Here you can find descriptions of Tampere University's FAME – Flagship of Advanced Mathematics for Sensing, Imaging and Modelling Doctoral education pilot's research topics currently available.The open positions are divided into three themes and nine possible topics described below. The preferred theme and topic should be mentioned in the application. If more than one theme or topic is chosen, their priority of the themes/topics should be mentioned. Please apply via <a href="https://tuni.rekrytointi.com/paikat/index.php?jid=2389&amp;key=&amp;o=A_RJ&amp;rspvt=740zvoqjwqo048w84c8osw0k8gogwow">our recruiting system</a>.

This theme revolves around the advancement of non-invasive diagnostic tools and treatment planning for neurological conditions, particularly epilepsy, through enhanced electrophysiological imaging and stimulation techniques. It includes the development of novel mathematical and computational methods to improve the accuracy of EEG/MEG source localization, the exploration of temporal interference stimulation as a precise brain stimulation method, and the use of electrical impedance tomography (EIT) for stroke assessment. These projects aim to refine our understanding and manipulation of brain activity, offering potential improvements in the clinical management of neurological disorders. The interdisciplinary approach, requiring advanced computational, mathematical, and engineering skills, underscores the complexity of brain function and the innovative strategies being pursued to address its disorders.

Theme description

This PhD research project focuses on enhancing the precision of epileptic source localization using EEG data through the integration of standardized Kalman Filtering (KF) and sLORETA weighting techniques. The project aims to leverage the temporal dynamics captured by Kalman Filtering and the spatial resolution improvements offered by sLORETA weighting to address the challenges of localizing epileptic sources, especially in scenarios involving deep brain areas and significant noise levels.

Key objectives include advancing the theoretical foundations of Kalman Filtering within EEG source localization, developing an integrated approach that combines KF with sLORETA weighting for better accuracy, and specifically improving the method's performance in noise handling and deep source localization. The research will entail software development for implementing the integrated method, followed by validation studies using both simulated and real-world EEG data to demonstrate its effectiveness compared to existing localization methods.

The anticipated outcomes encompass the creation of a novel, more accurate method for non-invasive epilepsy diagnostics, validated through comprehensive studies, and encapsulated in a user-friendly software tool optimized for clinical and research applications.This work is expected to significantly contribute to epilepsy treatment planning, potentially leading to improved surgical outcomes and patient care for those with drug-resistant epilepsy.

Skills required: advanced mathematical and statistical modeling capabilities, proficiency in computational methods and numerical optimization, strong programming skills, particularly in MATLAB or Python, understanding principles of EEG signal processing and neurophysiology, data analysis expertise.

Topic 1: Spatio-temporal electro/magnetoencephalographic source localization via standardized approaches

This PhD research project focuses on developing advanced conductance models for Deep Brain Stimulation (DBS), interference stimulation, and monitoring. The goal is to improve techniques for source timing and localization in clinical and research settings.&nbsp;The research aims to enhance the precision and effectiveness of DBS by refining the models that describe electrical conductance in brain tissues and improving methods for monitoring and interference stimulation. Key objectives include: (1) developing conductance models that accurately reflect the electrical properties of brain tissues during DBS and interference stimulation, (2) enhancing source timing and localization techniques through improved computational methods, (3) integrating these models into clinical practice to improve the outcomes of DBS therapy for various neurological conditions. The anticipated outcomes will contribute significantly to the field of neuroengineering, providing new tools and techniques for more effective and precise DBS interventions.&nbsp;Skills required: strong background in electrical and biomedical engineering, proficiency in computational modeling and numerical methods, experience with DBS technologies and neurophysiological monitoring, strong programming skills, particularly in MATLAB or Python, understanding of signal processing and neurophysiology.&nbsp;

Topic 14 (MET): Development of conductance models for DBS, interference stimulation and monitoring to improve source timing and localization techniques

This PhD research project aims to investigate the anatomical and functional connectivity in patients undergoing Deep Brain Stimulation (DBS) treatment. The primary objective is to understand how DBS affects brain connectivity and how these changes correlate with clinical outcomes. This research will contribute to the optimization of DBS therapies, enhancing their effectiveness and predictability for various neurological conditions.&nbsp;Key objectives include: (1) mapping anatomical connectivity in DBS patients using advanced imaging techniques, (2) analyzing functional connectivity changes pre- and post-DBS treatment, (3) correlating connectivity changes with clinical outcomes to identify biomarkers for DBS efficacy. The anticipated outcomes will provide deeper insights into the mechanisms of DBS, leading to improved patient selection, treatment planning, and overall therapeutic outcomes.&nbsp;Skills required: strong background in neuroimaging and neuroscience, proficiency in data analysis and statistical modeling, experience with imaging modalities such as MRI and fMRI, strong programming skills, particularly in Python or MATLAB, understanding of DBS technologies and neurophysiological principles.&nbsp;

Topic 15 (MET): Anatomical Connectivity and Functional Connectivity in DBS Patients

Theme I: Electrophysiological Stimulation and Imaging of the Brain

This theme highlights the application of computational modeling and advanced imaging techniques across various biological and biomedical contexts, from forest and tree structure reconstruction using LiDAR technology for forest and ecology research &nbsp;to the simulation of blood flow and its impact on neural activity. Projects under this theme seek to bridge the gap between detailed data collection (using lidar, etc.) and the actionable insights required for environmental conservation, improved medical diagnostics, and understanding complex biological processes like blood circulation and cancer tissue analysis. The emphasis on machine learning, statistical modeling, and the integration of diverse data types reflects a broader trend toward interdisciplinary innovation in tackling pressing challenges in biology and medicine.

This research aims to offer a novel approach to investigating blood flow and molecular transport in deformable arteries by considering the fluid (blood) and the structure (vessel) at the same time, as well as the impact of this circulation on neurons. To explore this subject, Tampere University has expertise in modelling blood flow and its effect on the electrical conductivity of brain tissue. Based on this new modelling framework, the objective of the project is to develop the current mathematical model and investigate the effect of blood flow on the neurovascular system. Capillaries deliver oxygen and energy (ATP) to neurons and remove waste products. Astrocytic functions regulate the extracellular space around neurons known as neuro-vascular coupling. Thus, the objective of the project is to determine how capillary blood flow and astrocytic functions affect the frequency of neuronal activity. Blood is a non-Newtonian fluid that is governed by the Navier-Stokes equation and the continuity equation for solving blood flow problems.In this study, we will focus on the derivation that blood vessels are not rigid tubes. The cerebrovascular network, which is made up of approximately 100 billion vessels, or 400 miles, with intricate topologies, complex geometries, and networks across spatial scales (i.e., vessel diameters ranging from micrometers to millimeters), transports essential molecules like glucose and oxygen to and eliminates metabolic waste products like carbon dioxide and amyloid from approximately 200 billion brain cells (both neurons and non-neurons). Blood microcirculation connects a dense capillary network to arterioles and venules, supplying neurons with oxygen and eliminating their neurotoxic waste. Skills required: We are seeking PhD students who have a background in applied mathematics and physics, particularly fluid dynamics or related fields; proficiency in computational methods and numerical optimization; strong programming skills, particularly in MATLAB or Python; and collaboration skills for international and interdisciplinary teamwork.

Topic 6: Modelling cerebral capillary blood flow and its impact on neural activity

Biopsies – small tissue samples – are taken for various clinical diagnostics concerning e.g. cancer and bowel diseases. These are normally sliced to micrometre thin specimen, stained, and imaged with microscope. These provide huge histological 2D images of one slice of the 3D sample. Methods to assess the entire sample are crucially needed. Some developments in AI based image analysis and stacking of the histological 2D images to gain the 3D structure are underway. We have developed X-ray micro-CT imaging and provided promising results for genuine 3D imaging of the sample. However, this method is relatively slow for clinical use and lacks some details needed. We propose to integrate various 3D imaging platforms namely micro-CT, synchrotron tomography, and various optical imaging tools with mathematical modelling, tomography, and AI methods to overcome these for future hybrid 3D imaging methods. The candidate will work with our clinical and imaging collaborators and mathematical modellers to develop these tools. Skills required: Understanding of physical and mathematics principles, good programming skills and good understanding of deep learning are great advantages.

Topic 7 (MET): Multiscale hybrid 3d imaging of cancer biopsies

The goal of this PhD research project is to develop better modeling tools for tree structure modeling and measurements. With better forest measurements, we can better understand forest ecosystems and, for example, their carbon cycle.&nbsp;Lidar or laser scanning is a 3D measurement technique where the visible surfaces of surroundings of the scanner are sampled with 3D point clouds. Geometric shapes and dimensions, such as diameters, areas and closed volumes, can be measured from the point cloud data. Objects to be measured can be trees in a forest, which can be modeled as collections of simple shapes such as cylinders. Methods have been published to do this, but they rely on optimizing the input parameters so that each modeling is not based on previous reconstructions.&nbsp;In this project, we develop methods for modeling the 3D structure of trees from laser scanner data. In particular, we investigate how to make the reconstruction of the model adaptive and learning-based, so that information from previous reconstructions is used to guide the reconstruction process.Skills required:&nbsp;Good programming skills, e.g. in Python or MATLAB, strong background and understanding of deep learning and data science, proficiency in numerical and statistical modeling.

Topic 11 (ITC): Adaptive and learning based quantitive structure tree model reconstruction

This PhD research project is centered on the control of mathematical models of fluid flow processes, with a specific focus on blood flow in the brain.&nbsp;The primary objective is to develop innovative methods for manipulating the behavior of solutions to nonlinear partial differential equation (PDE) models that describe these flow processes through the use of external control signals.&nbsp;This research is particularly driven by the potential applications in blood flow control, aiming to apply the general theoretical findings to specific blood flow models. The project will explore several critical areas: (1) developing new control methods for nonlinear PDE models of fluid flow. (2) applying these methods to blood flow models to influence and regulate blood flow within the brain. (3) advancing the theoretical foundations of mathematical control theory as applied to fluid dynamics. The anticipated outcomes include the creation of advanced control techniques for fluid flow models, validated through rigorous mathematical analysis and practical applications. These techniques could have significant implications for medical and engineering fields, particularly in improving blood flow management and treatment strategies in clinical settings.&nbsp;Skills required:&nbsp;strong background in mathematical analysis, particularly functional analysis and the theory of partial differential equations, experience in control theory or control engineering, proficiency in MATLAB.&nbsp;

Topic 12 (ITC): Control of fluid flow models

This PhD research project focuses on advancing the field of cardiovascular research through the development of computer models and simulations of the electromechanical function of the heart. Current models lack the ability to describe the biological feedback mechanisms that link changes in stimuli and surrounding conditions to gene expression and cellular function.&nbsp;This project aims to fill this gap by integrating phenotypic plasticity into cardiomyocyte models. Key objectives of the research include: (1) extending human cardiomyocyte models to include descriptions of energy production and consumption, (2) integrating biochemical models of gene expression dynamics into cardiomyocyte models, (3) employing the novel modelling framework to study maladaptive changes in cell and tissue function that lead to arrhythmias and contractile dysfunction, (4) investigating disease mechanisms of hypertrophic cardiomyopathy and exploring potential drug targets. The anticipated outcomes will significantly enhance the predictive and explanatory value of cardiac models, benefiting digital twin technology and aiding in the simulation of age-dependent changes and disease progression.&nbsp;Skills required: strong scientific programming skills (e.g., Python, MATLAB), expertise in optimization and parameterization, proficiency in numerical methods, understanding of cardiac physiology, basic knowledge of machine learning.&nbsp;

Topic 13 (MET): Computer modelling and simulations of phenotypic plasticity in electromechanical function of the heart

Theme II: Modelling and Imaging in Biology and Biomedicine

The third theme extends the application of inverse modeling techniques beyond traditional domains, exploring their utility in diverse fields such as augmented and alternative communication (AAC) systems and asteroid exploration. It encompasses projects aimed at making AAC systems more responsive to user needs through multimodal sensor inputs and improving our understanding of asteroid interiors to advance space exploration. These endeavors illustrate the versatility of inverse modeling as a tool for extracting detailed information from complex systems, whether enhancing communication aids for individuals with disabilities or probing the mysteries of the solar system. The focus on interdisciplinary collaboration and the development of innovative methodologies underscores the transformative potential of inverse modeling across a wide range of applications.

This project offers a unique opportunity for a PhD student to contribute to a cutting-edge space mission, advancing the knowledge of asteroid interior structures and the broader application of non-invasive imaging technologies. The aim is to conduct an exploratory study for radar tomography of Dimorphos, the asteroid moon of 65803 Didymos, aiming to leverage and validate full-wave inversion approaches within the context of the Juventas Radar (JuRa) experiment, part of ESA's HERA mission. The investigation into the internal structures of small Solar System bodies (SSSBs) like Dimorphos is of significant interest due to its implications for understanding the Solar System's collisional history, where direct observational data are sparse.

The project involves a comprehensive approach, encompassing theoretical and computational modelling, experimental validation through high-precision analogue models, and sophisticated data analysis techniques. 

Key aspects of the PhD student’s work will include developing numerical models for simulating RT data that accommodate the complex shape and internal configurations of Dimorphos, using high-performance computing resources to manage the significant computational load. Further, the student will apply and refine various full-wave inversion techniques to reconstruct Dimorphos' internal dielectric permittivity structure from RT data. This task may incorporate the use of machine learning for enhancing the ability to differentiate between internal structures, such as voids, layers, or fractures within the asteroid.

The interdisciplinary nature of this work spans applied mathematics, space physics, computational science, and electrical engineering, offering a rich domain for innovation and scientific discovery. Collaboration with an international team of scientists and contribution to the collective efforts of the JuRa workgroup are integral to this project. The student's findings will be shared with the broader scientific community through publications and presentations, contributing valuable insights to the fields of planetary science and radar tomography. 

Skills required: applied mathematics and physics, particularly in inverse problems and wave propagation, computational science and numerical modelling skills. proficiency in high-performance computing (HPC) environments, programming skills in MATLAB, Python, C++, and CUDA, knowledge of signal processing and radar data analysis, understanding of space physics and planetary science, collaboration skills for international and interdisciplinary teamwork.

Doctoral Education Pilot for Advanced Mathematics for Sensing, Imaging and Modelling (FAME): themes and research topics

Theme I: Electrophysiological Stimulation and Imaging of the Brain

Theme description

Topic 1: Spatio-temporal electro/magnetoencephalographic source localization via standardized approaches

Topic 14 (MET): Development of conductance models for DBS, interference stimulation and monitoring to improve source timing and localization techniques

Topic 15 (MET): Anatomical Connectivity and Functional Connectivity in DBS Patients

Theme II: Modelling and Imaging in Biology and Biomedicine

Theme description

Topic 6: Modelling cerebral capillary blood flow and its impact on neural activity

Topic 7 (MET): Multiscale hybrid 3d imaging of cancer biopsies

Topic 11 (ITC): Adaptive and learning based quantitive structure tree model reconstruction

Topic 12 (ITC): Control of fluid flow models

Topic 13 (MET): Computer modelling and simulations of phenotypic plasticity in electromechanical function of the heart

Theme III: Mathematical Inverse Modelling in a Broader Context

Theme description

Topic 10: Advancing asteroid exploration - radar tomography of Dimorphos

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