This thesis is divided in the following order. The first, two chapters respectively deal with the physiological and mathematical background necessary for the study of heat flow in female breast. Chapter-3 is devoted to analytical and numerical solutions to study temperature distribution in spherical organs of a human body for a one dimensional steady state case. Chapter-4 and 5 deals with two dimensional finite element models to study temperature distribution in semi spherical shaped human breast with and without abnormalities like tumor.
The development of quantitative methods and computer technology has facilitated the formation of new models in medical and biological sciences. Further, the application of mathematical methods in solving many real world problems of medicine and biology has yielded fruitful results. Despite advancements in instrumentations technology and biomedical equipments, it is not always possible to perform experiments in medicine and biology due to various reasons. Thus mathematical modeling and simulation is viewed as an viable alternative in such situations. The problems of biology and medicine pose new challenges for modeling and simulation.
Attempts are in progress world wide for mathematical modeling of control systems of human body as these systems are highly sophisticated systems and poorly understood. The temperature regulation system of a human body is one of the important control systems involved is maintaining structure and function of human body organs. The study of temperature regulation system of human body organs is quite interesting both from application and mathematical point of view. The modeling of these problems poses new challenges for mathematics. In view of above the theoretical study entitled “Computational Models To Study Temperature Distribution In Extended Spherical And Ellipsoidal Shaped Human Organs” has been taken up.
Table of Contents
1. PHYSIOLOGICAL BACKGROUND
1.1 INTRODUCTION
1.2 THERMOREGULATION
1.2.1 THERMOANALYSIS
1.2.2 THERMOGENESIS
1.2.3 HEAT TRANSPORT FROM CORE TO THE BODY SURFACE THROUGH SKIN
1.3 SKIN AND SUBDERMAL TISSUES
1.3.1 EPIDERMIS
1.3.2 DERMIS
1.3.3 SUBDERMAL TISSUES
1.4 BLOOD CIRCULATORY SYSTEM
1.5 BLOOD FLOW AND METABOLIC ACTIVITY IN SST REGION
1.6 BREAST
1.6.1 LOCATION
1.6.2 THE SKIN OF BREAST
1.6.3 STAGES OF BREAST DEVELOPMENT
1.6.4 MATURITY OF THE BREASTS
1.6.5 AGING OF THE BREAST
1.7 CANCER
1.7.1 CAUSES OF CANCER
1.7.2 ORIGINS OF CANCER
1.7.3 TYPES OF TUMORS
1.7.4 BREAST CANCER
1.7.5 VASCULAR BED IN TUMOR
1.7.6 METABOLIC ACTIVITY IN TUMOR
1.8 CONCLUDING REMARKS
2. MATHEMATICAL BACKGROUND
2.1 INTRODUCTION
2.2 MATHEMATICAL MODEL
2.3 DEVELOPMENT OF THE SUBJECT
2.4 MATHEMATICAL AND COMPUTATIONAL METHODS
2.5 NUMERICAL TECHNIQUES
2.5.1 FINITE DIFFERENCES METHOD
2.5.2 FINITE ELEMENT METHOD
2.5.2.1 THE RITZ METHOD
2.5.2.2 VARIATIONAL (RAYLEIGH - RITZ) FINITE ELEMENT METHOD
2.5.2.3 WEIGHTED RESIDUAL APPROACH
2.5.2.4 COLLOCATION METHOD
2.5.2.5 GALERKIN'S APPROACH
2.5.2.6 LEAST SQUARES APPROACH
2.6 ANALYTICAL METHOD
2.6.1 THE LAPLACE TRANSFORM
2.6.2 FOURIER SERIES
2.6.3 BESSEL'S FUNCTION
2.7 CONCLUDING REMARKS
3. ANALYTICAL AND FINITE ELEMENT MODELS OF TEMPERATURE DISTRIBUTION IN EXTENDED SPHERICAL ORGANS OF HUMAN BODY
3.1 INTRODUCTION
3.2 CLOSED FORM SOLUTION OF HEAT FLOW IN PERIPHERAL REGIONS OF SPHERICAL SHAPED HUMAN ORGANS
3.2.1 MATHEMATICAL MODEL AND SOLUTION
3.2.2 NUMERICAL RESULTS & DISCUSSION
3.3 FINITE ELEMENT SOLUTION OF HEAT FLOW IN PERIPHERAL REGIONS OF SPHERICAL ORGANS BREAST OF HUMAN BODY
3.3.1 MATHEMATICAL MODEL
3.3.2 NUMERICAL RESULT & DISCUSSION
3.4 CONCLUDING REMARKS
4. COAXIAL CIRCULAR SECTOR BASED FINITE ELEMENT MODEL TO STUDY TEMPERATURE DISTRIBUTION IN PERIPHERAL LAYERS OF SEMI SPHERICAL SHAPED HUMAN BREAST
4.1 INTRODUCTION
4.2 MATHEMATICAL MODEL
4.3 SOLUTION OF THE PROBLEM
4.4 NUMERICAL RESULTS & DISCUSSION
4.4.1 CASE I
4.4.2 CASE II
4.5 CONCLUDING REMARKS
5. TRIANGULAR RING ELEMENTS BASED FINITE ELEMENT MODEL TO STUDY EFFECT OF MALIGNANT TUMOR ON TEMPERATURE DISTRIBUTION IN PERIPHERAL REGIONS OF SEMI SPHERICAL SHAPED HUMAN BREAST
5.1 INTRODUCTION
5.2 TWO DIMENSIONAL FINITE ELEMENT MODEL TO STUDY TEMPERATURE DISTRIBUTION IN PERIPHERAL REGIONS OF EXTENDED SPHERICAL HUMAN ORGANS INVOLVING UNIFORMLY PERFUSED TUMORS
5.2.1 MATHEMATICAL MODEL
5.2.2 NUMERICAL RESULTS & DISCUSSION
5.3 FINITE ELEMENT MODEL TO STUDY THE EFFECT OF NON UNIFORMLY PERFUSED TUMOR ON TEMPERATURE DISTRIBUTION IN PERIPHERAL REGIONS OF EXTENDED SPHERICAL HUMAN ORGANS
5.3.1 MATHEMATICAL MODEL
5.3.2 NUMERICAL RESULTS AND DISCUSSION
5.4 CONCLUDING REMARKS
6. FINITE ELEMENT MODEL TO STUDY TEMPERATURE DISTRIBUTION IN SST REGIONS OF ELLIPTICAL SHAPED HUMAN BREAST UNDER DIFFERENT STAGES OF DEVELOPMENT
6.1 INTRODUCTION
6.2 MATHEMATICAL MODEL
6.3 NUMERICAL RESULTS & DISCUSSION
6.3.1 CASE I
6.3.2 CASE II
6.4 CONCLUDING REMARKS
7. FINITE ELEMENT MODEL TO STUDY TEMPERATURE DISTRIBUTION IN SST REGIONS OF SEMI ELLIPTICAL SHAPED HUMAN BREAST INVOLVING MALIGNANT TUMORS
7.1 INTRODUCTION
7.2 TWO DIMENSIONAL FINITE ELEMENT MODEL TO STUDY THE EFFECT OF UNIFORMLY PERFUSED TUMORS ON TEMPERATURE DISTRIBUTION IN PERIPHERAL REGIONS OF ELLIPSOIDAL SHAPED HUMAN BREAST
7.2.1 MATHEMATICAL MODEL
7.2.2 NUMERICAL RESULTS & DISCUSSION
7.3 TWO DIMENSIONAL FINITE ELEMENT MODEL TO STUDY TEMPERATURE DISTRIBUTION IN PERIPHERAL REGIONS OF ELLIPTICAL SHAPED HUMAN ORGANS INVOLVING NON UNIFORMLY PERFUSED TUMORS
7.3.1 MATHEMATICAL MODEL
7.3.2 NUMERICAL RESULTS AND DISCUSSION
7.4 CONCLUDING REMARKS
8. THREE DIMENSIONAL FINITE ELEMENT MODEL OF TEMPERATURE DISTRIBUTION IN DERMAL REGIONS OF SEMI SPHERICAL SHAPED HUMAN BREAST
8.1 INTRODUCTION
8.2 MATHEMATICAL MODEL
8.3 NUMERICAL RESULTS AND DISCUSSION
8.4 CONCLUDING REMARKS
9. THREE DIMENSIONAL FINITE ELEMENT MODEL OF TEMPERATURE DISTRIBUTION IN DERMAL REGIONS OF SEMI ELLIPTICAL SHAPED HUMAN BREAST
9.1 INTRODUCTION
9.2 MATHEMATICAL MODEL
9.3 NUMERICAL RESULTS AND DISCUSSION
9.4 CONCLUDING REMARKS
10. CONCLUSION AND FUTURE PROSPECTS
10.1 CONCLUSION
10.2 FUTURE PROSPECTS
Research Objectives and Core Themes
The research focuses on the development and application of mathematical and finite element models to analyze thermal distribution in human breast tissue, considering various shapes, stages of development, and the presence of malignant tumors under different environmental conditions.
- Modeling heat flow in spherical and ellipsoidal human breast regions using finite element analysis.
- Investigating the influence of environmental parameters such as atmospheric temperature and rate of evaporation on thermal profiles.
- Analyzing the impact of tumor growth and different levels of metabolic activity on tissue temperature.
- Examining temperature variations across different developmental stages of breast tissue.
- Developing computational tools to facilitate thermographic detection of abnormalities in breast tissue.
Excerpt from the Book
1.1 INTRODUCTION
A large number of physical and physiological processes are taking place at each level of the hierarchy of the system and subsystems in a human or animal body in-order to maintain the structure and function of the each component of the body. A number of control systems are present in a human body to regulate these processes like; (1) Fluid control system (2) Temperature control system etc. The temperature control (regulation) system is one of the very important control systems of a human body. It regulates the body core temperature at a constant temperature of 37°C by maintaining balance between heat generation within the body and heat loss from the body to the environment [35,39]. Any abnormality in these processes or subsystems can affect the control system, thus causing the diseases or any disorder in the human body organs due to some loss of function.
Various physical and physiological processes like blood flow, metabolic heat generation, thermal conduction, radiation, convection and evaporation are taking place in order to maintain this thermal balance of the body with the environment. Any abnormality in the structure, physiological parameters or environmental conditions can disturb this thermal balance of the body with the environment. A notable example is of cancer which is an abnormality of growth leading to abnormal rates of metabolic activity in the tissue [23].
The study of thermal problems of a human body under normal and abnormal conditions can give us a better understanding of relationships among various parameters which can be useful to biomedical scientists for development of protocols for detection and treatment of diseases or disorders caused by these abnormalities in the system. In view of the above an attempt has been made here to study thermoregulation in extended spherical and ellipsoidal organs of a human body especially breast with special relevance to cancerous tumors [1,8].
Summary of Chapters
Chapter 1: Provides the physiological background of thermoregulation, skin structure, and the nature of breast cancer.
Chapter 2: Outlines the mathematical and computational methods, specifically finite element techniques, used for modeling heat transfer.
Chapter 3: Presents analytical and finite element models for temperature distribution in spherical human body organs.
Chapter 4: Focuses on a coaxial circular sector-based finite element model for semi-spherical human breasts.
Chapter 5: Uses triangular ring elements to study the effect of malignant tumors in semi-spherical human breasts.
Chapter 6: Investigates temperature distribution in elliptical human breasts across various stages of development.
Chapter 7: Extends finite element modeling to semi-elliptical human breasts involving malignant tumors.
Chapter 8: Develops a three-dimensional finite element model for the dermal regions of semi-spherical human breasts.
Chapter 9: Presents a three-dimensional finite element model for the dermal regions of semi-elliptical human breasts.
Chapter 10: Summarizes the findings and discusses potential future research directions.
Keywords
Thermoregulation, Finite Element Method, Heat Flow, Human Breast, Malignant Tumor, Metabolic Heat Generation, Thermal Distribution, Ellipsoidal Models, Biomathematics, Tissue Layers, Temperature Profiles, Numerical Simulation, Bio-heat Transfer.
Frequently Asked Questions
What is the primary focus of this research?
The research primarily focuses on developing mathematical and computational finite element models to accurately predict temperature distribution within human breast tissue under various physiological and environmental conditions.
What are the central thematic areas?
The core themes include human thermoregulation, the impact of tumor metabolic activity, structural variations of the breast (spherical vs. ellipsoidal), and the effects of environmental variables like humidity and temperature.
What is the primary research goal?
The goal is to provide biomedical scientists with enhanced thermal modeling capabilities, which could improve protocols for the detection and diagnosis of breast cancer and other thermal abnormalities.
Which scientific methodology is employed?
The study primarily utilizes the Finite Element Method (FEM) to solve partial differential equations related to heat transfer, supported by numerical analysis and MATLAB-based simulations.
What topics are covered in the main body of the work?
The main body systematically explores physiological basics, mathematical model formulations, and progressively complex finite element simulations for different geometries (spherical/elliptical) and pathological states (presence of tumors).
Which keywords define the work?
Key terms include thermoregulation, Finite Element Method, malignant tumors, heat flow, bio-heat transfer, and breast tissue modeling.
How does tumor presence affect the modeling approach in Chapters 5 and 7?
In these chapters, the models are adapted to account for the uncontrolled metabolic heat generation of malignant tissues compared to normal tissues, requiring the division of the dermal layer into finer mesh elements to accurately represent the tumor's geometry and metabolic activity.
Why are different geometries (spherical vs. ellipsoidal) analyzed?
The models consider different geometries because the actual human breast is not perfectly spherical; it varies in shape and size based on age, genetic factors, and developmental stages, requiring more sophisticated elliptical models for realistic representation.
- Quote paper
- Akshara Makrariya (Author), 2013, Heat flow in female breast. Temperature distribution in semi spherical shaped human breast with and without abnormalities, Munich, GRIN Verlag, https://www.grin.com/document/1152372
