Sunday, February 25, 2024

Breast cancer detection using enhanced IRI-numerical engine and inverse heat transfer modeling: model description and clinical validation – Scientific Reports

This work aims to further validate a novel IRI detection algorithm developed at Rochester Institute of Technology (RIT) using data from a clinical study conducted at Rochester General Hospital (RGH). The main research objective of the current work is to evaluate the efficacy of the IRI-Numerical Engine in a small sample size of twenty-three patients. A positive outcome, in terms of predictive ability, will be used to determine if the study should be expanded into a large sample set. From the results, it is clear that our methodology is accurately predicting the positive and negative cases, confirming the need to expand the study to a statistically meaningful larger sample size for determination of the sensitivity and specificity of this technique. The IRI-Numerical Method is an enhanced packaged version of the work conducted by Gonzalez-Hernandez et al.34 and Recinella et al.41 for a more efficient and accurate detection algorithm.

The main components of this study are as follows: (i) capturing of multi-view IR images in a clinical environment, (ii) generating patient-specific digital breast models (DBMs) from MRI for thermal modeling, (iii) conducting thermal simulations of breast cancer using ANSYS Fluent, and (iv) implementing a detection algorithm that utilizes the surface temperatures from multi-view IR images and thermal simulations to detect and predict the size and location of breast tumors. The IRI clinical imaging procedures and clinical data were first compiled by Owens51. The procedures for generating patient-specific DBMs, thermal simulation of breast cancer using the DBMs, and the detection algorithm were first developed by Gonzalez-Hernandez52. In this study, enhancements to the detection algorithm are conducted and packaged as the IRI-Numerical Engine. Details of each procedure, collected data, and enhancements are described below.

Clinical setup and imaging

The clinical study started under an Institutional Review Board (IRB) protocol developed at RGH, where thirty biopsy-proven breast cancer patients were recruited. Pathology reports and other clinical data were collected from the thirty patients who were imaged with both MRI and IRI. Recruitment and imaging of patients was conducted between March 2018 and September 2019. Patients were recruited if they were reported to have a palpable breast mass, or a confirmed mass in the screening mammography. The patients that underwent biopsy for confirmation and pre-op MRI were selected for IRI image capture and analysis. Patients with missing MRI and IR data were not selected for this study, reducing the patient cohort from thirty to twenty-three. All patients were required to fill out an informed consent form, previously approved by the RGH IRB, to participate in the study. Human subjects training (Good Clinical Practice and Good Documentation Practice) and the Collaborative Institutional Training Initiative were conducted for all personnel working on the project. All patient data was de-identified before use in any of the methods described in this work. All methods in this work that utilized any patient data (MRI and IR images, and patient reports) followed the human subjects research guidelines and regulation established in the RGH IRB.

Image acquisition

The MRI and multi-view IR images were both captured in the same prone position with a GE 3T MRI scanner and an inhouse IRI imaging system, respectively. The IRI imaging system consisted of a sturdy retrofitted imaging table with a 23 cm hole and an a FLIR SC6700 IR camera. This IR camera has a 640 × 512 pixel resolution and a thermal sensitivity of 20 mK, or 0.02 °C. The imaging table has a 5 cm layer of foam placed on top for comfort and a layer of disposable paper placed on top of the foam in accordance with hospital hygienic procedures. Patients were asked to disrobe from the waist up while wearing a hospital gown with an opening in the front and to lie down on the table in the prone position with one breast going through the hole. IR images were obtained at 8 views (45° intervals) at a 25° vertical tilt of each breast. Figure 2 shows an illustration of the IRI procedure and example IR images of a breast. IR images were captured after 10 min of acclimation to obtain steady-state temperatures of the breast surface. Details of image acquisition and setup, as well as patient recruitment and preparation are described in Recinella et al.41 and Owens51.

Figure 2

Depiction of IRI image capture setup with (a) illustrating the IR camera position relative to the body and (b) example IR images of a patient’s left breast associated with the position number. All images are taken clockwise starting at the head of the patient with the camera tilted upwards at a tilt angle of 25° giving access to the chest wall in addition to the breast surface. Hot spots and breast vascular regions are captured in the IR images. The hotspot shows up in views 1, 7, and 8. Vascular regions are more prominent in views 1–4.

Patient-specific thermal simulation of breast cancer

A method for generating patient-specific 3D breast geometries, or digital breast models (DBMs), from MRI data for thermal simulations of breast tumors was developed by Gonzalez-Hernandez52. The method utilized image processing and 3D reconstruction to generate the models. This work utilizes this method to generate patient-specific DBMs from MRI for the additional patients. The MRI data was only used to generate the computational domain for thermal analysis, but not to model the tumor shape, size, or position. Any tumor information from the MRI or other clinical data was strictly used for comparison and validation purposes.

Model generation

The patient-specific DBM generation method established by Gonzalez-Hernandez et al.33 was utilized to generate models for sixteen additional patients using the available MRI data, giving thirty-two additional DBMs for analysis. The method consists of image processing methods such as noise filtering, edge detection and segmentation, as well as 3D reconstruction and computer graphic methods. The steps for patient-specific DBM generation are as follows:

  1. 1.

    Select the breast and a small region that connects to the chest wall.

  2. 2.

    Filter any noise in the MRI using a median filter on each MRI slice.

  3. 3.

    Conduct edge detection to outline the breast shape for each MRI slice.

  4. 4.

    Use the outlines to segment the entire breast shape on each MRI slice.

  5. 5.

    Generate a 3D geometry by combining the segmented MRI slices.

  6. 6.

    Conduct 3D smoothening of the breast model.

  7. 7.

    Separate the breast model into a left breast model and a right breast model.

More details in relation to these steps and model generation are provided in Gonzalez-Hernandez et al.33 It is important to note that model generation is not limited to 3D reconstruction from MRI and can be conducted utilizing any other methods that can obtain the breast shape, such as a 3D scanner. The MRI is not needed in this technique: it was used for generating digital models since it was available. The digital model is then used for inverse heat transfer analysis in detecting tumors. Geometric characterization of the models was conducted by utilizing the geometric parameters W, H, and L34,41, as shown in Fig. 3. In Fig. 3, W and H are the width and height of the breast, respectively, measured from the front view in the x- and z-direction, respectively, and L is the length of the breast measured from the side view in the y-direction. A list of these measurements for each patient with their respective digital breast model is shown in Table 4.

Figure 3
figure 3

Example frontal and side view of Patient 11 DBM utilized for obtaining the height (H), width (W), and length (L), also known as the geometric characteristic measurements. These values are measured at the point of contact between the breast and the chest wall.

Table 4 The geometric characteristic measurements of the generated patients-specific DBMs for all twenty-three patients.


The terminology of key words utilized throughout this work are as follows:

  • Breast Tumor a mass of abnormally grown breast tissue.

  • Tissue Thermal Properties breast tissue thermal characteristic properties, such as thermal conductivity and blood perfusion, which determine how heat is transferred within the tissue.

  • Tumor Characteristics the major characteristics of the tumor that affect the heat distribution on the surface of the breast captured by the IR images. The major characteristics include the tumor’s metabolic heat generation rate and blood perfusion rate. The metabolic heat generation rate is a consequence of the increase in the tumor’s cellular metabolism, while the blood perfusion rate is a consequence of the increased vasculature of the tumor due to angiogenesis.

  • Bioheat Transfer Equations heat transfer equations utilized to model and describe the temperature distribution accounting for the heat transfer effects of biological entities inside the breast. In this work, Pennes’s bioheat equation is utilized, which accounts for the heat conduction in the tissue, metabolic activity of the tissue, and convective heat transfer from blood perfusion.

  • Boundary Conditions the thermal conditions of the environment interacting with the breast at specified boundary areas. In this work, the boundary conditions include the temperature at the chest wall, ambient temperature interacting at the breast surface, and the convection heat transfer due to natural convection from the ambient environment.

  • Thermal Simulations numerical methods, such as computational fluid dynamics (CFD) or finite difference methods, which are utilized to solve for the temperature distribution from heat transfer equations in complex problems or geometries through discretization of the geometry. In this work, ANSYS Fluent CFD software is utilized to discretize the geometry and solve the temperature distribution of Pennes’s bioheat equation.

  • Inverse Heat Transfer inverse modeling algorithms for heat transfer equations that utilize an iterative approach to solve for unknown parameters using known temperature distributions or temperature data at specified points. In this work, the Levenberg–Marquardt algorithm53 method is utilized with surface temperatures from patient IRI data to find the tumor heat source size (tumor diameter) within the breast geometry. The tumor heat source is placed outside the breast geometry when there is no tumor present.

  • Model Validation refers to comparing the predictive value with the MRI images for tumor size and pathological data for the cancer type.

Bioheat transfer modeling

Thermal simulations of breast cancer were conducted using ANSYS Fluent, Pennes’s bioheat equation25 and the findings by Gautherie24. In this work, tumors were modeled as metabolically active and highly perfused heat sources located within the breast. For thermal modeling, the healthy tissue and cancerous tissue region were modeled using the following:

$$\nabla \cdot \left( {k_{h} \nabla T} \right) + \rho_{b} c_{b} \omega_{h} \left( {T_{a} – T} \right) + Q_{h} = 0$$


$$\nabla \cdot \left( {k_{t} \nabla T} \right) + \rho_{b} c_{b} \omega_{t} \left( {T_{a} – T} \right) + Q_{t} = 0$$


$$Q_{t} = \frac{{3.27 \times 10^{6} }}{{468.5\ln \left( {100d_{t} } \right) + 50}}$$


$$k_{h} \left. {\frac{\partial T}{{\partial {\varvec{n}}}}} \right|_{A,B,C,D} = 0$$


$$\left. { – k_{h} \frac{\partial T}{{\partial {\varvec{n}}}}} \right|_{F} = h\left( {T – T_{\infty } } \right)$$


where the subscripts \(h\) and \(t\) describe the healthy and cancerous, or tumor, regions, respectively. These heat sources are implemented in ANSYS Fluent through a user-defined function (UDF). Once the DBMs were generated, thermal simulations using ANSYS Fluent software were conducted using a steady-state Pennes’s bioheat equation25 for healthy tissue (Eq. 2) and tumor tissue (Eq. 3) with metabolic activity of the tumor (Eq. 4) from the work established by Gautherie24. A convective boundary condition is assigned to the breast surface (Eq. 5 and label F), constant temperature is assigned to the chest wall (Eq. 6 and label E), and no heat flux boundary conditions are assigned to the side and top faces of the model (Eq. 7 and labels A–D). Computed temperatures images, also known as computed images, are generated after every thermal simulation involving the DBMs.

The healthy tissue region (Eq. 2) consists of a metabolic heat generation source term \(Q_{h}\) and a perfusion heat sink term \(\rho_{b} c_{b} \omega_{h} \left( {T_{a} – T} \right)\). The perfusion heat sink term models the body’s regulatory system due to blood flow in the local vasculature regions. This simplified model has been utilized throughout literature to accurately represent the regulatory system while reducing the need to utilize more complex vasculature thermal models54. The cancerous tissue region (Eq. 3) consists of a metabolic heat generation term of the tumor \(Q_{t}\) obtained from Eq. 4, which relates the metabolic heat generation as a function of the tumor diameter24. In addition, the effects of tumor angiogenesis and the tumor microenvironment are modeled through a perfusion heat source \(\rho_{b} c_{b} \omega_{t} \left( {T_{a} – T} \right)\). Both the metabolic heat generation term and perfusion heat source are based on the findings of Gautherie24 on malignant tumors being highly perfused and metabolically active.

The boundary conditions utilized in this method, Eqs. 57, were implemented on the model shown in Fig. 4a. The thermal simulation shown in Fig. 4b depicts a temperature distribution on the breast surface resulting from a tumor as a heat source based on its metabolic activity and the blood perfusion rate. The thermal physical property values utilized for thermal simulation of breast cancer in the work developed by Gonzalez-Hernandez52 and further validated by Gonzalez-Hernandez et al.33,34 are shown in Table 5. The values from Table 5 are utilized in every digital breast model for this study. Previous studies have shown that the metabolic activity and location of the tumor played a significant role in the surface temperature while the other properties were negligible28,30,34,54. Gonzalez-Hernandez et al.34 conducted a thermal sensitivity analysis to validate that the tumor size and locations have an effect on the detection of breast tumors. This was due to the relationship between the metabolic activity and the tumor diameter based on the findings from Gautherie24 represented in Eq. 4. More details of the modeling and thermal simulation process is described in Gonzalez-Hernandez52 and Gonzalez-Hernandez et al.33.

Figure 4
figure 4

Example of a (a) patient-specific DBM with labeled boundary regions and (b) thermal simulation of breast cancer for the same patient-specific DBM. Labels A–D are the side regions that are given a no heat flux boundary condition. Label E is the chest wall region given a constant temperature boundary condition. Label F is the breast surface region given a convection boundary condition.

Table 5 Table of thermal physical properties utilized for thermal simulations of breast cancer obtained from literature as provided by Gonzalez-Hernandez et al.33,34.

IRI-numerical engine

Using the methods to generate patient-specific DBMs and conduct thermal simulations of breast cancer, an inverse heat transfer approach was developed with IR images to detect and localize a tumor34,41,51,52,55. This approach utilized the surface temperatures of the breast captured by the IR camera and compared them to the surface temperatures of the thermal simulated model. This algorithm then tries to back calculate the tumor size and location to match the surface temperatures of the IR images. In the absence of a tumor, the algorithm places the tumor either along the chest boundary wall or the farthest outside corner of the domain to simulate the lack of heat source. This is due to an additional constraint to the algorithm that places the tumor within the computational domain. When the algorithm places the tumor at the boundary and corner points, the effect of this tumor heat source is negligible. This allows the algorithm to be utilized to detect the presence and absence of a tumor based on the presence or absence of a heat source in the breast domain and its effect on the surface temperature. Recinella et al.41 showed that the temperature from local vasculature captured by the IR camera did not have an effect on the detection of breast cancer. This is due to the larger effect of the tumor heat source in comparison to the localized thermal variations from the breast’s vasculature. Enhancements to this algorithm were conducted for this work in the form of an enhanced image registration, improved computational flow, and parallel processing for thermal simulation.

Inverse heat transfer approach

In the inverse heat transfer approach, computed temperature images of the simulated model were generated from the thermal simulation and compared with corresponding IR images through image registration and an iterative inverse heat transfer algorithm known as the Levenberg–Marquardt algorithm53. Figure 5 shows the flowchart for this developed algorithm replicated from Gonzalez-Hernandez et al.34. This algorithm was validated with seven biopsy-proven breast cancer patients and is a preliminary basis to this work. An initial tumor of size 1.8 cm was placed at the center of each breast model and simulated to obtain computed images. This is conducted for any case regardless of the presence or absence of a breast tumor. Gonzalez-Hernandez et al.34 showed that the final outcomes of the algorithm were independent of the initial guess. This work utilizes this initial guess as a standardization method for all patient cases. Image registration was conducted on the computed and IR images where a Region of Interest (ROI) for each was obtained and analyzed by the inverse heat transfer algorithm, also known as the IRI detection algorithm. Gonzalez-Hernandez et al.34, through a sensitivity analysis, established that the size of the ROI played a role in computational time but had minimal effect on the detection results. The algorithm checks to see if the surface temperatures in the ROIs match. If they do not match, the algorithm generates new parameters for the thermal simulation to generate a new computed image based on the new tumor size and location. This was conducted until the algorithm was able to predict the tumor size and location corresponding to the temperatures of the IR images. Further details of the IRI detection algorithm and process are described in Gonzalez-Hernandez52 and Gonzalez-Hernandez et al.34.

Figure 5
figure 5

Flowchart of the inverse heat transfer breast detection process using IR images developed by Gonzalez-Hernandez52 and validated by Gonzalez-Hernandez et al.34. The process for the algorithm starts with the thermal simulation conducted on the patient-specific model with initial parameters. This generates a computed image that gets aligned, or registered, with the IR image at the corresponding view. The ROI is extracted for the given views and are analyzed by the IRI detection algorithm. If there is no match, a new parameter is generated for thermal simulation and the cycle starts all over again. If there is a match, then the algorithm ends, and the outcome is given. Any red arrow indicates the initial inputs needed for the algorithm to start. The main detection process can be followed using the blue arrows. The flowchart legend on the left shows this distinction between paths as well as the distinction and significance of the shapes. A rhombus indicates the typing to be a data. A diamond indicates a decision process. A rectangle indicates a computational or algorithm process. And a rounded rectangle indicates the outcome of the algorithm.

Enhanced image registration

The IR images and MRI images of the patients were both captured in the prone position, making image registration an effective technique to align the surface temperatures between the IR images and DBM. Image registration is the process of aligning two or more images by geometrically transforming the images to match the spatial coordinates of another image called the reference image56. The images that are being transformed to match the reference image are called the sensed images. In this work, the referenced images are the IR images, also referred to as the referenced IR images, and the sensed images are the computed images generated from the thermal simulations. The study conducted by Gonzalez-Hernandez et al.34 utilized an intensity-based multimodal similarity image registration algorithm using MATLAB’s Image Processing Toolbox. In this study, an intensity-based multimodal affine image registration algorithm was utilized on the IR reference images and sensed images. Prior to image registration, pre-processing was conducted by converting all images from RGB to grayscale as required by the MATLAB image registration function57. After pre-processing, the optimizer and metric for the image registration function had to be configured to change the registration type to multimodal image registration58. The transformation type was selected to be an affine transformation, which allows the sensed image to translate, rotate, scale, and shear so that it matches the reference images. The intensity-based multimodal affine image registration enhanced and aided the registration process as well as accounted for any distortion captured by the IR camera. This enhanced image registration process was packaged into an algorithm that allows user interaction through two main user-interfaces (UIs). In the first UI, the user can select the portion of the image containing the breast to go through the image registration process. Once the user has selected the breast area, the ROI can be selected for analysis through the second UI. Figure 6 shows an example of the image registration process and example outcomes provided by the enhanced algorithm.

Figure 6
figure 6

Example of the enhanced image registration and ROI extraction processes utilized in this work. Image registration is conducted between the computer-generated image (sensed image) and the reference IR image. A registered overlap image is then created and utilized to obtain the ROI that will be utilized by the detection algorithm.

Improved computational flow

To improve workflow and computational flow of the IRI-Numerical Engine, enhancements to the algorithm are developed. The enhancements include coupling the image registration algorithm with the detection algorithm, UIs, and the development of fail-safe procedures. Figure 7 shows the flowchart for the IRI-Numerical Engine algorithm with the enhancements conducted in this work. One of the first enhancements that was added is a Domain Input UI which allows the user to input the computational domain of the patient-specific model. The computational domain values can be obtained directly from ANSYS Fluent to have more precise spatial coordinates for the tumor location. This UI is utilized to generate the initial tumor based on the computational domain of the DBMs. Another enhancement added to the algorithm is the coupling of the enhanced image registration process and the detection algorithm. Previously, manual image registration was conducted and tested prior to running the IRI-Numerical Engine to ensure alignment of the sensed and IR images. In this work, the image registration setup process is part of the algorithm through several UIs incorporated with the image registration algorithm described in the previous section. The purpose of these UIs is to ensure the registration and ROI extraction were conducted correctly by checking with the user and allowing the user to restart or reselect when needed. If the user selects to restart, geometry re-alignment is conducted in ANSYS Fluent where the camera is rotated to the appropriate view and new computed images are saved. One main feature of the IRI-Numerical Engine is a fail-safe procedure that ensures that all data and setups generated by the IRI-Numerical Engine were saved at every iteration. This allows for the analysis to continue from the previously saved iteration even after any type of malfunction.

Figure 7
figure 7

Flowchart for the IRI-Numerical Engine for enhanced and robust breast cancer detection. The process starts with the IRI-Numerical Engine asking the user through the Domina Input UI to manual input the domain of the patient-specific model to generate the initial parameters. The patient-specific model and initial parameters are then utilized by ANSYS Fluent to conduct thermal simulation of breast cancer. The Geometric Alignment UI in Fluent then rotates and moves the model around to match the IR image views and once finished computed images are generated. The computed images and associated IR images go through an Image Registration UI which logs the images and compares them through an alignment decision algorithm. If they are not aligned, the Image Registration UI waits for new computed images for comparison. If they are aligned, the ROI Selector UI is activated, and the user can select the ROI to be generated by the ROI Generator. From here the process is the same as the inverse heat transfer breast detection process shown in Fig. 5, but a fail-safe procedure is conducted by saving after the creation of the new parameters. The flowchart legend on the left shows the significance and distinction between shapes, shape colors, and arrow colors. All enhancements are shown in orange and the one new shape added is the trapezoid which indicates a UI process.

Incorporation of parallel processing

Another main feature of the new algorithm was the incorporation of parallel processing of ANSYS Fluent thermal simulation for faster computational time. Parallel processing is the computational method that allows computational processing to be split and simultaneously computed through multiple threads of a computer processing unit (CPU) or graphics processing unit (GPU), multiple CPUs or GPUs, or a cluster of computers59. In ANSYS Fluent, parallel processing is conducted by partitioning the computational mesh and assigning each partition to a compute node to be processed simultaneously60. For this work, the simulations and IRI-Numerical Engine were performed on two machines: (i) Intel® Core™ i7-6700 3.40 GHz workstation with 4 cores, 8 threads and 32 GB RAM, and (ii) Intel® Xeon® E5-2630 v4 2.20 GHz with 10 cores, 20 threads and 32 GB RAM. Parallel processing was set up using the ANSYS Fluent UI with simulations utilizing all threads for each machine. All UDFs that were utilized in ANSYS Fluent to incorporate Eqs. 24. To read the tumor parameters, the UDFs had to be rewritten to run in parallel processing. The UDFs were further enhanced by incorporating functions that interacted with the main IRI detection algorithm and the fail-safe procedures.

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