Characterizing local rings via homological dimensions and regular sequences

Let (R,m) be a Noetherian local ring of depth d and C a semidualizing R-complex. Let M be a finite R-module and t an integer between 0 and d. If G_C-dimension of M/IM is finite for all ideals I generated by an R-regular sequence of length at most d-t then either G_C-dimension of M is at most t or C is a dualizing complex. Analogous results for other homological dimensions are also given.Comment: Final version, to appear in J. Pure Appl. Algebra. 9 pages. Uses XY-pi

A New Generation of Polymer/Ceramic Composite Biomaterials for Bone Regeneration

There is a substantial emerging interest for fundamental and applied research on the reinforcement of polymeric materials using nanotechnology. In the biomedical industry, development of novel bone cement composite materials with enhanced mechanical properties is of tremendous potential importance. The most universally used injectable bone cement is made of poly(methyl methacrylate) (PMMA); however, the major disadvantage of PMMA is its non-biodegradability. Polymers such as poly(propylene fumarate) (PPF) and polycaprolactone (PCL) are biodegradable, but suffer from a lack of mechanical properties. The aim of this research was to test the efficacy of these biodegradable polymers integrating nanotechnology for the development of composite biomaterials with improved mechanical properties sufficient for bone cements. This goal was investigated through a range of different studies. Focusing on nanostructured titania (n-TiO2) initially, titania nanofibers (n-TiO2 fibers) and nanowires (n-TiO2 wires) were introduced into a PPF matrix for potential use as an orthopaedic biomaterial to treat skeletal bone defects and diseases such as osteonecrosis. PPF was modified with maleic anhydride to provide functionality for the coordination of PPF to the surface of TiO2 nanofibers through a ring-opening reaction. The synthesis and modification of PPF were confirmed by NMR (1H and 13C) and XPS. The reaction chemistry of the functionalized PPF and nano-TiO2 was also investigated by XPS and FTIR analyses. The PPF-grafted nano-TiO2 was further employed in the development of bone cement composites by crosslinking/polymerization in the presence of N-vinyl pyrrolidone. Mechanical testing of the resulting bone cement composites demonstrated a significant enhancement of the tensile and flexural properties attributed to the chemical bonding between the PPF matrix and TiO2 nanofibers. On the basis of the determined mechanical properties, an optimum composition was found at 5 wt% loading of n-TiO2 fiber (0.5% in the starting composition) which provided a significant increase in Young’s modulus (153%), tensile strength (113%), flexural modulus (196%), and flexural strength (126%) when compared with the unfilled PPF. These improvements were attributed to the chemical linkage of the filler to the polymer matrix which enhances the transfer of a mechanical load to the n-TiO2 fiber, leading to an increase in the mechanical properties of the bone cement composite. Secondly, bone formation is an angiogenesis-dependent process, and the need for treatment modalities that enhance neovascularization is especially important for bone regeneration in necrotic bone. A bone cement system capable of delivering an angiogenic modulator in a controlled manner may have the ability to boost the angiogenic response when injected to an osteonecrotic lesion. Therefore, an angiogenic agent, ginsenoside Rg1, was incorporated into an orthopedic PPF-based cement. Additionally, Sr-doped TiO2 nanofibers synthesized in supercritical CO2 were added to the cement formulation as an alternative radiopacifier to enable visualization of the bone cement composites and potential monitoring of the healing and loosening processes. XPS analysis showed that Sr2+ was doped in the crystalline matrix of anatase with the formation of SrTiO3. The strong interfacial adhesion between PPF and nanofibers were characterized by SEM, FTIR, XPS, and thermal analyses and mechanical testing. The Sr-doped n-TiO2 fibers were shown to provide reasonably higher radiopacity to the PPF matrix, which is 0.32 ± 0.03 mm Al, than the unmodified fibers at the same loading level (0.20 ± 0.01 mm Al). In addition, bone cement composites loaded with ginsenoside Rg1 were found to provide a high drug release without sacrificing the mechanical properties of the bone cement. Furthermore, tube formation bioassays suggested that human umbilical vein endothelial cell lines would rearrange and align into a tubular structure in the presence of ginsenoside Rg1. Consequently, the proposed cement combines the immediate mechanical support given by the chemical bonding between the filler/polymer and optimum radiopacity (0.30 ± 0.12 mm Al) due to the incorporation of the Sr-doped TiO2 nanofibers to PPF matrix. Thirdly, because of the unique biological activities of ginsenoside Rg1, upregulating in vitro proliferation, migration, chemo-invasion, and tube formation in human umbilical vein endothelial cells (HUVECs), Rg1 can be incorporated into scaffold materials for bone tissue engineering applications. This incorporation could be achieved by encapsulation of ginsenoside Rg1 in biodegradable microspheres of PPF. Rg1-loaded PPF microspheres were prepared by both a double emulsion and a microfluidic technique for the first time in this research. The size and morphology of the Rg1-loaded PPF microspheres were characterized by SEM, showing unimodal 50-65 μm size diameters using the microfluidic technique, ideal for easy flowing powders required in commercial formulations. The PPF microspheres produced from the microfluidic technique gave high encapsulation efficiencies of up to 95.35 ± 0.82%, while those obtained from a conventional double emulsion method gave a much broader size distribution in the range of 2-45 μm with lower encapsulation efficiencies of 78.48 ± 1.68%. Release profiles were studied and quantified by UV-Vis spectrophotometry, with the results showing a lower initial burst in the release of Rg1 from the unimodal microspheres prepared by the microfluidic technique than from the double emulsion method. The burst effect was followed by a slow release profile which can be used for long term drug delivery applications to maintain the ginsenoside Rg1 concentration for an extended time period. Moreover, the released Rg1 showed a significant stimulatory effect on angiogenesis behavior and tube formation in human umbilical vein endothelial cells (HUVECs). Therefore, PPF microspheres developed in this study have potential for next-generation biomedical agents in drug-release devices for bone tissue engineering. Finally, the use of hydroxyapatite HAp is rather limited for heavy load-bearing applications due to low mechanical reliability and poor processability. Therefore, immobilization of a biocompatible metal/metal oxide on the surface of HAp has been receiving increased attention for applications involving the enhancement of mechanical properties of biocompatible prostheses. A novel nanostructured HAp and a composite of HAp and TiO2 with ultrafine structure and significantly improved mechanical properties were prepared using combined co-precipitation and sol-gel method in the green solvent, scCO2, and incorporated into polycaprolactone (PCL) matrix to develop scaffolds with enhanced physical and mechanical properties for bone regeneration. SEM and TEM analyses were employed to examine the morphology of the HAp nanoplates and HAp-TiO2 nanocomposites. The presence of Ti, O, Ca, and P in the HAp-TiO2 nanocomposites was detected by EDX. In addition, the effect of metal alkoxide concentration, reaction temperature, and pressure on the morphology, crystallinity, and surface area of the resulting nanostructured composites was examined using SEM, XRD, and the BET method. Chemical composition of the products were characterized using FTIR, XPS, and XANES analyses. TGA analysis was performed to investigate thermal behavior of the synthesized nanomaterials. Mechanical testing revealed a significant increase in the Young’s modulus (88.6%), tensile strength (122%), flexural modulus (47%), and flexural strength (59.6%) of PCL/HAp-TiO2 composites containing 20 wt % HAp-TiO2 compared to PCL/HAp composites

Development of Novel Collagen-targeted Protein-based MRI Contrast Agent for Imaging of Chronic Liver and Heart Diseases

Chronic diseases and conditions such as liver and heart diseases are among the most common, costly, and preventable of all health problems. As of 2012 in the U.S., about half of all adults—117 million people—had one or more chronic health conditions. Aortic aneurysm and liver fibrosis are among the most common chronic diseases which are generated by the formation and deposition of excess extracellular matrix proteins (largely type I collagen) as a result of a reparative process, represents one of the most major global health problems. Collagen type I is one of the major diagnostic biomarkers and therapeutic targets for many chronic diseases including heart and liver diseases. Early diagnosis, noninvasive detection and staging of these diseases, remain as one of the major clinical barriers which can lead to effective treatment and stop further progression toward major clinical consequences. MRI as one the popular imaging modalities has several unique advantages for monitoring slow progression and detection of disease with high resolution without using radiation, however, there is an unmet medical need to develop MRI contrast agents with desired sensitivity and collagen specificity. In this dissertation, the successful design of a protein-based contrast agent with collagen type I targeting capability (ProCA32.collagen1) is reported to diagnose and stage liver and heart diseases in many mouse models of caner, fibrosis and aortic aneurysm. ProCA32.collagen1 exhibits the highest relaxivity values for r1 (34 ± 0.12 mM-1.s-1) and r2 (50 ± 0.16 mM-1.s-1) per Gd3+ at 1.4 T and r1 (21.3 ± 0.5 mM-1.s-1) and r2 (108.5 ± 1.2 mM-1.s-1) at 7.0 T. ProCA32.collagen1 can detect both early (Ishak 3 of 6) and late stage mouse liver fibrosis as well as early stage nonalcoholic steatohepatitis (Ishak 1 of 6) in different models with strong metal binding affinity and selectivity. The targeted contrast agent is also capable of detecting disease heterogeneity with high collagen type I binding affinity with dissociation constant of Kd=1.42 ± 0.2 mM. ProCA32.collagen1 has largely reduced dose and strong resistance against transmetallation (104-1012-fold higher metal selectivity for Gd3+ over Ca2+ and Zn2+) compared to existing contrast agents. ProCA32.collagen1 is expected to have strong translational potential to improve detection of different diseases at early stages with high confidence, and subsequently monitor disease progression and patient response to treatment

Prostate Tumor Volume Measurement on Digital Histopathology and Magnetic Resonance Imaging

An accurate assessment of prostate tumour burden supports appropriate treatment selection, ranging from active surveillance through focal therapy, to radical whole-prostate therapies. For selected patients, knowledge of the three-dimensional locations and sizes of prostate tumours on pre-procedural imaging supports planning of effective focal therapies that preferentially target tumours, while sparing surrounding healthy tissue. In the post-prostatectomy context, pathologic measurement of tumour burden in the surgical specimen may be an independent prognostic factor determining the need for potentially life-saving adjuvant therapy. An accurate and repeatable method for tumour volume assessment based on histology sections taken from the surgical specimen would be supportive both to the clinical workflow in the post-prostatectomy setting and to imaging validation studies correlating tumour burden measurements on pre-prostatectomy imaging with reference standard histologic tumour volume measurements. Digital histopathology imaging is enabling a transition to a more objective quantification of some surgical pathology assessments, such as tumour volume, that are currently visually estimated by pathologists and subject to inter-observer variability. Histologic tumour volume measurement is challenged by the traditional 3–5 mm sparse spacing of images acquired from sections of radical prostatectomy specimens. Tumour volume estimates may benefit from a well-motivated approach to inter-slide tumour boundary interpolation that crosses these large gaps in a smooth fashion. This thesis describes a new level set-based shape interpolation method that reconstructs smooth 3D shapes based on arbitrary 2D tumour contours on digital histology slides. We measured the accuracy of this approach and used it as a reference standard against which to compare previous approaches in the literature that are simpler to implement in a clinical workflow, with the aim of determining a method for histologic tumour volume estimation that is both accurate and amenable to widespread implementation. We also measured the effect of decreasing inter-slide spacing on the repeatability of histologic tumour volume estimation. Furthermore, we used this histologic reference standard for tumour volume to measure the accuracy, inter-observer variability, and inter-sequence variability of prostate tumour volume estimation based on radiologists’ contouring of multi-parametric magnetic resonance imaging (MPMRI). Our key findings were that (1) simple approaches to histologic tumour volume estimation that are based on 2- or 3-dimensional linear tumour measurements are more accurate than those based on 1-dimensional measurements; (2) although tumour shapes produced by smooth through-slide interpolation are qualitatively substantially different from those obtained from a planimetric approach normally used as a reference standard for histologic tumour volume, the volumes obtained were similar; (3) decreasing inter-slide spacing increases repeatability of histologic tumour volume estimates, and this repeatability decreases rapidly for inter-slide spacing values greater than 5 mm; (4) on MPMRI, observers consistently overestimated tumour volume as compared to the histologic reference standard; and (5) inter-sequence variability in MPMRI-based tumour volume estimation exceeded inter-observer variability