Dr Subhash C Mishra Professor Department of Mechanical Engineering Indian Institute of Technology Guwahati Guwahati, Assam-781039, India April 2015 My sincere thanks also go to the Department of Mechanical Engineering at IIT Guwahati, especially those members of my PhD committee for their input, valuable discussions and accessibility.
List of Publications from this Thesis Work
SYNOPSIS
The size and location of the malignancy in the breast also influence the temperature of the skin surface. A rectangular two-dimensional geometry of the breast tissue is taken into account, and the inverse analysis is performed using the GA.
CONTENTS
THERMAL MODELING AND INVERSE ANALYSIS OF
EQUIVALENCE OF PENNES BIOHEAT EQUATION
LIST OF TABLES
NOMENCLATURE
CHAPTER
INTRODUCTION
- Cancer Statistics
- Breast Cancer
- Work Done in the Area of Bioheat Transfer
- Summary
Sometimes, breast cancer starts in the stromal tissue, the fatty and fibrous connective tissue of the breast. Various issues regarding the effect of tumor location, size, and shape were discussed in their work.
PROBLEM STATEMENTS AND GEOMETRY
- Motivation for the Proposed Work
- Problem Statements and Roadmap
- Geometry
- Summary
- Fourier’s Law of Heat Conduction
- Bioheat Transfer
- Pennes bio-heat equation
- Wulff continuum model
- Normalized Form of Governing Bioheat Equations
- Finite Volume Method
- Finite Element Method
- Inverse Analysis
- Genetic algorithm
- Curve fitting technique
- Summary
Attention is paid to estimating the nature of the tumor in biological tissue. Its measurement in an indirect way can therefore reveal different characteristics of the abnormality in the tissue. It requires a well-defined geometry of the tissue and the considered conditions to which the tissue is exposed.
The details of the considered geometry along with the problems are described in the following sections. The normalized form of PBHE and WCM for 1-D geometry is given by Eqs. In this work, to demonstrate the feasibility of the approach, the temperature obtained by solving Eq.
Similar temperature profiles are the basis for estimating tumor size and location in contrast analysis.
THERMAL MODELING OF A 2-D TISSUE
- Validation
- Validation of the numerical solver
- Equivalence of 2-D and 3-D numerical simulation of human breast
- Thermal Analysis of a Tissue
- Based on properties given by Gonz´alez (2007)
- Inverse Analysis
- Genetic algorithm
- Curve fitting technique
- Summary
As the size (volume) of the tumor increases, the temperature in the tissue increases. This increase is due to the fact that as the size of the tumor increases, so does the rate of heat production. Inverse analysis of skin surface temperature for the purpose of non-invasive tumor detection.
An inspection of Table 4.3 shows that the errors in the position estimates are within 3%. For a given tumor size, another database of area values versus different tumor sizes and locations, skin surface temperature distributions had a Gaussian profile.
The Gaussian temperature profile obtained was specific to the specific tumor size and location.
THERMAL MODELING AND INVERSE ANALYSIS OF A REALISTIC BREAST
Geometry
Figures 5.2a and 5.2b show schematically the triangular and tetrahedral FEM grids considered for both breast geometries. With known thermophysical properties, subject to the initial and boundary conditions, numerical solution of Eq. 3.6) gives the temperature distribution in the tissue. Consideration of the 2-D semicircular section instead of a full-scale 3-D hemispheric model will be justified by comparing the temperature profiles along the surface and centerline for cases with and without a tumor.
Similar to the 2-D rectangular tissue domain, the presence of a tumor shows a particular pattern of Gaussian temperature profiles along the breast skin surface, and these profiles are similar in nature for different cases of tumor positions and sizes. By taking the similarity of these temperature profiles along the skin surface, the current work estimates the size and location of malignancy inside the 2-D semicircular section of the breast.
Validation
- Closeness of 2-D semicircular and 3-D hemispherical model of breast
- Validation with experimental data
In the human breast, when a tumor appears, compared to normal tissue, a large increase in metabolic heat generation rate Qm and blood perfusion rate b has been observed. For the 2-D semicircular domain (Fig. 5.1b) located in the xy plane, the thermophysical properties and boundary conditions remain the same as for the 3-D model (Fig. 5.1a). Following the similar pattern of temperature profiles in the breast, with and without tumor, a maximum overestimation of 0.6oC from the 2-D geometry was observed, justifying the applicability of the assumption.
Having shown that the midline (Fig. 5.3a) and skin surface (Fig. 5.3b) temperature profiles of the 2-D semicircular geometry closely match that of the 3-D hemispherical geometry, in the following, effects of tumor size and location on the temperature profiles is presented for the 2-D geometry. Prior to the numerical simulations and the application, the model, the solver and the considered initial and boundary conditions are validated with the experimental data available in the literature (Gautherie, 1980). In the presence of a tumor, although a higher value of the blood perfusion rate is observed, due to a very high value (65 times more than the healthy tissue) of metabolic heat generation rate, a significant change in the skin surface temperature is observed.
Effects of Tumor Size and Location on the Skin Surface Temperature
As the tumor size increases from 1 cm to 3 cm, the net amount of volumetric heat generation also increases, and the effect is to increase the surface temperature of the breast skin (Fig. 5.6a). It is further observed that the peak of the skin surface temperature profile appears exactly along the center line of the tumor. The increase in the value of the blood perfusion rate is not able to compensate for the growth, leading to an increase in the temperature of the entire breast along with the surface of the skin.
Closer the tumor to the skin surface, more is the rise in temperature of the breast skin. In the present study, the skin surface temperature profile of the breast is the basis of the inverse analysis to estimate different characteristics of a tumor. After analyzing the effect of the size rt and the depth Rro on the skin surface of the breast, the effect of the.
The effect on the temperature profiles is clearly seen by the displacement of the temperature dome.
Inverse Analysis
Similarly, for the tumor at the same depth, the variation of location of the tumor at 0 is shown in Fig. For a particular size and location of the tumor within the breast, the uniqueness of the temperature profiles was observed even for the 3-D case. A study of the various parameters of the Gaussian temperature profiles reveals the uniqueness of the distribution.
Skin surface temperature distribution of the chest of any suspected patient is obtained using any state-of-art measurement technique. A Gaussian temperature distribution of the skin surface obtained in this way ensures the presence of a tumor in the breast. An analysis of the temperature contour of the skin provides the location of maximum temperature on the skin.
With a maximum error of 5.5% in the estimation of tumor location, the tumor size is estimated with good accuracy (3.45%).
Effect of Measurement Error on Inverse Analysis
Analysis of the obtained profiles using the developed database and algorithm gives estimated values of tumor size and location. With a location estimation accuracy well below 20%, the tumor size is estimated to be 0.5 cm smaller than the actual value for Case 7 (Table 5.6). Therefore, even after obtaining a Gaussian profile from curve fitting, the solver could not estimate the tumor properties.
The obtained estimation of the location of the tumors for these cases is well below 11% and the sizes are estimated accurately (Table 5.7). The accuracy of the estimation can be further improved by considering multiple sizes of tumors while creating the database. Only with knowledge of the skin surface temperature profile, the proposed CFM simultaneously estimates size and location with good accuracy.
In the current approach, the size and location are estimated using the breast skin surface temperature profile without knowledge of any thermophysical property of the tissue and tumor.
Summary
EQUIVALENCE OF PENNES AND WULFFS’
MODELS
- Comparison of Numerical Results with Experimental Data
- Calculation of Local Mean Blood Velocity
- Effect of Boundary Conditions
- Summary
The use of PBHE and WCM requires knowledge of blood perfusion rate and blood velocity, respectively. The main objective of the current work is to establish the equivalence between PBHE and WCM for 1-D planar tissue in order to relate blood perfusion rate and blood velocity. Therefore, in order to have the same temperature profile, according to Eq. 6.4), the second term in the RHS of both equations must be the same.
In PBHE, the inhomogeneity of the breast tissues is neglected and the tissue and tumor are considered to be homogeneous. The most important assumption in the derivation of the relation Ap Aw2 is that the metabolic heat generation rate Qm 0. The results of the present work for a 3-D hemispherical tissue were also compared with the experimental results available in the literature.
The validity of the 1-D planar model was verified against the experimental results of hemispherical (3-D) tissue.
CONCLUSIONS AND SCOPE OF FUTURE WORK
Future Scope
In the present work, skin surface temperature profiles are used to detect cancer in a breast using the newly proposed algorithm (ie, CFM). The work can be extended to an in vivo analysis to check the applicability of the method. In a human breast, the grade of a tumor is determined by the growth rate of the cells in it.
Although the current work mainly focused on human breast, the CFM can be investigated to find its applicability in other tissues with tumors of random shape in the human body.
Das, K., Singh, R., Mishra, S.C., 2013, Numerical analysis to detect tumor presence and estimate its size and location in tissue. Multi-parameter estimation of the transient conduction-radiation problem using the lattice Boltzmann method and the finite volume method together with genetic algorithms, Numer. A spectral element method for solving the Pennes bioheat transfer equation using triangular and quadrilateral elements.
Thermopathology of breast cancer: measurement and analysis of temperature and blood flow in vivo, Ann. Development and comparison of DTM, DOM, and FVM formulations for short-pulse laser transport through a participating medium. Application of the lattice Boltzmann method to the solution of the energy equation of a 2-D transient conduction-radiation problem.
Analytical analysis of the Pennes equation for bioheat transfer with sinusoidal heat flux on the skin surface.
