基于米塔格-勒弗勒核的生物热分数顺序模型的多参数通用化特殊函数形式解决方案受热记忆冲击的影响
Muhammad Bilal Riaz1,2, Aziz Ur Rehman3, Jan Martinovic1
1IT4Innovations, VSB-Technical University of Ostrava, Ostrava, Czech Republic.
PloS one
|March 8, 2024
概括
本研究开发了一种分数数学模型来分析生物组织中的热冲击和热传递,并结合热记忆效应来进行更准确的模拟.
科学领域:
- 生物医学工程 生物医学工程
- 数学建模的数学建模
- 热传递热量转移的方法
背景情况:
- 了解生物组织中的热传递对于医学应用至关重要.
- 像Pennes方程这样的现有模型在捕捉复杂的热行为方面存在局限性.
- 热内存的概念及其对热传播的影响需要进一步研究.
研究的目的:
- 开发一种先进的数学模型,用于生物组织中的热传递.
- 分析热冲击的动态和热记忆的影响.
- 为了提高准确性,纳入一种新的分数建模方法.
主要方法:
- 作为基础框架,利用了一个扩展的Pennes方程.
- 采用了普拉巴卡尔的分数运算符和一个时间分数的富里埃定律,并使用了一般化的米塔格-莱弗勒内核.
- 应用拉普拉斯变换和逆拉普拉斯变换用于分析解决方案.
主要成果:
- 开发了一种具有有限热波传播速度的分数传热模型.
- 分析了热冲击和热记忆参数 (α,β,γ,a0,b0) 的影响.
- 在拉普拉斯和实域中获得分析解决方案,以图形形式呈现.
结论:
- 分数模型准确地表示热传递动态,包括热记忆.
- 该研究提供了对各种参数对热冲击现象的影响的见解.
- 这些发现提供了更全面的了解生物组织中的热传递.
相关概念视频
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Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
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01:23Maxwell's Thermodynamic Relations
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02:19Le Chatelier's Principle: Changing Temperature
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01:26Linear Approximation in Frequency Domain
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01:18Second Order systems II
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In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
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01:26Thermodynamic Potentials
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