We present a theoretical framework based on an extension of Dynamical Density Functional Theory (DDFT) to describe the structure and dynamics of cells in living tissues and tumours. DDFT is a microscopic statistical mechanical theory for the time evolution of the density distribution of interacting many-particle systems. The theory accounts for cell pair-interactions, different cell types, phenotypes and cell birth and death processes (including cell division), in order to provide a biophysically consistent description of processes bridging across the scales, including the description of the tissue structure down to the level of the individual cells. Analysis of the model is presented for a single species and a two-species cases, the latter describing competition between a cancerous and healthy cells. In suitable parameter regimes, model results are consistent with biological observations. Of particular note, divergent tumour growth behaviour, mirroring metastatic and benign growth characteristics, are shown to be dependent on the cell pair-interaction parameters.

Thesis (MSc)--Stellenbosch University, 2011. / ENGLISH ABSTRACT: For solid tumours to grow and metastise, they need to pass through two distinct stages: the avascular growth phase in which the tumour remains in a limited diffusion size and the vascular growth phase where the invasion may take place. In order to accomplish the transition from the former to the latter growth phase, a solid tumour may secrete a substance known as tumour angiogenesis factor (TAF) into the surrounding tissues to stimulate its own blood vessels. Once the tumour has its own blood supply, it can invade other parts of the body destroying healthy tissues organs by secreting the matrix degrading enzymes (MDE). During the invasion, the adhesion both cell-cell and cell-matrix play an extremely important role. In this work, we review some mathematical models dealing with various stages of development of solid tumours and the resulting reaction diffusion equations are solved using the Crank-Nicolson finite differences scheme. We also present a system of reaction-diffusion-taxis partial differential equations, with nonlocal (integral) terms describing the interactions between cancer cells and the host tissue. We then investigate the local and global existence of the solution of the previous model using the semigroup method and Sobolev embeddings. / AFRIKAANSE OPSOMMING: Daar is twee afsonderlike fases nodig vir soliede kanker gewasse om te groei en kwaadaardig te word: die avaskulêre groeifase waarin die gewas tot ’n sekere diffusie grootte beperk word en die vaskulêre groei fase waar die indringing plaasvind. Ten einde die oorgang tussen die twee fases te bewerkstellig, skei die soliede gewas ân stof in die omliggende weefsel af wat bekend staan as âtumor angiogenese factorâ (TAF). Dit stimuleer die vorming van die gewas se eie bloedvate. Wanneer die gewas sy eie bloedtoevoer het, kan dit ander dele van die liggaam indring en gesonde orgaanweefsel vernietig deur die afskeiding van die âmatrix degrading enzymesâ (MDE). Gedurende hierdie proses speel die sel-sel en sel-matriks interaksies ân belangrike rol. In hierdie werk het ons ân paar wiskundige modelle vergelyk wat die verskillende stadiums van die ontwikkeling van soliede gewasse beskryf. Die gevolglike diffusiereaksie vergelykings is opgelos deur gebruik te maak van die âCrank-Nicolson finite differences schemeâ. Ons bied ook ’n stelsel van âreaction-diffusion-taxisâ, met nie-lokale (integrale) terme wat die interaksies tussen kankerselle en die gasheerweefsel beskryf. Ons stel dan ondersoek in na die lokale en globale bestaan van die oplossing van die vorige model, met behulp van die semi-groep metode en die Sobolev ingebeddings.

Cancer is a generic term for a large group of diseases where cells of the body lose their normal mechanisms for growth so that they grow in an uncontrolled way. One of the most common treatments of cancer is chemotherapy that aims to kill abnormal proliferating cells; however normal cells and other organs of the patients are also adversely affected. In practice, it's often difficult to maintain optimum chemotherapy doses that can maximise the abnormal cell killing as well as reducing side effects. The most chemotherapy drugs used in cancer treatment are toxic agents and usually have narrow therapeutic indices, dose levels in which these drugs significantly kill the cancerous cells are close to the levels which sometime cause harmful toxic side effects. To make the chemotherapeutic treatment effective, optimum drug scheduling is required to balance between the beneficial and toxic side effects of the cancer drugs. Conventional clinical methods very often fail to find drug doses that balance between these two due to their inherent conflicting nature. In this investigation, mathematical models for cancer chemotherapy are used to predict the number of tumour cells and control the tumour growth during treatment. A feedback control method is used so as to maintain certain level of drug concentrations at the tumour sites. Multi-objective Genetic Algorithm (MOGA) is then employed to find suitable solutions where drug resistances and drug concentrations are incorporated with cancer cell killing and toxic effects as design objectives. Several constraints and specific goal values were set for different design objectives in the optimisation process and a wide range of acceptable solutions were obtained trading off among different conflicting objectives. Abstract v In order to develop a multi-objective optimal control model, this study used proportional, integral and derivative (PID) and I-PD (modified PID with Integrator used as series) controllers based on Martin's growth model for optimum drug concentration to treat cancer. To the best of our knowledge, this is the first PID/I-PD based optimal chemotherapy control model used to investigate the cancer treatment. It has been observed that some solutions can reduce the cancer cells up to nearly 100% with much lower side effects and drug resistance during the whole period of treatment. The proposed strategy has been extended for more drugs and more design constraints and objectives.

Glucocorticoids, key hormonal regulators of the stress response, powerfully influence inflammation and metabolism. Reducing excessive glucocorticoid exposure is beneficial in treating metabolic and cognitive disorders, but manipulating systemic endogenous glucocorticoids risks compromising their beneficial effects. The enzyme 11β-hydroxysteroid dehydrogenase type 1 (11β-HSD1) activates glucocorticoids in target tissues and thus inhibition of this enzyme presents a clinical opportunity to reduce tissue-specific glucocorticoid action. Active glucocorticoids also exert potent angiostatic effects by binding the glucocorticoid receptor (GR), and 11β-HSD1 inhibitors have proven beneficial in models of myocardial infarction by promoting angiogenesis. The possibility that 11β-HSD1 inhibitors may increase pathological angiogenesis, such as that seen in solid tumours, remains unaddressed. This project tested the hypothesis that 11β-HSD1 inhibition promotes tumour growth as a result of increased angiogenesis, using murine models of squamous cell carcinoma (SCC) and pancreatic ductal adenocarcinoma (PDAC). Murine SCC or PDAC cells were injected (1x106 cells/flank) into WT female mice fed either standard diet, or diet containing the 11β-HSD1 inhibitor UE2316 (175 mg/kg, N=6/group), or into 11β-HSD1 knockout (Del1) mice fed standard diet. Developing tumours were measured by callipers over several weeks, before animals were culled and tissues collected. SCC tumours grew more rapidly in UE2316-treated mice to reach a significantly (P < 0.01) larger final volume (0.158 ± 0.037 cm3) than in control mice (0.051 ± 0.007 cm3). PDA tumours were unaffected by 11β-HSD1 inhibition or deletion. Immunofluorescent co-staining of tumour sections for CD31/α-smooth muscle actin revealed no differences in vessel density, and RT-qPCR showed no difference in angiogenic factor expression, after 11β-HSD1 inhibition/deletion in either tumour type. GR and 11β-HSD1 RNA expression were greater in SCC vs PDAC tumours (P < 0.001), as was 11β-HSD1 activity (P < 0.0001). In studies using the aortic ring assay of ex vivo angiogenesis, 11β-HSD1 deletion, but not inhibition with UE2316, was shown to prevent glucocorticoid-mediated angiostasis. The growth/viability of tumour cell lines was not affected by UE2316 or corticosterone, as assessed by live cell imaging using the Incucyte imaging system. RNA-sequencing of SCC tumours revealed that multiple factors involved in the innate immune/inflammatory response were reduced in UE2316-treated tumours, and that extracellular matrix regulation was also altered by UE2316. Imaging of tumour sections using Second Harmonic Generation microscopy confirmed that UE2316 altered Type I collagen deposition in SCC (P < 0.001) but not PDAC. 11β-HSD1 inhibition can increase tumour growth, possibly via suppression of inflammatory/immune cell signalling and alteration of the extracellular matrix, and tumours with higher GR and 11β-HSD1 content, such as SCC, may be more at risk. Interestingly this investigation found no evidence of increased angiogenesis in vivo or ex vivo after UE2316 treatment, suggesting that 11β-HSD1 inhibition does not promote angiogenesis in all ischaemic environments. Future work must focus on the effects of 11β-HSD1 inhibition on the immune and extracellular matrix component of the tumour microenvironment. While promotion of pathological angiogenesis does not appear to pose a major threat, 11β-HSD1 inhibitors may still interact with the immune and inflammatory environment in tumours to the detriment of health.

Background and aims: Laparoscopic technique was quickly adopted in general surgery because of less pain, quicker recovery and shorter hospital stay. In the 1990´s several reports on port site metastases restrained the enthusiasm to use laparoscopic surgery in malignant diseases. The numerous reports on port site metastases initiated a debate whether laparoscopic surgery would increase the risk of tumour spread and growth. Personal experience of two patients who devloped port site metastases from an incidental gall bladder cancer (GBC) after laparoscopic cholecystectomy (LC), encouraged us to study the incidence of wound metastases from GBC after laparoscopic and open cholecystectomy (OC). Experimentally we examined whether pneumoperitoneum would increase the risk of tumour development. Several studies had demonstrated that minimally invasive procedures exert a less negative influence on the immune system and may have beneficial effects for cancer patients. We wanted to compare the long term survival after OC and LC and if the occurence of port site metastases had any impact on survival. Material and methods: A questionnaire was sent out to all major hospitals in Sweden requesting information obout the number of port site metastases encountered 1991-94. Data on all pateints with verfied GBC were obtained from the Swedish Oncological Centres. Data on all patients with GBC registered with surgical codes for cholecystectomy were collected from the National Board of Health and Welfare (EpC). The patient files were scrutinized and long term survival data was achieved (EpC). In the first experiment on Wistar Fu rats, adenocarcinoma cells were injected intraperitoneally in animals insufflated with air, CO2 and not insufflated controls. In the following studies, rats were similarly insufflated with air,CO2 and compared to not insufflated controls. Laser Doppler blood flow in the abdominal wall was concomitantly measured. To study the effect of reduced blood flow, one rectus muscle was clamped and the other not and laser Doppler Blood flow was measured in both rectus muscles. Adenocarcinoma cells were injected into the rectus muscles in all animals at the induction of pneumoperitoneum/clamping. Results: 14 of 55 patients developed wound metastases from GBC after LC and 12 of 187 after OC. Gallbladder perforation was overrepresented in patients with wound metastases. Improved survival was noted after LC in patients with T3 tumours. Experimentally, air and CO2 equally increased intraperitoneal tumour development, Insufflation with air,CO2 and clamping decreased blood flow in the abdominal wall and increased tumour growth at the same site. Conclusion: Despite a high rate of wound metastases, LC does not seem to worsen the prognosis of GBC and may even have a positive effect on survival. Perforation of the malignant gallbladder seems to be associated with an increased risk of metastatic formation. In the experimental setting, pneumoperitoneum seems to increase tumour development. Other features of laparoscopic surgery such as decreased blood flow in the abdominal wall may contribute to increased risk of tumour progress.

A brief introduction to cancer biology and treatment is presented with a focus on current clinical advances in the delivery of chemotherapy and antiangiogenic therapies. Mathematical oncology is then surveyed with summaries of various models of tumor growth, tumor angiogenesis and other relevant biological entities such as angiogenic growth factors. Both strictly time-dependent ordinary differential equation (ODE)-based and spatial partial differential equation (PDE)-based models are considered. These biological models are first developed into an ODE model where various treatment options can be compared including different combinations of drugs and dosage schedules. This model gives way to a PDE model that includes the spatially heterogeneous blood vessel distribution found in tumors, as well as angiogenic growth factor imbalances. This model is similarly analyzed and implications are summarized. Finally, including the effects of interstitial fluid pressure into an angiogenic activity model is performed. This model displays the importance of factor convection on the angiogenic behaviour of tumours.

A brief introduction to cancer biology and treatment is presented with a focus on current clinical advances in the delivery of chemotherapy and antiangiogenic therapies. Mathematical oncology is then surveyed with summaries of various models of tumor growth, tumor angiogenesis and other relevant biological entities such as angiogenic growth factors. Both strictly time-dependent ordinary differential equation (ODE)-based and spatial partial differential equation (PDE)-based models are considered. These biological models are first developed into an ODE model where various treatment options can be compared including different combinations of drugs and dosage schedules. This model gives way to a PDE model that includes the spatially heterogeneous blood vessel distribution found in tumors, as well as angiogenic growth factor imbalances. This model is similarly analyzed and implications are summarized. Finally, including the effects of interstitial fluid pressure into an angiogenic activity model is performed. This model displays the importance of factor convection on the angiogenic behaviour of tumours.

Yes / 5,7-Dihydro-3,9,10,11-tetramethoxybenz[c,e]oxepin-4-ol 1, prepared from a dibenzyl ether precursor via Pd-catalysed intramolecular direct arylation, possesses broad-spectrum in vitro cytotoxicity towards various tumour cell lines, and induces vascular shutdown, necrosis and growth delay in tumour xenografts in mice at sub-toxic doses. The biological properties of 1 and related compounds can be attributed to their ability to inhibit microtubule assembly at the micromolar level, by binding reversibly to the same site of the tubulin αβ-heterodimer as colchicine 2 and the allocolchinol, N-acetylcolchinol 4.

Cancer is a generic term for a large group of diseases where cells of the body lose their normal mechanisms for growth so that they grow in an uncontrolled way. One of the most common treatments of cancer is chemotherapy that aims to kill abnormal proliferating cells; however normal cells and other organs of the patients are also adversely affected. In practice, it¿s often difficult to maintain optimum chemotherapy doses that can maximise the abnormal cell killing as well as reducing side effects. The most chemotherapy drugs used in cancer treatment are toxic agents and usually have narrow therapeutic indices, dose levels in which these drugs significantly kill the cancerous cells are close to the levels which sometime cause harmful toxic side effects. To make the chemotherapeutic treatment effective, optimum drug scheduling is required to balance between the beneficial and toxic side effects of the cancer drugs. Conventional clinical methods very often fail to find drug doses that balance between these two due to their inherent conflicting nature. In this investigation, mathematical models for cancer chemotherapy are used to predict the number of tumour cells and control the tumour growth during treatment. A feedback control method is used so as to maintain certain level of drug concentrations at the tumour sites. Multi-objective Genetic Algorithm (MOGA) is then employed to find suitable solutions where drug resistances and drug concentrations are incorporated with cancer cell killing and toxic effects as design objectives. Several constraints and specific goal values were set for different design objectives in the optimisation process and a wide range of acceptable solutions were obtained trading off among different conflicting objectives. Abstract v In order to develop a multi-objective optimal control model, this study used proportional, integral and derivative (PID) and I-PD (modified PID with Integrator used as series) controllers based on Martin¿s growth model for optimum drug concentration to treat cancer. To the best of our knowledge, this is the first PID/I-PD based optimal chemotherapy control model used to investigate the cancer treatment. It has been observed that some solutions can reduce the cancer cells up to nearly 100% with much lower side effects and drug resistance during the whole period of treatment. The proposed strategy has been extended for more drugs and more design constraints and objectives. / Libyan Ministry of Higher Education

Brustkrebs ist die häufigste Krebstodesursache bei Frauen in den Industrienationen mit einer jährlich ansteigenden Neuerkrankungsrate (Senn und Niederberger 2002). Durch vorangegangene Untersuchungen wurde bereits deutlich, dass das Peptidhormon Relaxin unter in vitro Bedingungen maßgeblich zur Tumorprogression von Mammakarzinomen beiträgt (Binder et al. 2002). Die vorliegende Arbeit hat untersucht, ob Relaxin diese Wirkung auch in vivo auf Mammakarzinome ausübt. Relaxin ist ein multifunktionales Hormon. Es ist ein Aktivator verschiedenerWachstumsund Transkriptionsfaktoren (Samuel et al. 2007a) und nimmt eine Schlüsselfunktion im Bindegewebsstoffwechsel ein, indem es durch eine Steigerung der MMP-Expression zur bindegewebigen Erweichung führt (Unemori et al. 1996). Im Krebsgeschehen schafft das Peptidhormon damit die Voraussetzungen für Tumorwachstum und Metastasierung (Bingle et al. 2002). Für die Fragestellung der vorliegenden Arbeit wurde das Brustkrebsmodell der BalbneuT- Maus eingesetzt, die aufgrund der transgenen HER2-Überexpression spontan Mammakarzinome entwickelt. Es wurden 45 weibliche Tiere mit beginnendem Wachstum von Mammatumoren auf eine Relaxin- (n=22) und eine Kontrollgruppe (n=23) aufgeteilt. Den Tieren wurde über eine unter das Nackenfell implantierte osmotische Minipumpe (Fa. Alzet, Modell 2004; Kupertura, Kanada) im Falle der Relaxin-Gruppe Relaxin und im Falle der Kontrollgruppe isotone Natriumchloridlösung verabreicht. Danach wurden die Tiere 10-49 Tage beobachtet und daraufhin eingeschläfert. Es wurden die Tumoren, Biopsien von Leber, Lunge und Nieren sowie Blutproben entnommen. Um beurteilen zu können, ob die Tumoren der Relaxin-behandelten Tiere ein schnelleres Wachstum zeigten, wurden Tumorvolumina und -gewichte zu den unterschiedlichen Tötungszeitpunkten erfasst. Weiterhin wurden im Tumorgewebe immunhistochemisch der Proliferationsmarker Ki67, der Makrophagenmarker MAC 387, der Relaxinrezeptor RXFP1 sowie die Steroidhormonrezeptoren für 17!-Östradiol (ER) und Progesteron (PR) bestimmt. Zusätzlich wurde die RXFP1-spezifische mRNA molekularbiologisch im Tumorgewebe dargestellt. Außerdem wurden die peripheren Hormonkonzentrationen von Relaxin, 17!-Östradiol (E2) und Progesteron (P4) ermittelt. Die Ergebnisse der vorliegenden Arbeit konnten den Beweis erbringen, dass Relaxin auch in vivo dasWachstum von Mammakarzinomen unterstützt. Relaxin bewirkte im vorliegenden Experiment eine Rekrutierung von Tumor-assoziierten Makrophagen (TAMs) ins tumorumgebenden Bindegewebe. Dadurch erfolgte dort die Synthese verschiedener Faktoren und Enzyme, welche zur bindegewebigen Erweichung, Apoptosehemmung und zu einer gesteigerten Zellproliferation führten (Bingle et al. 2002; Devetzi et al. 2008). Weiterhin induzierte die exogene Relaxingabe eine vermehrte E2-Synthese, was sich ebenfalls wachstumsfördernd und apoptosehemmend auswirkte und somit die Tumorproliferation unterstützt hat (Catalano et al. 2009; Lewis-Wambi und Jordan 2009). Die Expression des RXFP1 im Tumorgewebe wurde durch Relaxin über eine gesteigerte E2- Synthese (Wilson et al. 2008) gefördert, ebenso wie die Expression des ER. Weiterhin führte Relaxin zu einer gesteigerten P4-Synthese und zur gesteigerten Expression des PR im Tumorgewebe über einen derzeit noch unbekannten Mechanismus. Aufgrund der maßgeblichen Bedeutung des Peptidhormons für das Progressionsverhalten von Mammakarzinomen kann die Bestimmung der Relaxinblutspiegel bei Brustkrebspatientinnen deshalb in Zukunft ein wichtiges Hilfsmittel bei der Wahl der richtigen Therapie und bei der Prognosebeurteilung werden.