Two fluid numerical model for coastal applications

Wave breaking is an important coastal process, influencing hydro-morphodynamic processes such as turbulence generation and wave energy dissipation, run-up on the beach and overtopping of coastal defence structures. During breaking, waves are complex mixtures of air and water (“white water”) whose properties affect velocity and pressure fields in the vicinity of the free surface and, depending on the breaker characteristics, different mechanisms for air entrainment are usually observed. Several laboratory experiments have been performed to investigate the role of air bubbles in the wave breaking process (Chanson & Cummings, 1994, among others) and in wave loading on vertical wall (Oumeraci et al., 2001; Peregrine et al., 2006, among others), showing that the air phase is not negligible since the turbulent energy dissipation involves air-water mixture. The recent advancement of numerical models has given valuable insights in the knowledge of wave transformation and interaction with coastal structures. Among these models, some solve the RANS equations coupled with a free-surface tracking algorithm and describe velocity, pressure, turbulence and vorticity fields (Lara et al. 2006 a-b, Clementi et al., 2007). The single-phase numerical model, in which the constitutive equations are solved only for the liquid phase, neglects effects induced by air movement and trapped air bubbles in water. Numerical approximations at the free surface may induce errors in predicting breaking point and wave height and moreover, entrapped air bubbles and water splash in air are not properly represented. The aim of the present thesis is to develop a new two-phase model called COBRAS2 (stands for Cornell Breaking waves And Structures 2 phases), that is the enhancement of the single-phase code COBRAS0, originally developed at Cornell University (Lin & Liu, 1998). In the first part of the work, both fluids are considered as incompressible, while the second part will treat air compressibility modelling. The mathematical formulation and the numerical resolution of the governing equations of COBRAS2 are derived and some model-experiment comparisons are shown. In particular, validation tests are performed in order to prove model stability and accuracy. The simulation of the rising of a large air bubble in an otherwise quiescent water pool reveals the model capability to reproduce the process physics in a realistic way. Analytical solutions for stationary and internal waves are compared with corresponding numerical results, in order to test processes involving wide range of density difference. Waves induced by dam-break in different scenarios (on dry and wet beds, as well as on a ramp) are studied, focusing on the role of air as the medium in which the water wave propagates and on the numerical representation of bubble dynamics. Simulations of solitary and regular waves, characterized by both spilling and plunging breakers, are analyzed with comparisons with experimental data and other numerical model in order to investigate air influence on wave breaking mechanisms and underline model capability and accuracy. Finally, modelling of air compressibility is included in the new developed model and is validated, revealing an accurate reproduction of processes. Some preliminary tests on wave impact on vertical walls are performed: since air flow modelling allows to have a more realistic reproduction of breaking wave propagation, the dependence of wave breaker shapes and aeration characteristics on impact pressure values is studied and, on the basis of a qualitative comparison with experimental observations, the numerical simulations achieve good results.

Use of VEGFR-2 targeted microbubbles (BR55, Bracco imaging) for the early ultrasound evaluation of response to antiangiogenic treatment in a xenograft model of hepatocarcinoma

Aim: To evaluate the early response to treatment to an antiangiogenetic drug (sorafenib) in a heterotopic murine model of hepatocellular carcinoma (HCC) using ultrasonographic molecular imaging. Material and Methods: the xenographt model was established injecting a suspension of HuH7 cells subcutaneously in 19 nude mice. When tumors reached a mean diameter of 5-10 mm, they were divided in two groups (treatment and vehicle). The treatment group received sorafenib (62 mg/kg) by daily oral gavage for 14 days. Molecular imaging was performed using contrast enhanced ultrasound (CEUS), by injecting into the mouse venous circulation a suspension of VEGFR-2 targeted microbubbles (BR55, kind gift of Bracco Swiss, Geneve, Switzerland). Video clips were acquired for 6 minutes, then microbubbles (MBs) were destroyed by a high mechanical index (MI) impulse, and another minute was recorded to evaluate residual circulating MBs. The US protocol was repeated at day 0,+2,+4,+7, and +14 from the beginning of treatment administration. Video clips were analyzed using a dedicated software (Sonotumor, Bracco Swiss) to quantify the signal of the contrast agent. Time/intensity curves were obtained and the difference of the mean MBs signal before and after high MI impulse (Differential Targeted Enhancement-dTE) was calculated. dTE represents a numeric value in arbitrary units proportional to the amount of bound MBs. At day +14 mice were euthanized and the tumors analyzed for VEGFR-2, pERK, and CD31 tissue levels using western blot analysis. Results: dTE values decreased from day 0 to day +14 both in treatment and vehicle groups, and they were statistically higher in vehicle group than in treatment group at day +2, at day +7, and at day +14. With respect to the degree of tumor volume increase, measured as growth percentage delta (GPD), treatment group was divided in two sub-groups, non-responders (GPD>350%), and responders (GPD<200%). In the same way vehicle group was divided in slow growth group (GPD<400%), and fast growth group (GPD>900%). dTE values at day 0 (immediately before treatment start) were higher in non-responders than in responders group, with statistical difference at day 2. While dTE values were higher in the fast growth group than in the slow growth group only at day 0. A significant positive correlation was found between VEGFR-2 tissue levels and dTE values, confirming that level of BR55 tissue enhancement reflects the amount of tissue VEGF receptor. Conclusions: the present findings show that, at least in murine experimental models, CEUS with BR55 is feasable and appears to be a useful tool in the prediction of tumor growth and response to sorafenib treatment in xenograft HCC.

Changes in tumor stiffness for early prediction of tumor response to sorafenib: a proof-of-concept study with elastosonography in an animal model of Hepatocellular Carcinoma (HCC)

Background and aims: Sorafenib is the reference therapy for advanced Hepatocellular Carcinoma (HCC). No method exists to predict in the very early period subsequent individual response. Starting from the clinical experience in humans that subcutaneous metastases may rapidly change consistency under sorafenib and that elastosonography a new ultrasound based technique allows assessment of tissue stiffness, we investigated the role of elastonography in the very early prediction of tumor response to sorafenib in a HCC animal model. Methods: HCC (Huh7 cells) subcutaneous xenografting in mice was utilized. Mice were randomized to vehicle or treatment with sorafenib when tumor size was 5-10 mm. Elastosonography (Mylab 70XVG, Esaote, Genova, Italy) of the whole tumor mass on a sagittal plane with a 10 MHz linear transducer was performed at different time points from treatment start (day 0, +2, +4, +7 and +14) until mice were sacrified (day +14), with the operator blind to treatment. In order to overcome variability in absolute elasticity measurement when assessing changes over time, values were expressed in arbitrary units as relative stiffness of the tumor tissue in comparison to the stiffness of a standard reference stand-off pad lying on the skin over the tumor. Results: Sor-treated mice showed a smaller tumor size increase at day +14 in comparison to vehicle-treated (tumor volume increase +192.76% vs +747.56%, p=0.06). Among Sor-treated tumors, 6 mice showed a better response to treatment than the other 4 (increase in volume +177% vs +553%, p=0.011). At day +2, median tumor elasticity increased in Sor-treated group (+6.69%, range –30.17-+58.51%), while decreased in the vehicle group (-3.19%, range –53.32-+37.94%) leading to a significant difference in absolute values (p=0.034). From this time point onward, elasticity decreased in both groups, with similar speed over time, not being statistically different anymore. In Sor-treated mice all 6 best responders at day 14 showed an increase in elasticity at day +2 (ranging from +3.30% to +58.51%) in comparison to baseline, whereas 3 of the 4 poorer responders showed a decrease. Interestingly, these 3 tumours showed elasticity values higher than responder tumours at day 0. Conclusions: Elastosonography appears a promising non-invasive new technique for the early prediction of HCC tumor response to sorafenib. Indeed, we proved that responder tumours are characterized by an early increase in elasticity. The possibility to distinguish a priori between responders and non responders based on the higher elasticity of the latter needs to be validated in ad-hoc experiments as well as a confirmation of our results in humans is warranted.

A Unified Model for XVA, including Interest Rates and Rating

We start in Chapter 2 to investigate linear matrix-valued SDEs and the Itô-stochastic Magnus expansion. The Itô-stochastic Magnus expansion provides an efficient numerical scheme to solve matrix-valued SDEs. We show convergence of the expansion up to a stopping time τ and provide an asymptotic estimate of the cumulative distribution function of τ. Moreover, we show how to apply it to solve SPDEs with one and two spatial dimensions by combining it with the method of lines with high accuracy. We will see that the Magnus expansion allows us to use GPU techniques leading to major performance improvements compared to a standard Euler-Maruyama scheme. In Chapter 3, we study a short-rate model in a Cox-Ingersoll-Ross (CIR) framework for negative interest rates. We define the short rate as the difference of two independent CIR processes and add a deterministic shift to guarantee a perfect fit to the market term structure. We show how to use the Gram-Charlier expansion to efficiently calibrate the model to the market swaption surface and price Bermudan swaptions with good accuracy. We are taking two different perspectives for rating transition modelling. In Section 4.4, we study inhomogeneous continuous-time Markov chains (ICTMC) as a candidate for a rating model with deterministic rating transitions. We extend this model by taking a Lie group perspective in Section 4.5, to allow for stochastic rating transitions. In both cases, we will compare the most popular choices for a change of measure technique and show how to efficiently calibrate both models to the available historical rating data and market default probabilities. At the very end, we apply the techniques shown in this thesis to minimize the collateral-inclusive Credit/ Debit Valuation Adjustments under the constraint of small collateral postings by using a collateral account dependent on rating trigger.

Developing a radiomic based machine learning model to identify patients with resected non-small-cell lung cancer at high risk of relapse

Background There is a wide variation of recurrence risk of Non-small-cell lung cancer (NSCLC) within the same Tumor Node Metastasis (TNM) stage, suggesting that other parameters are involved in determining this probability. Radiomics allows extraction of quantitative information from images that can be used for clinical purposes. The primary objective of this study is to develop a radiomic prognostic model that predicts a 3 year disease free-survival (DFS) of resected Early Stage (ES) NSCLC patients. Material and Methods 56 pre-surgery non contrast Computed Tomography (CT) scans were retrieved from the PACS of our institution and anonymized. Then they were automatically segmented with an open access deep learning pipeline and reviewed by an experienced radiologist to obtain 3D masks of the NSCLC. Images and masks underwent to resampling normalization and discretization. From the masks hundreds Radiomic Features (RF) were extracted using Py-Radiomics. Hence, RF were reduced to select the most representative features. The remaining RF were used in combination with Clinical parameters to build a DFS prediction model using Leave-one-out cross-validation (LOOCV) with Random Forest. Results and Conclusion A poor agreement between the radiologist and the automatic segmentation algorithm (DICE score of 0.37) was found. Therefore, another experienced radiologist manually segmented the lesions and only stable and reproducible RF were kept. 50 RF demonstrated a high correlation with the DFS but only one was confirmed when clinicopathological covariates were added: Busyness a Neighbouring Gray Tone Difference Matrix (HR 9.610). 16 clinical variables (which comprised TNM) were used to build the LOOCV model demonstrating a higher Area Under the Curve (AUC) when RF were included in the analysis (0.67 vs 0.60) but the difference was not statistically significant (p=0,5147).