Department of Mathematics

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Author: search.filters.author.Dr. Ayesha SohailSubject: search.filters.subject.Mathematics

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Now showing 1 - 4 of 4
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    Comparative Study of Different Fractional Operators on the Stochastic Diffusion Equation
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Rana Talha Ahmad; CIIT/FA19-RMT-021/LHR; Dr. Ayesha Sohail; LHR TP 7436
    In this work, we studied ecological model of fractional order prey-predator with Holling type II functional response and harvesting effect. Fractional Order Operators along with existence and uniqueness properties are defined. Finally, numerical simulations are performed to see the convergence of solutions with the help of Backward Euler’s method.
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    Hybrid Modeling Approach for the Forecasting of the Fibrilization Process and the Resulting AD
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Mudassar Fiaz; CIIT/FA19-RMT-112/LHR; Dr. Ayesha Sohail; LHR TP 7429
    Imaging has played a variety of roles in the study of Alzheimer disease (AD) over the past four decades. Initially, computed tomography (CT) and then magnetic resonance imaging (MRI) were used diagnostically to rule out other causes of dementia. More recently, a variety of imaging modalities including structural and functional MRI and positron emission tomography (PET) studies of cerebral metabolism with fluoro- deoxy-D-glucose (FDG) and amyloid tracers such as Pittsburgh Compound-B (PiB) have shown characteristic changes in the brains of patients with AD. These modalities and their particular utilities are discussed in this thesis. Machine learning and deep learning have demonstrated a wonderful performance in the classification task. Important progress has been made in image recognition, mainly due to the availability of large-scale annotated datasets and the revival of convolutional neural networks (CNNs). The aim of this study is to help the neurologists in selection of appropriate classification method based on several parameters like accuracy, computer complexity, and low training data availability. The challenge for the future will be to combine imaging biomarkers to most efficiently facilitate diagnosis, disease staging, and, most importantly, development of effective disease-modifying therapies.
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    A Composite Modeling Approach for the 3D Simulations and Medical Imaging of Cardiac ATTR Amyloidosis
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Usman Ashiq; CIIT/FA19-RMT-031/LHR; Dr. Ayesha Sohail; LHR TP 7441
    Mathematical Modeling and Machine Learning is playing a key role in applied mathematics. Machine learning has witnessed a tremendous amount of attention over the last few years. Deep neural networks are now the state-of-the-art machine learning models across a variety of areas, from image analysis to natural language processing. These developments have a huge potential for medical imaging technology, medical data analysis, medical diagnostics and healthcare in general, slowly being realized. Imaging has played a variety of roles in the study of Cardiac Amyloid (CA) over the past four decades. We provide a short overview of Cardiac Amyloid and Medical imaging techniques used for diagnosis of amyloids in our heart as well as recent advances in techniques. We also working on different neural networks especially on CNN for diagnosis of cardiac amyloid with the aid of Resnet-50 network on MATLAB and tensor-flow on Python. This study aims to assist doctors in choosing an acceptable classification method for each patient's condition. The challenge for the future will be to availability to most efficient imaging data for this disease.
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    Numerical Solution of Coupled Delay Differential Equations in the Field of Oncology
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2020) Robia Arif; SP19-RMT-037; LHR TP 6484; Dr. Ayesha Sohail
    In the dissertation, the models of delay differential equations from the math- ematical biology are considered, focusing on the oncology. For the study of these kinds of models, one should be capable to establish linear stability of the steady states. In Chapter 2, I have apply the method on models. Adoptive im- munotherapy against cancer has received remarkable consideration. The cyto- toxic CD8+ T cells have been studied for a long time and experimented with re- ceptor engineering techniques through the creation of chimeric receptors called CAR (Chimeric Antigen Receptor). This fact puts a cell line in the background which, on the other hand, is fundamental for the organization of the antitumor response: “CD4+” T cells. In this article, a model is constructed in which the ability of “CD4+” T cells to induce control of the tumor cell population is ana- lyzed, using a mediator such as the cytokine IFN- , and to quantify the action of the same which, although indirect, also carry out a control of the persistence of the antitumor action itself. The model focuses on the modalities of cellular interaction where it is possible to imagine a future development on the basis of recent data and idealize a therapeutic scheme where “CD4+” T cells play a leading role. The linear stability analysis is analyzed and analysis of Hopf bifur- cation is established. Finally, the numerical simulations are executed to validate analytical results.