Here you can find descriptions of all Tampere University's FAME – Flagship of Advanced Mathematics for Sensing, Imaging and Modelling Doctoral education pilot's research topics.

The open positions are divided into three themes and 10 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. 
 
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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 project focuses on developing a mathematical framework based on causal inference approaches to estimate whole brain directed network dynamics from electroencephalography (EEG) recordings. It is well known that cognitive functions require co-ordinated interactions between several brain regions, which can be described in terms of directed functional brain networks. Such brain networks can be estimated from EEG recordings, which have excellent temporal resolution to also capture the dynamics of these interactions.  Current approaches to estimate such networks from EEG/MEG data either give only statistical associations with no information on the direction of interaction or can only identify directed networks for a small number of brain regions. Furthermore, majority of the approaches assume nature of interactions to be linear.  
 
Key objectives of the doctoral research include:

<ol>
	<li>&nbsp;Developing high-dimensional causal inference approaches that can reliably estimate whole-brain directed network dynamics</li>
	<li>Validation of the developed methods and comparison to the state-of-the art approaches using simulations that employ interconnected neural mass models and</li>
	<li>Application of the developed methods to EEG data from epilepsy patients. </li>
</ol>

The project is expected to contribute significantly in improving the estimation of whole-brain networks from EEG data that will benefit both clinicians and neuroscientists. The anticipated outcomes encompass novel open-source tools to estimate high-dimensional directed network from EEG recordings and improved characterization of directed brain networks in epilepsy. 

Skills required: Mathematical modelling, Signal processing, Data analytics, Probability and Statistics, Demonstrable experience in programming (preferably Python) and Background in neuroscience would be an advantage.

Topic 2: Causal inference approaches for estimating whole-brain directed functional networks from EEG data

This PhD research project focuses on unravelling the capabilities of electric field temporal interference stimulation (TIS) of neuronal system in vitro and the brain in situ. The main advantage of TIS over traditional brain stimulation methods is that the electric field thus, the stimulation action can be steered to a desired location in a volume conductor, such as an in vitro cell culture system or the human brain. TIS is emerging as a treatment of brain disorders, and it is expected to find applications also in in vitro cell culture and organoid development systems. However, the ultimate capabilities and limits of TIS are yet to be determined and there exist contradicting results regarding the capabilities of TIS to modulate neuronal systems. This PhD topic will develop computational models to decipher this. The research project can be performed using e.g., Comsol Multiphysics or other finite element modeling (FEM) platform simulations combined brain models/imagery from public sources adapted by the researcher to the task at hand. 

The key objectives regarding TIS for in vitro applications include

<ol>
	<li>creating an electromagnetic FEM simulator for the in vitro cell culture and electrophysiological measurement and stimulation (including TIS) system in use in our laboratory and verifying the simulator with the existing in vitro TIS measurement data, and</li>
	<li>extending the simulator to study TIS of structured 2D neuronal systems in vitro and possibly neuronal organoids in 3D volumes. Regarding human brain applications, the key objectives include</li>
	<li>electromagnetic FEM of a human head based on publicly available magnetic resonance imaging and diffusion tensor imaging data and simulating TIS in the created model</li>
</ol>

Here, the interesting aspects include the spatial steerability and selectiveness of TIS in the complex human brain and the effects of slight anatomic variations. 

The anticipated outcomes will

<ol>
	<li>outline the capabilities of TIS in in vitro environments and</li>
	<li>provide a FEM tool to design TIS for in vitro applications. The simulation of TIS in the brain will provide</li>
	<li>evidence on the capabilities of TIS in the human head</li>
</ol>

Skills required: advanced mathematical and numerical modeling capabilities, proficiency in computational methods, strong programming skills, particularly in MATLAB or Python, understanding principles of electromagnetism, in particular bio-electromagnetism and its stimulation.

Topic 3: Spatio-temporal electric field interference-based stimulation of the human brain and its neuronal in vitro applications

The work in general with the collaborators aims to solve an unmet clinical need – monitoring the stroke patient condition at intensive care. The solution integrates novel inverse solution methods developed in the consortium and the expertise on biological and physiological processes, measurements, and their computer simulations where the PHD project is aimed to provide new impact. Our electrical impedance-based tomography (EIT) monitoring technology has already shown great promise in physically highly realistic simulation studies and phantom laboratory setup and data from detailed computer simulations. A clinical test series will be started as part of the Academy of Finland Proof of Concept funding 2024-2025. This will include EIT measurements, and patient head imaging with CT and MRI.

The PhD project aim is to develop accurate finite element multiphysics (e.g. simulating electric fields, mechanical deformations, and tissue changes) simulation platform to simulate the EIT measurement in the patient head models and predict scenarios of the stroke development including hemorrhage development, brain tissue deformation and the tissue changes contributing to changes in electric impedances. The expected outcomes include better understanding of the capabilities of the EIT to assess the stroke patient development and prognostics. Candidate will work in a multidisciplinary environment with expertise on mathematical simulation, measurements, biological and clinical sciences. 

Skills required: advanced mathematical and statistical modelling capabilities, proficiency in computational methods and numerical optimization, programming skills, particularly in C or Python, understanding of physical principles and possible biophysics.

Topic 4: Imaging and modelling the haemorrhage in stroke during acute care

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 carbon estimation and biodiversity analysis using drone technology 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, hyperspectral imaging, 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.

Lidar or laser scanning is a technology for 3D measuring where the visible surfaces of surroundings of the scanner are sampled with 3D point clouds. From the point cloud data, the geometric shapes and dimensions such as diameters, surface areas, and enclosed volumes can be measured. The measured objects can be e.g. buildings or trees.

Often the objects can be estimated as collections of simple shapes, so-called geometric primitives, such as cylinders or balls. The laser scanning data is richer than the mere point cloud as it also includes the rays from the scanner to the points, and these rays can be helpful to restricting geometric primitive estimation from the data. Moreover, because the measurement has some uncertainty, the points can be better seen as 3D distributions modelling the uncertainty of the point location. In this case we can talk fuzzy clouds instead of point clouds. Thus, considering the rays and the uncertainty of the laser scanner measurements leads to generalized point clouds and how to fit simple shapes to this kind of data. 

In this doctoral research project, we develop mathematical, numerical and statistical methods to fit geometric primitives to generalised laser scanner data. In particular, we study first separately how the ray and the fuzzy cloud ideas can be used in geometric primitive reconstruction. Then we combine them both into one reconstruction method. We also study how to optimize or accurately approximate the methods to speed up the process for large scale modelling. For example, a large tree can be modelled with tens of thousands of cylinders.  

Possible research questions/goals:

<ul>
	<li>How to estimate geometric primitives from point clouds with high uncertainty using measurement simulations?</li>
	<li>How to define and optimise primitive fitting for ray-point data?</li>
	<li>How to use all the information, the rays and uncertainty distributions in primitive reconstruction?</li>
	<li>How to speed up the process to large scale modelling? </li>
</ul>

Skills required: A strong background in statistics, optimisation, numerical methods, and machine learning are great advantage.

Topic 5: Geometric primitive reconstruction with generalised point clouds

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: Multiscale hybrid 3D imaging of cancer biopsies

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.

Augmented and alternative communication (AAC) systems help people with disabilities and special needs. These systems are currently quite simple such as personalised communication books or mobile phone/tablet apps and they do not collect any information about the environment/contexts. Thus, these systems are not situation aware, and the user has all the responsibility to adapt their use in each situation. Moreover, the systems are in practise fixed to the initial programming and updating them is hard. If an AAC system would be more situation aware and capable for learning user’s habits, it could provide better way for communicating for the user. 

In this doctoral research project, we explore possible multimodal situational inputs, such as location, time, images, audio and how they can be used to improve the use of AAC systems. In particular we study how to reliably recognize different user situations based on multimodal sensor inputs and how to enable better communications. In the project there is also possibility for close collaboration with the application side such as speech therapist. 

Possible research questions/goals include:

<ol>
	<li>what sensor inputs are available and how to integrate them into AAC system use,</li>
	<li>how to classify/segment the input data into useful user situations in real time, and&nbsp;</li>
	<li>how to learn and update the systems recommendations based on situational awareness</li>
</ol>

Skills required: Strong background in statistics, machine learning, data science, and programming are great advantage.

Topic 8: Multi-sensor situation aware and learning based AAC systems

This PhD project intends to deepen the understanding of Bayesian statistics' theoretical foundations and expand its practical applications beyond traditional confines. The focus will be on exploring and advancing Hierarchical Bayesian Modeling (HBM) across diverse areas of advanced mathematical modeling. HBM, a sophisticated statistical framework, is adept at incorporating layers of uncertainties and prior knowledge, making it a versatile tool for various scientific domains.

The project aims to address the multifaceted challenges encountered in fields ranging from engineering, such as reliability analysis in nuclear power plants, to neuroscience, specifically in EEG/MEG source localization for brain activity mapping. The project's objectives are multi-fold, beginning with the enhancement of HBM methodologies to improve their adaptability, accuracy, and computational efficiency in complex scenarios. A significant aim is to apply these refined methodologies across different disciplines, demonstrating HBM's utility in solving real-world problems. This includes reliability assessment of infrastructure components and the nuanced task of localizing neural sources in the brain. Collaborating with industry and medical institutions to validate these methodologies against real-world data stands as a crucial activity, ensuring the practical applicability and effectiveness of HBM.

Research activities will encompass a thorough review of existing HBM approaches, the development of innovative statistical models, and the application of these models to diverse datasets. This process may involve creating new software tools or adapting existing ones to facilitate the application of HBM in various settings. The interdisciplinary approach adopted here seeks to demonstrate the potential of HBM in synthesizing complex data and prior information to navigate uncertain environments effectively. Expected outcomes of this project include robust HBM frameworks tailored to specific field applications, a significant contribution to the literature on Bayesian statistics, and practical problem-solving strategies for industry challenges.

Skills required: proficiency in statistics and applied mathematics, especially Bayesian statistics, statistical programming and computational skills in R, Python, or MATLAB, knowledge of mathematical modeling and its applications in various fields, familiarity with Bayesian methods and their real-world applications, collaborative skills for cross-disciplinary integration of knowledge, experience in data analysis and handling large datasets.

Topic 9: Expanding the Horizons of Hierarchical Bayesian Modelling: Applications and Innovations in Mathematical Modelling

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 2: Causal inference approaches for estimating whole-brain directed functional networks from EEG data

Topic 3: Spatio-temporal electric field interference-based stimulation of the human brain and its neuronal in vitro applications

Topic 4: Imaging and modelling the haemorrhage in stroke during acute care

Theme II: Modelling and Imaging in Biology and Biomedicine

Theme description

Topic 5: Geometric primitive reconstruction with generalised point clouds

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

Topic 7: Multiscale hybrid 3D imaging of cancer biopsies

Theme III: Mathematical Inverse Modelling in a Broader Context

Theme description

Topic 8: Multi-sensor situation aware and learning based AAC systems

Topic 9: Expanding the Horizons of Hierarchical Bayesian Modelling: Applications and Innovations in Mathematical Modelling

Topic 10: Advancing asteroid exploration - radar tomography of Dimorphos

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