S.D. = 0.05). For 11 of these neurons the in vivo calibration was verified by subsequently excising the posterior capsule and recording from the same neuron while subjecting the cable to measured uniaxial loads. Results showed good agreement between the in vivo and in vitro calibrations. Once calibrated these neurons can be used as load sensors to study in vivo joint loading.

Using In Vivo Cine and 3D Multi-Contrast MRI to Determine Human Atherosclerotic Carotid Artery Material Properties and Circumferential Shrinkage Rate and Their Impact on Stress/Strain Predictions

In vivo magnetic resonance image (MRI)-based computational models have been introduced to calculate atherosclerotic plaque stress and strain conditions for possible rupture predictions. However, patient-specific vessel material properties are lacking in those models, which affects the accuracy of their stress/strain predictions. A noninvasive approach of combining in vivo Cine MRI, multicontrast 3D MRI, and computational modeling was introduced to quantify patient-specific carotid artery material properties and the circumferential shrinkage rate between vessel in vivo and zero-pressure geometries. In vivo Cine and 3D multicontrast MRI carotid plaque data were acquired from 12 patients after informed consent. For each patient, one nearly-circular slice and an iterative procedure were used to quantify parameter values in the modified Mooney-Rivlin model for the vessel and the vessel circumferential shrinkage rate. A sample artery slice with and without a lipid core and three material parameter sets representing stiff, median, and soft materials from our patient data were used to demonstrate the effect of material stiffness and circumferential shrinkage process on stress/strain predictions. Parameter values of the Mooney-Rivlin models for the 12 patients were quantified. The effective Youngs modulus (YM, unit: kPa) values varied from 137 (soft), 431 (median), to 1435 (stiff), and corresponding circumferential shrinkages were 32%, 12.6%, and 6%, respectively. Using the sample slice without the lipid core, the maximum plaque stress values (unit: kPa) from the soft and median materials were 153.3 and 96.2, which are 67.7% and 5% higher than that (91.4) from the stiff material, while the maximum plaque strain values from the soft and median materials were 0.71 and 0.293, which are about 700% and 230% higher than that (0.089) from the stiff material, respectively. Without circumferential shrinkages, the maximum plaque stress values (unit: kPa) from the soft, median, and stiff models were inflated to 330.7, 159.2, and 103.6, which were 116%, 65%, and 13% higher than those from models with proper shrinkage. The effective Youngs modulus from the 12 human carotid arteries studied varied from 137 kPa to 1435 kPa. The vessel circumferential shrinkage to the zero-pressure condition varied from 6% to 32%. The inclusion of proper shrinkage in models based on in vivo geometry is necessary to avoid over-estimating the stresses and strains by up 100%. Material stiffness had a greater impact on strain (up to 700%) than on stress (up to 70%) predictions. Accurate patient-specific material properties and circumferential shrinkage could considerably improve the accuracy of in vivo MRI-based computational stress/strain predictions.

Using Uniaxial Pseudorandom Stress Stimuli to Develop Soft Tissue Constitutive Equations

AbstractA nonlinear systems identification method was used to develop constitutive equations for soft tissue specimens under uniaxial tension. The constitutive equations are developed from a single test by applying a pseudorandom Gaussian (PGN) stress input to the specimen, measuring the resulting strain, and calculating the Volterra–Wiener kernels. First and second order kernels were developed for two tissues with widely different properties, rat medial collateral knee ligaments, and rat skin. These kernels were used to predict the strain response to a variety of sinusoidal stress inputs. These predicted strains were compared with the measured strain response using the normalized mean squared error (NMSE). Results showed NMSEs in the range of 0.01–0.08 provided that the magnitudes of the applied stresses were present in the original PGN stress input. Overall, the method provides a means to develop soft tissue constitutive equations that can predict both nonlinear and viscoelastic behavior over a wide range of stress inputs.

MEASUREMENT OF JOINT CAPSULE TISSUE LOADING IN THE CAT KNEE USING CALIBRATED MECHANORECEPTORS

The vertical loading in the posterior capsule of the cat knee has been measured while the knee is rotated into hyperextension. Tissue loading was determined using a previously verified model of the capsule that represents its upper edge as a catenary suspension cable. Tensile loads in the cable were measured using the discharge of mechanoreceptive sensory neurons that had been calibrated as load sensors. The results revealed that the capsule is very lightly loaded in extension rotations. Less than 4% of the applied moment is sustained by the capsule.

Variation of arterial compliance within the cardiac pressure pulse

Past investigations of in vivo arterial behavior have concentrated on determining material properties based upon the maximum and minimum pressure and diameter measured over a pulse cycle. A new in vivo technique, based upon continuous measurement of pressure and flow, has been developed to study arterial compliance throughout the pulse cycle. Compliance in the abdominal aorta of rats showed different behavior during the rising and falling portion of the pressure pulse. Previous investigations of canine arteries which used different methods are consistent with these findings. This study demonstrates the utility of a new measurement technique and shows some trends in compliance within the pulse cycle which have neither been revealed by static tests nor by dynamic tests which focused on pulse averaged values.