C Mathematical and Quantitative Methods
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Landslides are frequent natural hazards in rugged terrain, when the resisting frictional force of the surface of rupture yields to the gravitational force. These forces are functions of geological and morphological factors, such as angle of internal friction, local slope gradient or curvature, which remain static over hundreds of years; whereas more dynamic triggering events, such as rainfall and earthquakes, compromise the force balance by temporarily reducing resisting forces or adding transient loads. This thesis investigates landslide distribution and orientation due to landslide triggers (e.g. rainfall) at different scales (6-4∙10^5 km^2) and aims to link rainfall movement with the landslide distribution. It additionally explores the local impacts of the extreme rainstorms on landsliding and the role of precursory stability conditions that could be induced by an earlier trigger, such as an earthquake.
Extreme rainfall is a common landslide trigger. Although several studies assessed rainfall intensity and duration to study the distribution of thus triggered landslides, only a few case studies quantified spatial rainfall patterns (i.e. orographic effect). Quantifying the regional trajectories of extreme rainfall could aid predicting landslide prone regions in Japan. To this end, I combined a non-linear correlation metric, namely event synchronization, and radial statistics to assess the general pattern of extreme rainfall tracks over distances of hundreds of kilometers using satellite based rainfall estimates. Results showed that, although the increase in rainfall intensity and duration positively correlates with landslide occurrence, the trajectories of typhoons and frontal storms were insufficient to explain landslide distribution in Japan. Extreme rainfall trajectories inclined northwestwards and were concentrated along some certain locations, such as coastlines of southern Japan, which was unnoticed in the landslide distribution of about 5000 rainfall-triggered landslides. These landslides seemed to respond to the mean annual rainfall rates.
Above mentioned findings suggest further investigation on a more local scale to better understand the mechanistic response of landscape to extreme rainfall in terms of landslides. On May 2016 intense rainfall struck southern Germany triggering high waters and landslides. The highest damage was reported at the Braunsbach, which is located on the tributary-mouth fan formed by the Orlacher Bach. Orlacher Bach is a ~3 km long creek that drains a catchment of about ~6 km^2. I visited this catchment in June 2016 and mapped 48 landslides along the creek. Such high landslide activity was not reported in the nearby catchments within ~3300 km^2, despite similar rainfall intensity and duration based on weather radar estimates. My hypothesis was that several landslides were triggered by rainfall-triggered flash floods that undercut hillslope toes along the Orlacher Bach. I found that morphometric features such as slope and curvature play an important role in landslide distribution on this micro scale study site (<10 km^2). In addition, the high number of landslides along the Orlacher Bach could also be boosted by accumulated damages on hillslopes due karst weathering over longer time scales.
Precursory damages on hillslopes could also be induced by past triggering events that effect landscape evolution, but this interaction is hard to assess independently from the latest trigger. For example, an earthquake might influence the evolution of a landscape decades long, besides its direct impacts, such as landslides that follow the earthquake. Here I studied the consequences of the 2016 Kumamoto Earthquake (MW 7.1) that triggered some 1500 landslides in an area of ~4000 km^2 in central Kyushu, Japan. Topography, i.e. local slope and curvature, both amplified and attenuated seismic waves, thus controlling the failure mechanism of those landslides (e.g. progressive). I found that topography fails in explaining the distribution and the preferred orientation of the landslides after the earthquake; instead the landslides were concentrated around the northeast of the rupture area and faced mostly normal to the rupture plane. This preferred location of the landslides was dominated mainly by the directivity effect of the strike-slip earthquake, which is the propagation of wave energy along the fault in the rupture direction; whereas amplitude variations of the seismic radiation altered the preferred orientation. I suspect that the earthquake directivity and the asymmetry of seismic radiation damaged hillslopes at those preferred locations increasing landslide susceptibility. Hence a future weak triggering event, e.g. scattered rainfall, could further trigger landslides at those damaged hillslopes.
Neuroinflammatory and neurodegenerative diseases such as Parkinson's (PD) and multiple sclerosis (MS) often result in a severe impairment of the patient´s quality of life. Effective therapies for the treatment are currently not available, which results in a high socio-economic burden. Due to the heterogeneity of the disease subtypes, stratification is particularly difficult in the early phase of the disease and is mainly based on clinical parameters such as neurophysiological tests and central nervous imaging. Due to good accessibility and stability, blood and cerebrospinal fluid metabolite markers could serve as surrogates for neurodegenerative processes. This can lead to an improved mechanistic understanding of these diseases and further be used as "treatment response" biomarkers in preclinical and clinical development programs. Therefore, plasma and CSF metabolite profiles will be identified that allow differentiation of PD from healthy controls, association of PD with dementia (PDD) and differentiation of PD subtypes such as akinetic rigid and tremor dominant PD patients. In addition, plasma metabolites for the diagnosis of primary progressive MS (PPMS) should be investigated and tested for their specificity to relapsing-remitting MS (RRMS) and their development during PPMS progression.
By applying untargeted high-resolution metabolomics of PD patient samples and in using random forest and partial least square machine learning algorithms, this study identified 20 plasma metabolites and 14 CSF metabolite biomarkers. These differentiate against healthy individuals with an AUC of 0.8 and 0.9 in PD, respectively. We also identify ten PDD specific serum metabolites, which differentiate against healthy individuals and PD patients without dementia with an AUC of 1.0, respectively. Furthermore, 23 akinetic-rigid specific plasma markers were identified, which differentiate against tremor-dominant PD patients with an AUC of 0.94 and against healthy individuals with an AUC of 0.98. These findings also suggest more severe disease pathology in the akinetic-rigid PD than in tremor dominant PD. In the analysis of MS patient samples a partial least square analysis yielded predictive models for the classification of PPMS and resulted in 20 PPMS specific metabolites. In another MS study unknown changes in human metabolism were identified after administration of the multiple sclerosis drug dimethylfumarate, which is used for the treatment of RRMS. These results allow to describe and understand the hitherto completely unknown mechanism of action of this new drug and to use these findings for the further development of new drugs and targets against RRMS.
In conclusion, these results have the potential for improved diagnosis of these diseases and improvement of mechanistic understandings, as multiple deregulated pathways were identified. Moreover, novel Dimethylfumarate targets can be used to aid drug development and treatment efficiency. Overall, metabolite profiling in combination with machine learning identified as a promising approach for biomarker discovery and mode of action elucidation.
Monoclonal antibodies (mAbs) are an innovative group of drugs with increasing clinical importance in oncology, combining high specificity with generally low toxicity. There are, however, numerous challenges associated with the development of mAbs as therapeutics. Mechanistic understanding of factors that govern the pharmacokinetics (PK) of mAbs is critical for drug development and the optimisation of effective therapies; in particular, adequate dosing strategies can improve patient quality life and lower drug cost. Physiologically-based PK (PBPK) models offer a physiological and mechanistic framework, which is of advantage in the context of animal to human extrapolation. Unlike for small molecule drugs, however, there is no consensus on how to model mAb disposition in a PBPK context. Current PBPK models for mAb PK hugely vary in their representation of physiology and parameterisation. Their complexity poses a challenge for their applications, e.g., translating knowledge from animal species to humans.
In this thesis, we developed and validated a consensus PBPK model for mAb disposition taking into account recent insights into mAb distribution (antibody biodistribution coefficients and interstitial immunoglobulin G (IgG) pharmacokinetics) to predict tissue PK across several pre-clinical species and humans based on plasma data only. The model allows to a priori predict target-independent (unspecific) mAb disposition processes as well as mAb disposition in concentration ranges, for which the unspecific clearance (CL) dominates target-mediated CL processes. This is often the case for mAb therapies at steady state dosing.
The consensus PBPK model was then used and refined to address two important problems:
1) Immunodeficient mice are crucial models to evaluate mAb efficacy in cancer therapy. Protection from elimination by binding to the neonatal Fc receptor is known to be a major pathway influencing the unspecific CL of both, endogenous and therapeutic IgG. The concentration of endogenous IgG, however, is reduced in immunodeficient mouse models, and this effect on unspecific mAb CL is unknown, yet of great importance for the extrapolation to human in the context of mAb cancer therapy.
2) The distribution of mAbs into solid tumours is of great interest. To comprehensively investigate mAb distribution within tumour tissue and its implications for therapeutic efficacy, we extended the consensus PBPK model by a detailed tumour distribution model incorporating a cell-level model for mAb-target interaction. We studied the impact of variations in tumour microenvironment on therapeutic efficacy and explored the plausibility of different mechanisms of action in mAb cancer therapy.
The mathematical findings and observed phenomena shed new light on therapeutic utility and dosing regimens in mAb cancer treatment.