Some of his recent research work including inverse problem, medical imaging, porous media and fluid mechanics are described below:

1. Current Research Project: Wavelet algorithms for a high-resolution image reconstruction in magnetic induction tomography

Dr. Kaffel has just started a new project which contributes to the intellectual development of a new approach that aims to improve patient access to medical imaging technology that is truly noninvasive and noncontact and relies solely upon natural tissue contrasts. Tissue electrical conductivity (EC) is usually different when diseased. One strategy for EC imaging is magnetic induction tomography (MIT).

In this recent research, he is making an effort to improve the quality of image reconstruction mainly via the image reconstruction of data acquired from single-coil MIT scanning, including solving the problem of image reconstruction with mesh-free methods. Though scanning single coil MIT approach is very new, it has progressed sufficiently to show promise. Single coil MIT promises to provide a low cost, lower resolution, imaging modality that could be used worldwide, especially in remote locations, since the instrumentation is small and low cost compared with existing imaging methods. The innovation would be a new efficient meshless high resolution image reconstruction algorithm for the EC convolution integral.

Analytical and numerical models are used to solve the problem for a particular system configuration and simulate the response to variations in material parameters (electrical conductivity or relative permittivity). This produces a matrix that can be inverted using the Singular Value Decomposition (SVD) technique, to provide an estimation of the original conductivity and/or permittivity distribution. The process of image reconstruction using the single coil scanning method depends upon inversion of a convolution integral. In order to proceed, the integral must be discretized over some suitable space that includes the target, a step currently achieved using finite elements. Though this has been shown feasible, it has major drawbacks, primarily related to the need to know target boundaries rather precisely. Here, he proposes to discretize the convolution integral using wavelets, with a goal of alleviating the problem of unknown boundaries and allowing us to automatically place needed spatial resolving power where it is most needed in the target domain. EC would be expressed as a superposition of appropriate wavelets – in fact, determining the most suitable wavelet system is one of the steps needed to go forward. Likely, the kernel of the convolution integral would also be superposed in wavelets, to simplify inversion. Usually, there are far more unknowns than available coil sensor data, requiring a regularized least squares solution.

This work will contribute to making single-coil MIT a reality by providing a meshless image reconstruction algorithm that could be implemented on an iPad, or equivalent. EC imaging will eventually become a viable tool in medicine, especially in remote, underserved communities worldwide. It will bring immediate benefits to interdisciplinary academic researchers in the fields of Computer Science, Engineering, Mathematics and Medical Physics. Specifically, groups with interests in high performance computing, applied linear algebra, optimisation and parallel algorithms will benefit from new technological developments in the form algorithmic developments. Applied mathematicians and engineers working in academia in computational electromagnetism, error estimation and adaptivity as well as inverse problems will also benefit from the technological developments in terms of the new computational procedures and implementations that will be developed. In addition, medical physicists working in academia on Magnetic Induction Tomography (MIT) devices will also benefit from a new imaging toolkit that will be developed as part of this study. The project will also adresss many challenging problems that exist in the current industrial/medical applications. Specifically, companies developing computational electromagnetics modelling software, medical device modelling software and companies developing imaging software for medical and industrial applications will benefit from the new technological developments in terms of new algorithms and implementations that will be developed as part of this project. Specific examples include improved linear algebra solution techniques on GPU processors and uncertainty quantification through error estimation. It will also bring benefits to companies developing imaging devices for medical and industrial processes, whereby, through the technological developments proposed, improved imaging resolution for MIT and other similar imaging devices will be accomplished. In the medium term, the project will help to inform members of the public sector such as national heath care decision makers and regional managers for health care providers considering the investment in new medical technologies for improving the quality of patient diagnosis. This will lead to operational changes whereby low cost MIT can be used to supplement existing high cost imaging modalities (MRI, CT) in the initial stages of diagnosis and for patient monitoring. In the longer term, the project will also benefit the general public by improving the health and well being of the nation through better imaging techniques to assist with medical diagnosis and monitoring of patients.

2. Research interests in thin porous media

Porous media are ubiquitous in nature, and effect our daily lives. Some related examples of problems that involve porous media are groundwater flow in soils, oil discovery and recovery, diffusion of antibiotics through porous bone grafts, the curing of concrete for roads. Multiphase flow through thin layers of porous media are also encountered in many industrial applications including the design of filters and the development of liquid-absorbing hygiene products such as wipes, paper towels, feminine pads and diapers. These products demand specific absorbent properties with storage of liquid playing a significant role. Flow through thin swelling porous media involves physical processes that take place on several spatial and temporal scales. Understanding these processes is critical for the development of these products.

One of his research concentrations is dealing with mathematical modeling, analyzing and solving partial and ordinary differential equations, and numerical analysis. Specifically, he was working on building, analyzing, and approximating solutions for a mass transport model in porous media. The focus of his recent research is mathematical modeling of unsaturated flow of a liquid through multiple layers of thin, swelling porous media. This problem is of particular importance for furthering the understanding of fluid flow and deformation processes in thin swelling porous media. For most thin porous media, experimental measurements can be made at small scale through x-ray tomography. Even though it is difficult to directly measure the pore-scale physical processes, it is necessary to understand how these "pore-scale" mechanics affect the mechanics at a larger, more easily measurable, scale. We call the larger scale the "macroscale", and this is where the vast majority of experimental measurements are made.

3. Kimberly Clark Project: On modeling unsaturated flow of a liquid through multiple layers of thin swelling porous media

Recently, Dr. Kaffel worked on one industrial project, for modeling the wicking problem in thin absorbent swelling porous media, in collaboration with the Kimberly-Clark Corp. group. Dr. Ahmed Kaffel' s research in porous media can accelerate a new product’s speed to market by simulating the potential product’s performance. Dr. Kaffel, is one of the few researchers worldwide capable of applying the volume averaging technique method --a rigorous technique to upscale flow and to solve such transport in porous media.

A new efficient macroscopic model for modeling partially saturated flow of a liquid in multilayered thin swelling porous media is rigorously developed and is currently used at Kimberly Clark Corporation for the diaper problem as it aims to develop fast and reasonable accurate simulations that will help predict and understand fluid flow and deformation processes in thin porous media. The goal of this study is also to work toward building numerical solutions to the developed model and matching to the data found in the Kimberly Clark experiments. This obtained model is very valuable for the development of superior consumer absorbent hygiene products and leads to the development of fundamental understanding in transport mechanisms, and numerical simulation tools for both characterizing absorbent materials as well as validation of flow and deformation models.

Using a novel volume averaging approach, a similar macroscopic model is also developed to study the water management in polymer electrolyte membrane fuel cells which is a critical challenge for the high performance of polymer electrolyte membrane fuel cells (PEMFCs). A new recent paper related to this problem is published in the International Journal of Heat and Mass Transfer [paper 1] . This framework yields a basis for further simulations in porous media. Depending on the application, the model will be adapted and used to solve other interesting thin porous media-related problems of common interests. “Companies create potential new products based on the market’s demands,” he mentioned. “By mathematical modeling and writing a computer program to simulate any potential product’s performance -to transport liquid, dry, or wick, for example--we can shave months off the testing and refining time. This is very valuable to companies.” The goal is to work with an established industry partner on new challenging projects. The porous-media problems that he will research include the development of new transport models in porous media which can be employed for several applications such as geology, chemical reactors, drying and liquid composite molding, combustion and biomedical systems like biological tissue generation in scaffolds, transport in brain tissues, MRI applications in analyzing the structure of porous media, transport of macromolecules in aortic media, blood flow through contracting muscles, interstitial fluid flow in axisymmetric soft connective tissue, thermal simulations within the brain after head injury, heat transfer in muscle and skin tissues.

4. Research interests in fluid mechanics

The theme of his PhD work at Virginia Tech is a study on the stability of parallel shear flows which constitutes one of the fundamental problems of fluid mechanics. He focused on the development and the analysis of computational tools for mathematical modeling of the hydrodynamic stability of the viscoelastic shear flows and their transition to turbulence and for describing the numerical simulations. We refer to the two papers [paper 2] and [paper 3] for more details about this work. Subsequently after his PhD, his research interests at the University of Maryland lie in the mathematical modeling of hydrodynamic stability of multiphase flow, which is of significant importance in many industrial and engineering applications. His expertise in perturbation analysis and computational fluid mechanics is playing a key role to push the frontiers of knowledge in this important area. He focused on the development of methods for perturbation analysis of interfacial instability in multiphase flow and higher order numerical methods for quantifying the long-term nonlinear evolution of unstable flow structures. Specically, the stability problem of a viscous two-layer annular flow in microchannels is studied to quantify unstable wave patterns with respect to the fluid dynamic mechanisms. Emphasis is placed on predicting and controlling the growth of interfacial instabilities which can lead to the rupture of the thin liquid films encountered in annular flows. This study has led to a fundamental improvement in scientific understanding in the area of the stability of multiphase flow and has produced two publications one in Physics of Fluids journal [paper 4] and another one in International journal of multiphase flows [paper 5] .

Aside from his research with flow stability problem he has experience working on other sub-field within fluid mechanics. He also had the chance to work in the department of Engineering Science and Mechanics (ESM) at Virginia Techin the past on a research project: "Numerical simulation of flow and dynamics for Unmanned Underwater Vehicles (UUV)", under the direction of Prof. A. Nayfeh . This study deals with the control of the (UUV) vehicles and addresses many challenging problems that exist in many many applications including sea bottom exploration for mining, characterizing of ocean surface, archeological research, tracking of underwater pollutants and their sources, equipment repair and installation for the offshore oil and gas industry among others. He had also collaborated with IMFT group to study free surface turbulent flows in a channel. Numerical simulations of free surface turbulent flows were carried out by using an anisotropic algebraic Reynolds stress model to predict the hydrodynamic response of an open channel with a bed roughness heterogeneity and new efficient closure models for the wall friction and the momentum dispersion were developed as shown in [paper 7] .