Seminar "Quantitative Biomedicine"

• Place: Weierstrass-Institute for Applied Analysis and Stochastics
  Place: Mohrenstraße 39, 10117 Berlin
  Place: Erhard Schmidt Lecture Room (ESH)
• Time: Mondays (monthly), 2:00PM - 3:00PM
• Organizers: Alfonso Caiazzo, Michael Hintermüller, Karsten Tabelow, Barbara Wagner

The Lens of the Eye: Bidomain Model of an Osmotic Pump

The lens of the eye has no blood vessels to interfere with vision. The lens is far too large for diffusion to provide food and clear wastes. Experimental, theoretical and computational work has shown that the lens supports its own microcirculation. It is an osmotic pump. We introduce a general non-electro-neutral model that describes the steady state relationships among ion fluxes, water flow and electric field inside cells, and in the narrow extracellular spaces within the lens. Using asymptotic analysis, we derive a simplified model based on physiological data. The model reduces to the first generation analytical models. The full model explains additional data of some significance.

Machine learning of molecular sensitive spectral and image data

Molecular sensitive imaging modalities, like multimodal imaging, e.g. the combination of coherent-anti-Stokes Raman scattering (CARS), second-harmonic generation (SHG) and two-photon-excited fluorescence (TPEF), and Raman spectroscopic imaging feature a unique potential for disease diagnostics and treatment monitoring. In proof-of-principle studies the potential of these both imaging modalities for cancer detection and diagnostics of chronic inflammatory bowel diseases could be demonstrated. In order to utilize the huge potential of multimodal imaging and Raman spectroscopic imaging for diagnostic tasks powerful machine learning methods are necessary, which translate the experimental imaging data into medical information. This translation process is composed of image standardization, correction procedures to eliminate corrupting contributions within the acquired images, image enhancement methods and feature extraction procedures in the case of multimodal imaging. For Raman spectroscopic imaging advanced signal processing for correcting and standardizing the spectral data is necessary. After this so-called pre-processing was carried out, models like regression or classification methods can be applied to extract medical relevant information. This contribution shows, how the pre-processing have to be tailored to the measurement modalities and how the feature extraction has to be adapted to the samples and the specific diagnostic task to be solved.

Post-Turing tissue pattern formation: Insights from mathematical modelling

Cells and tissue are objects of the physical world, and therefore they obey the laws of physics and chemistry, notwithstanding the molecular complexity of biological systems. What are the mathematical principles that are at play in generating such complex entities from simple laws? Understanding the role of mechanical and mechano-chemical interactions in cell processes, tissue development, regeneration and disease has become a rapidly expanding research field in the life sciences.To reveal the patterning potential of mechano-chemical interactions, we have developed two classes of mathematical models coupling dynamics of diffusing molecular signals with a model of tissue deformation. First we derived a model based on energy minimisation that leads to 4-th order partial differential equations of evolution of infinitely thin deforming tissue (pseudo-3D model) coupled with a surface reaction-diffusion equation. The second approach (full-3D model) consists of a continuous model of large tissue deformation coupled with a discrete description of spatial distribution of cells to account for active deformation of single cells. The models account for a range of mechano-chemical feedbacks, such as signalling-dependent strain, stress, or tissue compression. Numerical simulations show ability of the proposed mechanisms to generate development of various spatio-temporal structures. We compare the resulting patterns of tissue invagination and evagination to those encountered in developmental biology. We discuss analytical and numerical challenges of the proposed models and compare them to the classical Turing patterns as well as reaction-diffusion ODE models coupling diffusion-based cell-to-cell communication with intracellular signalling.

Modelling and Simulation for Treatment Planning: CFD methods for valve treatment

In aging population, the prevalence of heart valve diseases and heart failure with >8% of the population in their 70s (valve disease) and 10% in their 80s (heart failure) is one of the most relevant diseases for the healthcare system in industrial countries. Both diseases are chronic and can amplify each other. Wrongly treated valve diseases can lead to severe heart failure and vice versa. The prognosis of heart failure is still very poor (6-year mortality rate >67%). CFD approach promises precise diagnosis without invasive procedures. Furthermore, CFD allows predictiv modelling allowing to support clinicians with treatment decision as well as treatment planing and optimization. Finally CFD approach promises risk and cost minimization. Current CFD abilities, challenges and requirements for CFD translation into the clinical practice are presented and discussed.

Fluid dynamical models for tissue engineering

Tissue engineers aim to grow tissues in vitro to replace those in the body that have been damaged through age, trauma or disease. A common approach is to seed cells within a scaffold which is then cultured in a bioreactor. The key challenge it to provide the appropriate mechanical and biochemical cellular environment that promotes tissue growth in vitro. Fluid flows have a key role to play in addressing this challenge, as they can provide mechanical cues to cells (e.g. via fluid shear and pressure), and enhance the delivery of nutrients and growth factors (via advection). In this talk, I will explore how mechanistic mathematical models, in combination with state-of-the art experimental studies, can provide quantitative insights into the interplay between the fluid flows and the resulting tissue growth. Quantitative understanding of this interplay offers the exciting potential to manipulate the experimental design (e.g. scaffold porosity, bioreactor operating conditions) to establish defined mechanical cues that enhance the generation of complex 3D tissues in vitro.

Selected Modeling Approaches for Biomedical Applications and Biorobotics Tools

The effective deployment of theranostic agents (including drugs), smart-materials-based systems and interfaces to target regions (prospectively) in the human body where to perform the sought actions also requires theoretical models and physical tools. Modeling the delivery and the (remote) actuation/stimulation of the aforementioned agents/systems/interfaces, in particular, permits to compensate for experimental conditions hard to characterize and to better interpret the experimental results, thus paving the way for quantitative therapy design and control. This is complemented by model-based design of related experimental devices, flexible tools able to safely navigate anatomical pathways, and miniaturized effectors. In this talk I will firstly present the solution to an inverse problem, namely to determine the velocity profile in a vessel cross-section starting from the flow-rate, which is relevant to pulsatile biological flows (blood and cerebro-spinal fluid flows), with application, e.g., to magnetic particle targeting. Then I will address numerical models for intrathecal drug-delivery (drug infusion in the cerebro-spinal fluid, also accounting for transport to the spinal cord) and simplified analytical models for intra-tissue drug-delivery (particle transport into porous/poroelastic media, with application to intratumoral thermotherapy). Finally, I will overview model-based approaches for: piezoelectric nanoparticle-mediated cell stimulation; real-scale physical models of the blood-brain barrier; flexible biorobotics probes; miniature (bioinspired) actuators and effectors.

Numerical methods for variability modeling and biomarkers design

Many phenomena are modeled by deterministic differential equations, whereas the observation of these phenomena, in particular in life science, exhibit an important inter-subject variability. We will address the following question: how the model can be adapted to reflect the variability observed in a population? We will present a non-parametric and non-intrusive procedure based on offline computations of the deterministic model. The algorithm infers the probability density function of uncertain parameters from the matching of the observable statistical moments at different points in the physical domain. This inverse procedure is improved by incorporating a point selection algorithm that both reduces its computational cost and increases its robustness. The method will be illustrated for different models, based on Ordinary or Partial Differential Equations. In particular, applications to experimental data sets in cardiac electrophysiology will be presented.
In biophysics and medicine, the system of interest is often studied by monitoring quantities, called biomarkers, extracted from measurements. These biomarkers convey some information about relevant hidden quantities, which can be seen as parameters of an underlying model. We propose a strategy to automatically design biomarkers to estimate a given parameter. Such biomarkers are chosen as the solution of a sparse optimization problem. We will show applications in electrophysiology where our algorithm provides composite biomarkers which improve the parameter estimation and the classification problems.

Biomechanical modeling of the heart, and cardiovascular system - From sarcomeres to organ / system, with experimental assessments and patient-specific clinical validations

Cardiac contraction originates at a subcellular - molecular, indeed - scale, within specific components of the cardiomyocytes (i.e. cardiac cells) called sarcomeres. This contractile behaviour then needs to be integrated at the organ level, namely, with a specific structure and shape. Furthermore, this organ crucially interacts with other physiological systems, the first of which being blood circulation via the cardiac function itself, and also the nervous system that controls the heart via various regulation mechanisms, and these interactions must be adequately represented in order to obtain accurate and predictive model simulations. This presentation will provide an overview of the recent advances on cardiac modeling achieved in the M3DISIM group, with a particular focus on the key multiscale, multi-physics and integrated system modeling aspects that need to be addressed, with many associated challenges pertaining to numerical methods, model validation, and inverse problems, in particular.

Advances in Cardiac and Quantitative MRI

Cardiac Magnetic Resonance (CMR) imaging has become a clinically useful tool to assess different physiological parameter in one examination. The widespread use of cardiac MRI, however, is often hampered by the complexity of MRI and the long acquisition time. For this novel, 3D MR-acquisitions have been developed to obtain anatomical, functional and flow information of the whole heart. Fast acquisition can be achieved by advanced motion compensation and new reconstruction approaches. Furthermore, a more quantitative oriented diagnosis can be achieved by pixel-wise measurement of parameters. For instance, mapping of the relaxation times allows the assessment of tissue characteristics and the estimation of contrast agent concentration. In this talk an overview on the different technical developments are given and clinical applications are shown.

Beyond Poisson-Boltzmann : charge correlation effects in DNA adsorption and transport through nanopores

In soft matter systems electrostatic effects are often of utmost importance. Their mathematical description is commonly based on mean-field type theories, the standard approach being the Poisson-Boltzmann equation. This equation is known to fail if charge correlation effects, e.g., due to the presence of image charges at interfaces, become important. In this talk I will explain how one can go beyond the Poisson-Boltzmann equation in order to treat such mechanisms. As two exemplary applications I will discuss the correlation-induced adsorption of DNA on like-charged surfaces and the conversion of ionic currents in DNA translocation through nanopores.

Explorations into Ultrahigh Field Magnetic Resonance
Where Physics, Mathematics, Biology and Medicine Meet

The development of ultrahigh field magnetic resonance (UHF-MR) is moving forward at an amazing speed that is breaking through technical barriers almost as fast as they appear. UHF-MR has a staggering number of potential uses in neuroscience, neurology, radiology, cardiology, internal medicine, physiology, oncology, nephrology, ophthalmology and other related clinical fields. With almost 40,000 MR examinations already performed at 7.0 Tesla, the reasons for moving UHF-MR into clinical applications are more compelling than ever ... [>> read more as PDF]