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Mathematical Probe of Nanoparticle Aggregation in Capillary-Tissue System Applying Fractal Model. 应用分形模型对纳米颗粒在毛细管-组织系统中聚集的数学探讨。
Pub Date : 2025-01-01 DOI: 10.1615/CritRevBiomedEng.2024055532
Bhawini Prasad

Targeted drug delivery using nanoparticle-based technology represents an advance in tumor treatment aiming to improve drug retention in tumors and minimize side effects. This study explores nanoparticle aggregation as a mechanism of enhanced retention and controlled dispersion of therapeutic agents in tumor tissues. Unlike existing models that primarily focus on single-particle diffusion, this research investigates the aggregation dynamics of nanoparticles upon diffusion from capillaries into the surrounding tissue, using a fractal-based mathematical model. By incorporating fractal geometry, this model uniquely captures the complexity of nanoparticle interactions with heterogeneous tumor environments. The equations, solved using MATLAB, reveal that nanoparticles form aggregates of approximately 75 nm in the capillary, with an optimal fractal dimension of 2.8 promoting efficient aggregation and retention. These findings provide a new perspective on aggregation-controlled drug delivery systems, offering insights for enhancing nanoparticle bioavailability and therapeutic efficacy in tumors.

利用纳米颗粒为基础的靶向给药技术代表了肿瘤治疗的一项进步,旨在改善药物在肿瘤中的保留并最大限度地减少副作用。本研究探讨了纳米粒子聚集作为一种增强肿瘤组织中治疗剂保留和控制分散的机制。与现有的主要关注单颗粒扩散的模型不同,本研究使用基于分形的数学模型研究了纳米颗粒从毛细血管扩散到周围组织时的聚集动力学。通过结合分形几何,该模型独特地捕获了纳米颗粒与异质肿瘤环境相互作用的复杂性。利用MATLAB对方程进行求解,结果表明纳米颗粒在毛细管中形成约75 nm的聚集体,其最佳分形维数为2.8,有利于有效的聚集和滞留。这些发现为聚集体控制的药物传递系统提供了新的视角,为提高纳米颗粒在肿瘤中的生物利用度和治疗效果提供了新的见解。
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引用次数: 0
The Burn Grafting Image Reclamation Redefined with the Peak-Valley Approach. 用峰谷法重新定义烧伤嫁接图像复原。
Pub Date : 2025-01-01 DOI: 10.1615/CritRevBiomedEng.v53.i2.40
B P Pradeep Kumar, E Naresh, A Ashwitha, Kadiri Thirupal Reddy, N N Srinidhi

Burn injuries constitute a significant public health challenge, often necessitating the expertise of medical professionals for diagnosis. However, in scenarios where specialized facilities are unavailable, the utility of automated burn assessment tools becomes evident. Factors such as burn area, depth, and location play a pivotal role in determining burn severity. In this study, we present a classification model for burn diagnosis, leveraging automated machine learning techniques. Our approach includes an image reclamation system that incorporates the peak and valley algorithm, ensuring the removal of noise while consistently delivering high-quality results. By using skewness and kurtosis, we demonstrate substantial improvements in diagnostic accuracy. Our proposed system sources key features from enhanced grafting samples using peak valley transformation, enabling the computation of BQs and a unique bin analysis to enhance image reclamation. Our experimental results highlight efficiency gains, notably growing the matching features of graft samples for 14 matching images. The intended work involves the creation of a burn classification reclamation model. The proposed approach utilizes a support vector machine (SVM). The evaluation of the model will be conducted using an untrained catalogue, with a specific focus on its effectiveness in reclaiming images that necessitate grafts and distinguishing them from those that do not. Our approach holds promise in grafting sample reclamation in emergency settings, thereby expediting more accurate diagnoses and treatments for acute burn injuries. This work has the latent to save lives and improve patient upshots in burn traumas.

烧伤是一项重大的公共卫生挑战,往往需要医疗专业人员的专门知识进行诊断。然而,在没有专门设施的情况下,自动烧伤评估工具的效用变得明显。诸如烧伤面积、深度和位置等因素在决定烧伤严重程度方面起着关键作用。在这项研究中,我们提出了一个烧伤诊断的分类模型,利用自动机器学习技术。我们的方法包括一个图像复原系统,该系统结合了峰谷算法,确保在始终如一地提供高质量结果的同时去除噪声。通过使用偏度和峰度,我们证明了诊断准确性的实质性提高。我们提出的系统使用峰谷变换从增强的嫁接样本中获取关键特征,使bq的计算和独特的bin分析能够增强图像复原。我们的实验结果显示了效率的提高,特别是在14张匹配图像上增强了移植物样本的匹配特征。预期的工作包括创建一个燃烧分类回收模型。该方法采用支持向量机(SVM)。该模型的评估将使用未经训练的目录进行,特别侧重于其在回收需要移植的图像并将其与不需要移植的图像区分开来方面的有效性。我们的方法有望在紧急情况下移植样本回收,从而加快对急性烧伤的更准确的诊断和治疗。这项工作具有挽救生命和改善烧伤创伤患者结局的潜力。
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引用次数: 0
Nonlinear Dynamics and Stability Analysis of a Pandemic Model Using Homotopy Perturbation. 基于同伦摄动的流行病模型的非线性动力学与稳定性分析。
Pub Date : 2025-01-01 DOI: 10.1615/CritRevBiomedEng.2025055055
Garima Agarwal, Man Mohan Singh, Rashid Jan, Sunil Dutt Purohit

In this paper, we gave the numerical solution of the various population categories of susceptible, exposed, infected, and recovered (SEIR) mathematical models by using homotopy perturbation method, which is a technique that combines the perturbation and homotopy methods to solve nonlinear problems. Also, we discuss the susceptible population category and explore the graphical solution of all populations (SEIR) using the parameters α and β for both fractional and integer order. In the end, the stability analysis is also shown in the population graphs.

本文利用同伦摄动方法,给出了不同种群类别的易感、暴露、感染和恢复(SEIR)数学模型的数值解,这是一种将摄动和同伦方法结合起来求解非线性问题的技术。此外,我们还讨论了易感群体的类别,并探讨了所有群体(SEIR)的图形解,在分数阶和整数阶下使用参数α和β。最后,在总体图中也显示了稳定性分析。
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引用次数: 0
Editorial Preface: Mathematical Biology. 编辑前言:数学生物学。
Pub Date : 2025-01-01 DOI: 10.1615/CritRevBiomedEng.v53.i3.10
Dharmendra Tripathi, Kalpana Sharma, Rajashekhar Choudhari, Rajesh K Pandey, Sreedhara Rao Gunakala
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引用次数: 0
A New Approach to Population Growth Model Involving a Logistic Differential Equation of Fractional Order. 涉及分数阶Logistic微分方程的人口增长模型的新方法。
Pub Date : 2025-01-01 DOI: 10.1615/CritRevBiomedEng.2024055114
Deepika Jain, Alok Bhargava, Sumit Gupta

Population growth and its consequences remain one of the most pressing challenges of our time. The study of population dynamics, including factors like resource availability, disease, and environmental constraints, is fundamental for planning in various domains such as ecology, economics, and public health. One of the earliest models proposed to explain population growth was by Thomas Robert Malthus in the late 18th century. Malthus theorized that populations grow exponentially, while the food supply increases only in an arithmetic manner and that was explained by a mathematical model i.e. the population growth model. This imbalance, according to Malthus, could eventually lead to resource scarcity and population collapse. However, Malthus's model, though foundational, was simplistic in nature. Over time, a more refined and realistic model was developed by Pierre François Verhulst, a Belgian mathematician, which led to the formulation of the logistic growth model. This model involves a fractional differential equation (FDE) namely the logistic differential equation. Due to the significance of FDEs, several authors have proposed solutions for the model using different techniques. Our work finds this model's solution using the Laplace decomposition method (LDM) approach. The method represents a significant advancement in the tool case of applied mathematicians and scientists. Its ability to efficiently and accurately solve complex differential equations, especially FPDEs. The graphical interpretation of the behavior of the result is also mentioned and compare our results with exact solutions found in literature.

人口增长及其后果仍然是我们这个时代最紧迫的挑战之一。人口动态的研究,包括资源可用性、疾病和环境约束等因素,是生态学、经济学和公共卫生等各个领域规划的基础。最早提出解释人口增长的模型之一是由托马斯·罗伯特·马尔萨斯在18世纪晚期提出的。马尔萨斯的理论是人口呈指数增长,而食物供应只以算术方式增长,这可以用一个数学模型来解释,即人口增长模型。根据马尔萨斯的说法,这种不平衡最终可能导致资源短缺和人口崩溃。然而,马尔萨斯的模型虽然是基础的,但本质上是过于简单化的。随着时间的推移,比利时数学家Pierre franois Verhulst开发了一个更精细和更现实的模型,这导致了logistic增长模型的形成。该模型涉及分数阶微分方程(FDE),即logistic微分方程。由于fde的重要性,一些作者使用不同的技术提出了该模型的解决方案。我们的工作使用拉普拉斯分解方法(LDM)方法找到了该模型的解。该方法代表了应用数学家和科学家的工具箱中的一个重大进步。它能够高效、准确地求解复杂的微分方程,特别是fpga。还提到了结果行为的图形解释,并将我们的结果与文献中发现的精确解进行了比较。
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引用次数: 0
Editorial Preface: Mathematical Biology. 编辑前言:数学生物学。
Pub Date : 2025-01-01 DOI: 10.1615/CritRevBiomedEng.2025058392
Dharmendra Tripathi, Kalpana Sharma, Rajashekhar Choudhari, Rajesh K Pandey, Sreedhara Rao Gunakala
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引用次数: 0
A Numerical Comparison of Magnetic Nanoparticle Hyperthermia in Breast, Muscle, and Prostate Tumors. 磁性纳米粒子热疗在乳腺、肌肉和前列腺肿瘤中的数值比较。
Pub Date : 2025-01-01 DOI: 10.1615/CritRevBiomedEng.2025055746
Sreedhara Rao Gunakala, Victor M Job, P V S N Murthy, S Umakanthan, Vikash Ramcharitar

This study aims to compare the efficacy of magnetic nanoparticle hyperthermia for treating cancerous tissues in two distinct scenarios: breast and muscle/prostate tumors. Heat transfer dynamics during magnetic hyperthermia cancer therapy are explored using intravenously administered nanoparticles to a muscle/prostate tumor and intratumoral injection into a breast tumor. Utilizing non-Newtonian blood rheological models, we analyze a complex geometric domain for both tumor types and apply the mixed finite element technique for solving the governing equations. The impact of varying magnetic field frequencies and injected nanoparticle concentrations on heat transfer and nanoparticle transport within muscle/prostate, and breast tissues are examined numerically. Higher magnetic field frequencies and injected nanoparticle concentrations were found to increase localized heating in tumor regions, reduce therapy duration, and maximize thermal damage to cancer cells for both tumor configurations. This research provides valuable insights for optimizing magnetic hyperthermia parameters for different tumor types and also highlights the potential for personalized treatment strategies.

本研究旨在比较磁性纳米颗粒热疗在两种不同情况下治疗癌组织的疗效:乳房和肌肉/前列腺肿瘤。通过静脉注射纳米颗粒到肌肉/前列腺肿瘤和肿瘤内注射到乳房肿瘤,探索磁热疗癌症治疗期间的传热动力学。利用非牛顿血液流变模型,我们分析了两种肿瘤类型的复杂几何域,并应用混合有限元技术求解控制方程。数值研究了不同磁场频率和注射纳米颗粒浓度对肌肉/前列腺和乳腺组织内热传递和纳米颗粒运输的影响。研究发现,较高的磁场频率和注射的纳米颗粒浓度增加了肿瘤区域的局部加热,缩短了治疗时间,并对两种肿瘤形态的癌细胞造成了最大的热损伤。这项研究为优化不同肿瘤类型的磁热疗参数提供了有价值的见解,也突出了个性化治疗策略的潜力。
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引用次数: 0
A Review on Accelerated Magnetic Resonance Imaging Techniques: Parallel Imaging, Compressed Sensing, and Machine Learning. 加速磁共振成像技术综述:并行成像、压缩感知和机器学习。
Pub Date : 2025-01-01 DOI: 10.1615/CritRevBiomedEng.2024056909
Mitra Tavakkoli, Michael D Noseworthy

A concise overview of three major advancements in fast magnetic resonance imagine (MRI) reconstruction techniques is presented, focusing on their roles in enhancing image quality and reducing acquisition times. The first set of methods, parallel imaging techniques, includes sensitivity encoding (SENSE) and generalized autocalibrating partially parallel acquisitions (GRAPPA). SENSE utilizes spatial sensitivity information from multiple receiver coils to accelerate image acquisition by undersampling k-space data and reconstructing images using coil sensitivity profiles, allowing for faster scans. GRAPPA, another parallel imaging method, uses estimated weights from a calibration scan to fill in missing data in undersampled k-space and then reconstructs unaliased images. Additionally, this review explores sparse reconstruction techniques such as compressed sensing, which leverages the sparsity of images in a transformed domain to reconstruct high quality images from significantly fewer measurements, thus reducing scan times. The latest developments in machine learning applications for MRI acquisition are also discussed, highlighting how advanced algorithms are being used to improve image reconstruction, enhance diagnostic accuracy, and simplify workflow processes.

简要概述了快速磁共振成像(MRI)重建技术的三个主要进展,重点介绍了它们在提高图像质量和减少采集时间方面的作用。第一组方法,平行成像技术,包括灵敏度编码(SENSE)和广义自校准部分平行采集(GRAPPA)。SENSE利用来自多个接收器线圈的空间灵敏度信息,通过对k空间数据进行欠采样来加速图像采集,并使用线圈灵敏度剖面重建图像,从而加快扫描速度。GRAPPA是另一种并行成像方法,它使用校准扫描的估计权重来填充欠采样k空间中的缺失数据,然后重建未混叠的图像。此外,本文还探讨了稀疏重建技术,如压缩感知,它利用变换域中图像的稀疏性,从更少的测量中重建高质量的图像,从而减少扫描时间。本文还讨论了机器学习应用于MRI采集的最新发展,强调了如何使用先进的算法来改善图像重建,提高诊断准确性,简化工作流程。
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引用次数: 0
A Review on Blood Flow Simulation in Stenotically Diseased Arteries. 狭窄病变动脉血流模拟研究进展。
Pub Date : 2025-01-01 DOI: 10.1615/CritRevBiomedEng.2025055069
G Shankar, Dharmendra Tripathi, P Deepalakshmi, O Anwar Bég, Sireetorn Kuharat, E P Siva

Heart diseases which can lead to stroke and heart attacks, affect numerous individuals worldwide due to disruptions in blood flow within the body. A common underlying cause for such hemodynamic disorders is a constriction in the artery, which is known as a stenosis, which is attributable to a range of causes including atherosclerosis or plaque accumulation. Many theoretical and computational studies have been presented in this area providing a useful compliment to experimental (clinical) studies. These studies have benefited clinical practice by providing insights into complex fluid dynamics associated with cardiovascular disease and identifying robust methodologies for mitigating such diseases. This review therefore aims to provide an overview of recent mathematical and numerical modelling advancements in understanding blood flow in stenosed arteries which have served to expand the current understanding of disease onset and mitigation for patients. Many diverse aspects of stenotic hemodynamics have been addressed in a large body of literature under various assumptions, such as different fluid material models, artery channel characteristics and diverse analytical and numerical solution techniques. These studies have also considered a variety of multi-physical effects including heat transfer, mass diffusion, nanoparticle effects in actual clinical treatments. In this review, over 100 recent articles from reputable journals are appraised. The primary objectives of this review paper are to emphasize the methodologies used for modelling, numerical simulation, and robust evaluation of hemodynamic characteristics in arterial blood flow which provide a more sophisticated insight into hemodynamics associated with diseases and possible mitigation strategies. The tabular format outlines different aspects of geometries and blood behavior (fluids) examined in the period 2015-2025. This organized presentation and crystallization of key contributions in a single article will also serve as a valuable resource for multi-disciplinary researchers including mathematicians, bioengineers, computer scientists in addition to medical researchers. Future pathways are also outlined.

心脏病可导致中风和心脏病发作,由于体内血液流动中断,影响着世界各地的许多人。这种血流动力学紊乱的一个常见的潜在原因是动脉收缩,即狭窄,这可归因于一系列原因,包括动脉粥样硬化或斑块积聚。许多理论和计算研究已经在这一领域提出,为实验(临床)研究提供了有益的补充。这些研究通过提供与心血管疾病相关的复杂流体动力学的见解和确定减轻此类疾病的可靠方法,使临床实践受益。因此,本综述旨在概述最近在理解狭窄动脉血流方面的数学和数值模拟进展,这些进展有助于扩大目前对患者疾病发病和缓解的理解。狭窄血流动力学的许多不同方面已经在各种假设下的大量文献中得到解决,例如不同的流体材料模型,动脉通道特性以及各种分析和数值解决技术。这些研究还考虑了实际临床治疗中的各种多物理效应,包括传热、质量扩散、纳米颗粒效应。在这篇综述中,我们对来自知名期刊的100多篇近期文章进行了评价。这篇综述的主要目的是强调用于建模、数值模拟和动脉血流动力学特性稳健评估的方法,这些方法为与疾病相关的血流动力学和可能的缓解策略提供了更复杂的见解。表格格式概述了2015-2025年期间研究的几何形状和血液行为(流体)的不同方面。这种有组织的介绍和主要贡献的结晶在一篇文章中也将作为多学科研究人员的宝贵资源,包括数学家、生物工程师、计算机科学家和医学研究人员。还概述了未来的发展路径。
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引用次数: 0
A Review on Herbal Drugs and Natural Product Nano Formulations for Cancer Treatment. 肿瘤治疗用中药及天然纳米制剂研究进展。
Pub Date : 2025-01-01 DOI: 10.1615/CritRevBiomedEng.2025056287
Ankit Monga, Sanya Jain, Ginpreet Kaur, Veeranjaneyuluu Addepalli, Bunty Sharma, Damandeep Kaur, Ujjawal Sharma, Hardeep Singh Tuli

Nanomedicine has revolutionized the pharmaceutical and biological sciences industry by providing new frontiers and targets on the diagnosis and treatment of diseases. One promising development is the integration of natural products with nanoformulations, is emerging as a novel strategy in antitumor therapy. This combination has opened up new avenues for primary intervention and treatment due to targeted delivery of therapeutic agents against cancer. Researchers are trying to enhance and establish the safety and efficacy of naturally occurring bioactive compounds characterised by their anticancer potential. Polyphenols and other phytochemicals, along with functional foods, have high potency in circumventing tumors by the effective inhibition of the expansion of cancerous cells and induction of apoptosis. Incorporation of such natural products natural products through nanotechnology is therefore meant to enhance therapeutic efficacy with an improved safety profile. The aim will be to formulate these bioactive compounds as nanoformulations to achieve higher tumor site concentration, which would result in maximum anticancer effects and perhaps reduce the possible side effects associated with conventional therapies. This calls for collaboration among researchers and clinicians in establishing evidence-based guidelines and standardized protocols that ensure safety and efficacy in the use of such therapies.

纳米医学通过为疾病的诊断和治疗提供新的领域和目标,彻底改变了制药和生物科学行业。一个有希望的发展是天然产物与纳米制剂的整合,正在成为抗肿瘤治疗的一种新策略。由于靶向递送抗癌治疗剂,这种组合为初级干预和治疗开辟了新的途径。研究人员正在努力提高和确定天然存在的具有抗癌潜力的生物活性化合物的安全性和有效性。多酚和其他植物化学物质,以及功能性食品,通过有效抑制癌细胞的扩张和诱导细胞凋亡,在规避肿瘤方面具有很高的效力。因此,通过纳米技术掺入这些天然产品意味着在提高安全性的同时提高治疗效果。我们的目标是将这些生物活性化合物制成纳米制剂,以达到更高的肿瘤部位浓度,这将产生最大的抗癌效果,并可能减少与传统疗法相关的可能的副作用。这就要求研究人员和临床医生之间开展合作,建立以证据为基础的指南和标准化方案,以确保使用此类疗法的安全性和有效性。
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引用次数: 0
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Critical reviews in biomedical engineering
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