Regional comparisons of nano-mechanical properties of the human meniscus; structure and function

Osteoarthritis (OA) is a debilitating disease that is becoming more prevalent in today’s society. OA affects approximately 28 million adults in the United States alone and when present in the knee joint, usually leads to a total knee replacement. Numerous studies have been conducted to determine possible methods to halt the initiation of OA, but the structural integrity of the menisci has been shown have a direct effect on the progression of OA. Menisci are two C-shaped structures that are attached to the tibial plateau and aid in facilitating proper load transmission within the knee. The meniscal cross-section is wedge-like to fit the contour of the femoral condyles and help attenuate stresses on the tibial plateau. While meniscal tears are common, only the outer 1/3 of the meniscus is vascularized and has the capacity to heal, hence tears of the inner 2/3rds are generally treated via meniscectomy, leading to OA. To help combat this OA epidemic, an effective biomimetric meniscal replacement is needed. Numerous mechanical and biochemical studies have been conducted on the human meniscus, but very little is known about the mechanical properties on the nano-scale and how meniscal constituents are distributed in the meniscal cross-section. The regional (anterior, central and posterior) nano-mechanical properties of the meniscal superficial layers (both tibial and femoral contacting) and meniscal deep zone were investigated via nanoindentation to examine the regional inhomogeneity of both the lateral and medial menisci. Additionally, these results were compared to quantitative histological values to better formulate a structure-function relationship on the nano-scale. These data will prove imperative for further advancements of a tissue engineered meniscal replacement.

Application of well log tomography to the Dundee and Rogers City Limestones, Michigan Basin, USA

The Michigan Basin is located in the upper Midwest region of the United States and is centered geographically over the Lower Peninsula of Michigan. It is filled primarily with Paleozoic carbonates and clastics, overlying Precambrian basement rocks and covered by Pleistocene glacial drift. In Michigan, more than 46,000 wells have been drilled in the basin, many producing significant quantities of oil and gas since the 1920s in addition to providing a wealth of data for subsurface visualization. Well log tomography, formerly log-curve amplitude slicing, is a visualization method recently developed at Michigan Technological University to correlate subsurface data by utilizing the high vertical resolution of well log curves. The well log tomography method was first successfully applied to the Middle Devonian Traverse Group within the Michigan Basin using gamma ray log curves. The purpose of this study is to prepare a digital data set for the Middle Devonian Dundee and Rogers City Limestones, apply the well log tomography method to this data and from this application, interpret paleogeographic trends in the natural radioactivity. Both the Dundee and Rogers City intervals directly underlie the Traverse Group and combined are the most prolific reservoir within the Michigan Basin. Differences between this study and the Traverse Group include increased well control and “slicing” of a more uniform lithology. Gamma ray log curves for the Dundee and Rogers City Limestones were obtained from 295 vertical wells distributed over the Lower Peninsula of Michigan, converted to Log ASCII Standard files, and input into the well log tomography program. The “slicing” contour results indicate that during the formation of the Dundee and Rogers City intervals, carbonates and evaporites with low natural radioactive signatures on gamma ray logs were deposited. This contrasts the higher gamma ray amplitudes from siliciclastic deltas that cyclically entered the basin during Traverse Group deposition. Additionally, a subtle north-south, low natural radioactive trend in the center of the basin may correlate with previously published Dundee facies tracts. Prominent trends associated with the distribution of limestone and dolomite are not observed because the regional range of gamma ray values for both carbonates are equivalent in the Michigan Basin and additional log curves are needed to separate these lithologies.

Automated optimization of polymer extrusion dies using finite element analysis

An extrusion die is used to continuously produce parts with a constant cross section; such as sheets, pipes, tire components and more complex shapes such as window seals. The die is fed by a screw extruder when polymers are used. The extruder melts, mixes and pressures the material by the rotation of either a single or double screw. The polymer can then be continuously forced through the die producing a long part in the shape of the die outlet. The extruded section is then cut to the desired length. Generally, the primary target of a well designed die is to produce a uniform outlet velocity without excessively raising the pressure required to extrude the polymer through the die. Other properties such as temperature uniformity and residence time are also important but are not directly considered in this work. Designing dies for optimal outlet velocity variation using simple analytical equations are feasible for basic die geometries or simple channels. Due to the complexity of die geometry and of polymer material properties design of complex dies by analytical methods is difficult. For complex dies iterative methods must be used to optimize dies. An automated iterative method is desired for die optimization. To automate the design and optimization of an extrusion die two issues must be dealt with. The first is how to generate a new mesh for each iteration. In this work, this is approached by modifying a Parasolid file that describes a CAD part. This file is then used in a commercial meshing software. Skewing the initial mesh to produce a new geometry was also employed as a second option. The second issue is an optimization problem with the presence of noise stemming from variations in the mesh and cumulative truncation errors. In this work a simplex method and a modified trust region method were employed for automated optimization of die geometries. For the trust region a discreet derivative and a BFGS Hessian approximation were used. To deal with the noise in the function the trust region method was modified to automatically adjust the discreet derivative step size and the trust region based on changes in noise and function contour. Generally uniformity of velocity at exit of the extrusion die can be improved by increasing resistance across the die but this is limited by the pressure capabilities of the extruder. In optimization, a penalty factor that increases exponentially from the pressure limit is applied. This penalty can be applied in two different ways; the first only to the designs which exceed the pressure limit, the second to both designs above and below the pressure limit. Both of these methods were tested and compared in this work.

Sonic log prediction in carbonates

This work is conducted to study the complications associated with the sonic log prediction in carbonate logs and to investigate the possible solutions to accurately predict the sonic logs in Traverse Limestone. Well logs from fifty different wells were analyzed to define the mineralogy of the Traverse Limestone by using conventional 4-mineral and 3-mineral identification approaches. We modified the conventional 3-mineral identification approach (that completely neglects the gamma ray response) to correct the shale effects on the basis of gamma ray log before employing the 3-mineral identification. This modification helped to get the meaningful insight of the data when a plot was made between DGA (dry grain density) and UMA (Photoelectric Volumetric Cross-section) with the characteristic ternary diagram of the quartz, calcite and dolomite. The results were then compared with the 4-mineral identification approach. Contour maps of the average mineral fractions present in the Traverse Limestone were prepared to see the basin wide mineralogy of Traverse Limestone. In the second part, sonic response of Traverse Limestone was predicted in fifty randomly distributed wells. We used the modified time average equation that accounts for the shale effects on the basis of gamma ray log, and used it to predict the sonic behavior from density porosity and average porosity. To account for the secondary porosity of dolomite, we subtracted the dolomitic fraction of clean porosity from the total porosity. The pseudo-sonic logs were then compared with the measured sonic logs on the root mean square (RMS) basis. Addition of dolomite correction in modified time average equation improved the results of sonic prediction from neutron porosity and average porosity. The results demonstrated that sonic logs could be predicted in carbonate rocks with a root mean square error of about 4μsec/ft. We also attempted the use of individual mineral components for sonic log prediction but the ambiguities in mineral fractions and in the sonic properties of the minerals limited the accuracy of the results.

Erupted magma volume estimates at Santiaguito and Pacaya Volcanoes, Guatemala using digital elevation models

High resolution digital elevation models (DEMs) of Santiaguito and Pacaya volcanoes, Guatemala, were used to estimate volume changes and eruption rates between 1954 and 2001. The DEMs were generated from contour maps and aerial photography, which were analyzed in ArcGIS 9.0®. Because both volcanoes were growing substantially over the five decade period, they provide a good data set for exploring effective methodology for estimating volume changes. The analysis shows that the Santiaguito dome complex grew by 0.78 ± 0.07 km3 (0.52 ± 0.05 m3 s-1) over the 1954-2001 period with nearly all the growth occurring on the El Brujo (1958-75) and Caliente domes (1971-2001). Adding information from field data prior to 1954, the total volume extruded from Santiaguito since 1922 is estimated at 1.48 ± 0.19 km3. Santiaguito’s growth rate is lower than most other volcanic domes, but it has been sustained over a much longer period and has undergone a change toward more exogenous and progressively slower extrusion with time. At Santiaguito some of the material being added at the dome is subsequently transported downstream by block and ash flows, mudflows and floods, creating channel shifting and areas of aggradation and erosion. At Pacaya volcano a total volume of 0.21 ± 0.05 km3 was erupted between 1961 and 2001 for an average extrusion rate of 0.17 ± 0.04 m3 s-1. Both the Santiaguito and Pacaya eruption rate estimates reported here are minima, because they do not include estimates of materials which are transported downslope after eruption and data on ashfall which may result in significant volumes of material spread over broad areas. Regular analysis of high resolution DEMs using the methods outlined here, would help quantify the effects of fluvial changes to downstream populated areas, as well as assist in tracking hazards related to dome collapse and eruption.

Variations of the FEAST Eigenvalue Algorithm

FEAST is a recently developed eigenvalue algorithm which computes selected interior eigenvalues of real symmetric matrices. It uses contour integral resolvent based projections. A weakness is that the existing algorithm relies on accurate reasoned estimates of the number of eigenvalues within the contour. Examining the singular values of the projections on moderately-sized, randomly-generated test problems motivates orthogonalization-based improvements to the algorithm. The singular value distributions provide experimentally robust estimates of the number of eigenvalues within the contour. The algorithm is modified to handle both Hermitian and general complex matrices. The original algorithm (based on circular contours and Gauss-Legendre quadrature) is extended to contours and quadrature schemes that are recursively subdividable. A general complex recursive algorithm is implemented on rectangular and diamond contours. The accuracy of different quadrature schemes for various contours is investigated.