Mathematical Modeling of Breast Cancer Based on the Caputo–Fabrizio Fractal-Fractional Derivative

Idrees, Muhammad; Alnahdi, Abeer; Jeelani, Mdi

doi:10.3390/fractalfract7110805

Cited by 5 publications

(3 citation statements)

References 47 publications

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“…https://www.indjst.org/ 1. • Optimization through Solver and Activation Functions: Different combinations of solver and activation functions were experimented with to find the most optimal configuration for the CNN (6,7,11) . Various activations like identity, logistic, tanh, and relu were tested in combination with solvers such as lbfgs, sgd, and adam.…”

Section: Methodsmentioning

confidence: 99%

Detection of Early-Stage Breast Cancer using Electromagnetic Sensor with Aid of the Convolution Neural Network

Prashanthi,

Prathibha,

Thippesha

2024

IJST

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Objectives: This study aimed to develop an end-to-end system for the diagnosis of breast cancer using a novel combination of a monopole electromagnetic sensor and Convolutional Neural Network (CNN). Methods: The research involved the design and simulation of an electromagnetic sensor, utilizing a denim gene substrate, to capture dielectric changes within breast tissue across a broad spectrum (1GHz to 10GHz). The recorded data was processed by a pre-trained CNN to identify irregularities in the breast's internal structure. Findings: Through extensive simulations, the electromagnetic sensor displayed a remarkable sensitivity to changes in the dielectric properties of breast tissue. The CNN analysis accurately identified the presence of cancer cells and estimated tumor size with an impressive 98% accuracy and a 1% tolerance margin. This method significantly outperformed existing models in both accuracy and efficiency, reducing the need for costly imaging techniques. Novelty: This research offers a non-invasive, cost-effective solution for early-stage breast cancer detection. Unlike traditional imaging techniques, this approach provides accurate diagnostics without the need for extensive equipment or high-cost procedures.

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Section: Methodsmentioning

confidence: 99%

Detection of Early-Stage Breast Cancer using Electromagnetic Sensor with Aid of the Convolution Neural Network

Prashanthi,

Prathibha,

Thippesha

2024

IJST

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“…Fractional calculus enables the differentiation and integration of non-integer orders, extending beyond traditional calculus. Cancer research finds application by modeling anomalous diffusion processes, characterizing tumor behavior more accurately, and incorporating memory effects into models, deepening our understanding of tumor dynamics [59][60][61][62].…”

Section: Mathematical Modelingmentioning

confidence: 99%

Personalized Plasma Medicine for Cancer: Transforming Treatment Strategies with Mathematical Modeling and Machine Learning Approaches

Ramaswamy,

Keidar

2023

Applied Sciences

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Plasma technology shows tremendous potential for revolutionizing oncology research and treatment. Reactive oxygen and nitrogen species and electromagnetic emissions generated through gas plasma jets have attracted significant attention due to their selective cytotoxicity towards cancer cells. To leverage the full potential of plasma medicine, researchers have explored the use of mathematical models and various subsets or approaches within machine learning, such as reinforcement learning and deep learning. This review emphasizes the significant application of advanced algorithms in the adaptive plasma system, paving the way for precision and dynamic cancer treatment. Realizing the full potential of machine learning techniques in plasma medicine requires research efforts, data sharing, and interdisciplinary collaborations. Unraveling the complex mechanisms, developing real-time diagnostics, and optimizing advanced models will be crucial to harnessing the true power of plasma technology in oncology. The integration of personalized and dynamic plasma therapies, alongside AI and diagnostic sensors, presents a transformative approach to cancer treatment with the potential to improve outcomes globally.

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“…Applying the C-F definition to system modeling can solve the singularity problem and simplify the calculation process. Over the past few years, the C-F definition has been widely used in various fields such as thermodynamics [21,22], medicine [23][24][25], and power electronics [26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Modeling and Analysis of Caputo–Fabrizio Definition-Based Fractional-Order Boost Converter with Inductive Loads

Yu,

Liao,

Wang

2024

Fractal Fract

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This paper proposes a modeling and analysis method for a Caputo–Fabrizio (C-F) definition-based fractional-order Boost converter with fractional-order inductive loads. The proposed method analyzes the system characteristics of a fractional-order circuit with three state variables. Firstly, this paper constructs a large signal model of a fractional-order Boost converter by taking advantage of the state space averaging method, providing accurate analytical solutions for the quiescent operating point and the ripple parameters of the circuit with three state variables. Secondly, this paper constructs a small signal model of the C-F definition-based fractional-order Boost converter by small signal linearization, providing the transfer function of the fractional-order system with three state variables. Finally, this paper conducts circuit-oriented simulation experiments where the steady-state parameters and the transfer function of the circuit are obtained, and then the effect of the order of capacitor, induced inductor, and load inductor on the quiescent operating point and ripple parameters is analyzed. The experimental results show that the simulation results are consistent with those obtained by the proposed mathematical model and that the three fractional orders in the fractional model with three state variables have a significant impact on the DC component and steady-state characteristics of the fractional-order Boost converter. In conclusion, the proposed mathematical model can more comprehensively analyze the system characteristics of the C-F definition-based fractional-order Boost converter with fractional-order inductive loads, benefiting the circuit design of Boost converters.

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Mathematical Modeling of Breast Cancer Based on the Caputo–Fabrizio Fractal-Fractional Derivative

Cited by 5 publications

References 47 publications

Detection of Early-Stage Breast Cancer using Electromagnetic Sensor with Aid of the Convolution Neural Network

Detection of Early-Stage Breast Cancer using Electromagnetic Sensor with Aid of the Convolution Neural Network

Personalized Plasma Medicine for Cancer: Transforming Treatment Strategies with Mathematical Modeling and Machine Learning Approaches

Modeling and Analysis of Caputo–Fabrizio Definition-Based Fractional-Order Boost Converter with Inductive Loads

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