A novel in silico platform for a fully automatic personalized brain tumor growth

Journal Pre-proof A novel in silico platform for a fully automatic personalized brain tumor growth

Mojtaba Hajishamsaei, Ahmadreza Pishevar, Omid Bavi, Majid Soltani PII:

S0730-725X(19)30461-8

DOI:

https://doi.org/10.1016/j.mri.2019.12.012

Reference:

MRI 9362

To appear in:

Magnetic Resonance Imaging

Received date:

19 July 2019

Revised date:

7 December 2019

Accepted date:

31 December 2019

Please cite this article as: M. Hajishamsaei, A. Pishevar, O. Bavi, et al., A novel in silico platform for a fully automatic personalized brain tumor growth, Magnetic Resonance Imaging(2018), https://doi.org/10.1016/j.mri.2019.12.012

This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

© 2018 Published by Elsevier.

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A novel in silico platform for a fully automatic personalized brain tumor growth Mojtaba Hajishamsaei a, Ahmadreza Pishevar a, Omid Bavi b and Majid Soltani c-g,*

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Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran

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Department of Mechanical and Aerospace Engineering, Shiraz University of Technology, Shiraz, Iran

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Department of Mechanical Engineering, K. N. Toosi University of Technology, Tehran, Iran

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Advanced Bioengineering Initiative Center, Computational Medicine Center, K. N. Toosi University of

Technology, Tehran, Iran Cancer Biology Research Center, Cancer Institute of Iran, Tehran University of Medical Sciences, Tehran, Iran

f

Department of Electrical and Computer Engineering, University of Waterloo, ON, Canada

g

Centre for Biotechnology and Bioengineering (CBB), University of Waterloo, Waterloo, Ontario, Canada

*

Corresponding author:

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Majid Soltani

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453 Laurel Gate Dr., Waterloo, Ontario, N2T2S1, Canada Phone: (226)-888-4714 E-Mail: [email protected]

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ABSTRACT Glioblastoma Multiforme is the most common and most aggressive type of brain tumors grade four astrocytoma. Although accurate prediction of Glioblastoma borders and shape is absolutely essential for neurosurgeons, there are not many in silico platforms that can make such predictions. In the current study, an automatic patientspecific simulation of Glioblastoma growth is described. A finite element approach is used to analyze the magnetic resonance images from patients in the early stages of their tumors. For segmentation of the tumor, support vector machine method, which is an automatic segmentation algorithm, is used. Using in situ and in vivo

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data, the main parameters of tumor prediction and growth are estimated with high precision in proliferationinvasion partial differential equation, using genetic algorithm optimization method. The results show that for a

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as objective function, are 3.7 % and 17.4 %, respectively.

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C57BL mouse, the differences between the surface and perimeter of in vivo test and simulation prediction data,

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Keywords: Glioblastoma; Personalized tumor growth; Support vector machine; Genetic algorithm; Brain tumor

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1. Introduction Glioblastoma Multiforme (GBM) is the most inevitably lethal primary brain tumor. Despite major advances in therapy, patients treated with new and modern therapies have a median survival rate of approximately 15 months from diagnosis [1]. GBM happens to two to three per 100,000 adults per year and accounts for 17% of all brain tumors and more than half of all primary brain tumors [2]. GBM tumors are genetically diverse and heterogeneous and the tumor therapy and treatment may be different and patient-specific. Because of the complexity and uncertainty of the tumor growth process for each patient,

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image-based personalized tumor growth models are essential for the prediction of tumor growth and provision of a suitable treatment plan for the patient. The more accurate the prediction of GBM, the better the

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understanding of the tumor growth level and the better the subsequent treatment plan for patients.

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The image-based personalized tumor growth method requires (I) tumor medical images and tumor segmentation and detection, (II) a proper mathematical tumor growth model, and (III) an optimization algorithm. Increasing

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the accuracy of each of these leads to the improvement of the final models and outcomes.

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Magnetic resonance images (MRIs) are common medical images used for GBM diagnosis. Brain tumor segmentation has a significant role in medical image processing for status and treatment of patients. GBM

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segmentation can be manual, semi-automatic or fully automatic. Manual segmentation of brain tumor is often time-consuming and complex, which requires handling by experts.

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For semi-automatic segmentation, several software programs such as 3dslicer and Mimics have been developed. Depending on users, they yield different results and are generally used in clinical research. Even if these are

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easy to implement, nevertheless tumor segmentation should be modified [3]. Ayachi et al. (2009) proposed a pixel-based segmentation method on MRI brain images using SVM. The results of distinguishing tumor and normal tissue pixels on the basis of several features were validated, using the experimental gliomas dataset [4]. El-Melegy et al. (2014) proposed an automatic segmentation with fuzzy cmeans (FCM) algorithm for glioma detection based on MRI datasets. Their results with FCM algorithm were approved by

two radiologists

with validity above 90 percent [5]. Meier (2016) proposed

Brain Tumor Image Analysis Software (BraTumIA) for automatic brain tumor image analysis. The inputs to this software are four T1, T1+Gd, and T2, FLAIR MRI sequences and the outputs are volumetric data about the brain, skull and tumor compartments (Necrotic, Hypoxic and Normoxic tissue and Edema) [6, 7]. Recently, an increasing number of mathematical and simulation models have been applied to various aspects of tumor growth and treatment. Modeling of glioma tumors is based on two processes of proliferation and

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invasion. Tumor proliferation is the increase in tumor cells as a result of cell growth and cell division and tumor invasion is the migration of tumor cells into neighboring tissues[8]. Swanson presented the proliferationinvasion (PI) model with reaction-diffusion equation which describes cell invasion and proliferation[9, 10]. Hogea et al. (2008) included the mechanical interaction between tumor and normal surrounding tissues to model mass effect, using linear elastic model [11]. Some researchers extended the image-based tumor growth model to describe the response to surgical resection [12], chemotherapy [13], radiotherapy [14, 15], combined chemoradiation therapy [16, 17], and anti-angiogenesis treatment [18, 19].

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A vital problem in image-based tumor growth modeling is the estimation of patient-specific and tumor-specific model parameters. In previous studies, Menze et al. [2011] estimated tumor growth parameters within the Bayesian

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framework from the statistical image observation [20]. Gooya [2012] proposed Glioma Image Segmentation and

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Registration (GLISTR) based on the personalization of a tumor growth model with mass effect [21]. Liu et al. [2015] predicted tumor growth by presenting a partial differential equations (PDE) model for specific patients

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using inverse methods and estimated parameters based on multimodal imaging data including CT and PET [22]. Le

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el al. [2017] proposed a Gaussian Process Hamiltonian Monte Carlo method (GPHMC) for estimation of reactiondiffusion tumor growth model parameters, adopting the Bayesian personalization method [23].

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Scheufelea [2017] introduced a PDE-constrained optimization method for parameter identification of tumor growth in clinical datasets [24]. Soltani [2018] proposed a patient-image based tumor growth model which

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involves using advection- diffusion- reaction PDE equation with Monte Carlo method optimization and validated it for two patients with MRI and PET [25]. In this study, we use Support Vector Machine (SVM)

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classification for automatic segmentation of GBM tumors. A GBM tumor growth prediction approach is proposed that involves a reaction-diffusion tumor growth model and a genetic algorithm optimization step. The results of our image processing tool show good correlation with experimental data and allow for new perspectives in Neuro-Oncology for tumor prediction and treatment plan.

2. Material and Methods The method adopted in the present study involves the following, detailed in three sub-sections. 2.1 MR Imaging and Tumor Segmentation MRI is the basic diagnostic Image processing tool among the types of scans, which is non-invasive and costeffective and provides good contrasts of tumors. In the case of brain tumor, it is essential that different matters

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of brain (skull, cerebrospinal fluid (CSF), white and gray matter) are identified as tumor growth is different in these areas. Patients’ MRI images are converted from DICOM files to the grayscale image formats, using Image processing tool in MATLAB. All the images are converted to 256×256 pixels grayscale images. For automatic tumor segmentation, Support Vector Machine (SVM) is used, which is a supervised classification prediction tool derived from the statistical learning theory [26]. SVM is an attractive and automatic method for classifying MRI brain images into two separate classes such as tumor and normal tissues. Using nonlinear distribution, this method is capable of delineating the best boundary between the tumor and normal tissues,

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without relying on prior knowledge.

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Dice similarity coefficient is a statistical validation metric for the evaluation of the performance of image processing and diagnosis of tumors and is a yardstick for precision and comparison with other methods

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involving manual segmentations. For GBM-edema complex, this coefficient is almost 85.7±3.8 [27]. SVM

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includes both training and testing steps. SVM with nonlinear kernel function trains itself by features given as an input to its learning algorithm to find the global minimum by selecting the suitable margins between the two

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classes [28].

Discriminate method involves pre-processing (filtering noise), tumor and tissue feature extraction, classification

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and post-processing. Firstly, in the preprocessing level, anisotropic diffusion filter is applied to the image by 10-

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connected neighborhood for reducing the contrast between consecutive pixels and filtering the noise. After creating the appropriate mask image, SVM classifier is used for accurate tumor detection and segmentation,

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using the MATLAB software. Figure 1 shows the flowchart of tumor segmentation.

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Figure 1. Flowchart of patient-image based tumor growth optimization framework.

2.2 Mathematical Model Image-based modeling of brain tumors is based on two processes: proliferation and invasion. The spatial macroscopic model that describes the spatio-temporal evolution of a tumor cell density can be expressed by [9]:

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𝜕𝑁 𝜕𝑡

𝑁

= ∇ ∙ (𝐷(𝑥)∇𝑁) + 𝜌𝑁(1 − )

N is concentration of tumor cells [ 𝑚𝑚2

tissues. 𝐷(𝑥)[

𝑦𝑒𝑎𝑟

(1)

𝐾

𝑐𝑒𝑙𝑙𝑠 𝑚𝑚3

] and the diffusion term states tumor cell migration into surrounding

] is migration rate that is defined as: 𝐷𝑤 𝐷(𝑥) = { 𝐷𝑔 𝐷𝑐𝑠𝑓

𝑥 ∈ 𝑤ℎ𝑖𝑡𝑒 𝑚𝑎𝑡𝑡𝑒𝑟(𝑊𝑀) 𝑜𝑓 𝑏𝑟𝑎𝑖𝑛 𝑥 ∈ 𝑔𝑟𝑎𝑦 𝑚𝑎𝑡𝑡𝑒𝑟(𝐺𝑀) 𝑜𝑓 𝑏𝑟𝑎𝑖𝑛 𝑥 ∈ 𝑐𝑒𝑟𝑒𝑏𝑟𝑜𝑠𝑝𝑖𝑛𝑎𝑙 𝑓𝑙𝑢𝑖𝑑(𝐶𝑆𝐹)

1 𝑦𝑒𝑎𝑟

] represents the overall rate of cell growth which comprises both cell

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capacity of the tissue and ρ [

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The second term on the right-hand side of Equation 1 describes tumor cell proliferation. K is the carrying

proliferation and death.

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Growth of gliomas, especially GBM, is anisotropic because gliomas do not infiltrate the ventricles or CSF and

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infiltration in gray matter is less than that in white matter [29]. Therefore, it is assumed that tumor cells spread only in gray and white matters.

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We impose a null Neumann condition for the cell volume fraction at the boundary of the skull: ∇𝑁 ∙ 𝑛̂ = 0, 𝑜𝑛 𝜕Ω, ∀𝑡 ∈ [0, 𝑇]

(2)

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where 𝑛̂ is the unit normal to the boundary.

The model has been implemented using finite element method for solving the PI equation which has been

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2.3 Personalization

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discretized on a regular square grid.

Model personalization provides estimated model parameters from medical images. We present two objective functions to estimate tumor growth parameters. The first one is the percentage difference between real tumor surface area and simulated tumor surface area and the second one is the percentage difference between real tumor perimeter and simulated tumor perimeter. A more informed selection of the objective function for optimization algorithm leads to a more accurate parameter estimation. Genetic algorithm, inspired by the concept of “natural selection” or survival of the fittest, is a robust algorithm widely used in optimization problems [30-35]. This method includes bio-inspired variables such as crossover and mutations in selecting across different generations. Using the MRI images, the tumor surface area and tumor perimeter are measured in three time intervals (follow-up) and the effective parameters involved in the tumor

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growth (i.e., ρ and Dw and Dg and DCSF) are estimated. We choose better objective function between tumor surface area and surface perimeter. Based on these values and solving the finite element modelling equations, the surface area and tumor perimeter in the third time interval (3rd time point), Ssim,t3, are predicted (Figure 1). The predicted value is then evaluated by the actual value obtained from the image of the tumor in the third time interval, SMRI,t3. The objective function is defined such that it minimizes the difference between real and simulation tumor surface area in the second time interval (Ssim,t2 - S MRI,t2). In addition, this objective function is repeated for tumor perimeter to select a better objective function. The values ρ and Dw and Dg are varied, using

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our optimization protocol, and the FEM modelling is updated based on these values to the point where the objective function has reached its minimum value. The objective function has been defined as Predicted surface

𝑆𝑠𝑖𝑚−𝑆𝑀𝑅𝐼 𝑆𝑠𝑖𝑚

|

(3)

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|

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area (Ssim) – Actual surface area (SMRI).

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It is notable that the values Dw and Dg and ρ cannot be any arbitrary value and can only change in a range that is idiosyncratic to the tumor and/or tissue (Dg is less Dw). However, a different objective function with tumor

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perimeter instead of tumor area has been adopted in order to have a good objective function (in case 2). The number of persons selected is 100 in initial generation and five top persons are chosen based on the value of

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their objective function (as parents for next generation) and 96 persons are added. This method does not restrict the reproduction of good parents, because elitism algorithm ensures the presence of the best people in the

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subsequent reproductions [31]. This process is repeated until the stopping criteria are met. The flowchart of the

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model appears in Figure 1. The whole procedure has been carried out, using COMSOL and MATLAB. We chose two cases for tumor growth prediction model and validation. Due to lack of human specimens with untreated brain tumors in the third time interval, we used an in-situ hypothetical model on a brain MRI to evaluate our genetic algorithm method. In this sample, the brain tissues were divided into three parts: white matter, gray matter and cerebrospinal fluid. In white matter, cancer cell proliferation was greater than that in gray matter, and tumor cells did not penetrate into the cerebrospinal fluid. The skull also plays the Neumann boundary condition. After using two different time intervals with initial parameters (diffusion coefficient for white and gray and cerebrospinal fluid and cell proliferation), optimization was performed based on the objective function of the tumor area difference. It was found that the estimated parameters are very close to initial hypothetical parameters.

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In the second case, we examined personalized image base tumor growth model on a mouse (in vivo case) with injecting CL261 cell into mouse brain that is similar to human brain tumor. This experiment was conducted by injecting GL261 glioma cells into several brain types of the C57BL mouse. The invasive GL261 cell is similar to Glioblastoma due to its having necrosis, bleeding, angiogenesis and inflammation features and growth and penetration characteristics of these tumor cells into the immune system of the mouse. Mice immune responses to these types of cells produce gliomas and are believed to include a pathological illness of the development of malignant glioma similar to that of humans.

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Imaging was carried out on days 15, 18 and 22 after the initial injection into the mouse skull. These imaging intervals were chosen to provide repeated images of the growing tumor, which is not harmful to the health of the

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mice. The T2-weighted image is used in this image. These experiments were conducted by Rutter in the

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University of North Carolina [36].

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3. Results and Discussion

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In case 1, the domain is taken to be a slice of human brain MRI that is embedded in a rectangle with 147*185 mm dimensions and a uniform spatial discretization with ∆𝑥 = 1 𝑚𝑚 and time step ∆𝑡 = 0.01 𝑑𝑎𝑦.

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The simulations were initiated with a hypothetical uniform small tumor surface that occupies 50% of cell capacity K (Figure 2). We assume that a tissue becomes cancerous when tumor cells occupy 16% of cell

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capacity. The second time interval for follow-up purposes is selected 100 days later [37]. In this case we simulate a GBM tumor on MRI with specific coefficients. Then we optimize and estimate parameters with

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genetic algorithm. SVM method is selected for tumor segmentation and direct finite element method is selected for Proliferation-Invasion (PI) equation with structural grids.

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Figure 2. The hypothetical images of tumors in different days by calculating the area with SVM. (A) The image of Initial tumor. (B) The image of tumor after 100 days. (C) Tumor surface area at initial state and (D) Surface area of the

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tumor after 100 days.

The results appearing in Table 1 show the correctness of the algorithm used and the small percentage error indicates the high accuracy of the method. Percentage difference of hypothetical tumor area and simulation on day 100 is 0.25%. Table 1. Parameter estimation with difference between the tumor area of the hypothesis and simulated on day 100 as objective function and the error percentage

estimated DW

Estimated Dg

Estimated ρ

Best selected person

50.653

15.676

6.854

Hypothesis tumor

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Percentage difference of hypothesis tumor area and simulation on day 100

0.25 15

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For case 2, the tumor volume is given to one of the mice and the image of a selected region of interest (ROI) of about 4.5 * 5 mm for the mouse is shown in the coronal area for three different times (See Figure 3). In the first frame, according to the experimental results [36], the implantation of cancer cells on mice and MRI-DWI imaging with two types of target function and tumor environment are optimized with genetic algorithm and the

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best parameters are used to predict tumor growth.

Figure 3. Calculated area and perimeter size of coronal images of a tumor in mice on different days. (A) Coronal images of a tumor in C57BL mouse on 15th, 18th and 22nd day, respectively (adapted with permission from [36]. (B) Tumor detected for three different days with MATLAB image processing toolbox with SVM algorithm.

Due to the movement of the mouse, the closest cuts are selected in the images. In the simulation, the finite element method is also used. The programming of the genetic algorithm is also carried out, using the MATLAB Software. The results of predicting tumor growth using the genetic algorithm and estimating the best parameters for tumor growth are shown in the following tables. In Tables 1 and 2, the results for the objective function are the difference between real and simulated tumor area and perimeter, respectively.

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Table 2. Parameter estimation with difference between the mouse tumor area of the actual and simulated cases on day 18 as objective function and the error percentage and prediction for day 22

Estimated D

Percentage difference of real tumor area and simulation on day 18

Difference in real tumor area and simulated on day 22

80.656

9.935

1>

56.61

80.336

10.002

1>

56.69

3

80.565

9.954

1>

56.63

4

83.921

9.209

1>

55.60

Best person

Estimated ρ

1 2

Table 3. Parameter estimation with difference between the mouse tumor perimeter of the actual and simulated cases on day 18 as objective function and the error percentage and prediction for day 22

198.115

10.354

2

197.128

10.444

3

197.488

10.411

4

197.448

10.415

Difference in real tumor perimeter and simulated on day 22

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Percentage difference of real tumor perimeter and simulation on day 18

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Estimated D

1

90.58

1

90.75

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Estimated ρ

1

90.691

1

90.697

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Best person

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In Figure 4, the tumor contours simulated on the 22nd day are compared with the two functions mentioned above, which indicates that compared with simulated and laboratory conditions, using the objective function

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provides better results about the difference in tumor area. Results for mouse data with using different objective

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17.4%, respectively.

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functions show that differences between estimated and mouse tumor surface and perimeter were 3.7% and

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4. Conclusion

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Fig 4. Comparison of the tumor simulated with the objective function of the difference between the perimeter and the area with the experimental results. (A) Detected area of the tumor on 18th and 22nd day, respectively. (B) The tumor simulated with the objective function of the difference in area on 18th and 22nd day, respectively. The error percentage for this objective function is calculated about 3.7 %. (C) The tumor simulated with the objective function of the difference in perimeter on 18th and 22nd day, respectively. The error percentage for this objective function is calculated about 17.4 %.

This study shows an efficient and fully automatic method to predict tumor growth model. The model is

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validated with an in vivo model (murine model) and an in situ GBM tumor growth. PI mathematical model is investigated on mouse MR images, which predicts model parameters and tumor growth. The PI model is numerically integrated, using a finite element method in two dimensions. SVM method is selected for tumor segmentation (with MATLAB Software). Proliferation-Invasion (PI) equation for tumor growth is modeled with direct finite element method, using the COMSOL Software. Effective parameters in PI model (D (for different brain matters) and ρ) are estimated with genetic algorithm and tumor is predicted. Different brain matters are segmented from the high resolution T2W images using the image processing toolbox of MATLAB. Simulation is carried out with COMSOL and optimization is done with MATLAB (COMSOL with MATLAB Livelink).Results for mouse data, using different objective functions show that differences between estimated and mouse tumor surface and perimeter are 3.7% and 17.4%, respectively and indicate that genetic algorithm has a good agreement for tumor prediction.

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Gooya A, Pohl KM, Bilello M, Cirillo L, Biros G, Melhem ER, et al. GLISTR: glioma image segmentation and registration. IEEE Trans Med Imaging 2012;31(10):1941-54. Liu Y, Sadowski SM, Weisbrod AB, Kebebew E, Summers RM, Yao JJMia. Patient specific tumor growth prediction using multimodal images. 2014;18(3):555-66. Lê M, Delingette H, Kalpathy-Cramer J, Gerstner ER, Batchelor T, Unkelbach J, et al. MRI based Bayesian personalization of a tumor growth model. 2016;35(10):2329-39. Scheufele K, Mang A, Gholami A, Davatzikos C, Biros G, Mehl MJCMiAM, et al. Coupling brain-tumor biophysical models and diffeomorphic image registration. 2019;347:533-67. Meghdadi N, Soltani M, Niroomand-Oscuii H, Yamani NJANB. Personalized image-based tumor growth prediction in a convection–diffusion–reaction model. Acta Neurologica Belgica 2018;118:1-9. Burges CJ. A tutorial on support vector machines for pattern recognition. Data mining and knowledge discovery 1998;2(2):121-67. Simi V, Joseph JJTEJoR, Medicine N. Segmentation of Glioblastoma Multiforme from MR Images–A comprehensive review. 2015;46(4):1105-10. Selvaraj D, Dhanasekaran RJIJoCS, Engineering I. Mri brain image segmentation techniquesA review. 2013:0976-5166. Unkelbach J, Menze BH, Konukoglu E, Dittmann F, Le M, Ayache N, et al. Radiotherapy planning for glioblastoma based on a tumor growth model: improving target volume delineation. Phys Med Biol 2014;59(3):747-70. Assareh E, Behrang M, Assari M, Ghanbarzadeh A. Application of PSO (particle swarm optimization) and GA (genetic algorithm) techniques on demand estimation of oil in Iran. Energy 2010;35(12):5223-9. Bavi O, Bavi N, Shishesaz M. Geometrical Optimization of the Overlap in Mixed Adhesive Lap Joints. The Journal of Adhesion 2013;89(12):948-72. Bavi O, Salehi M. Genetic algorithms and optimization of composite structures. 1. 1 ed. Tehran, Iran: Abed Pub. 978964-364861-9; 2008:1-220. Dasgupta J, Sikder J, Mandal D. Modeling and optimization of polymer enhanced ultrafiltration using hybrid neural-genetic algorithm based evolutionary approach. Applied Soft Computing 2017;55:108-26. Sangdani M, Tavakolpour-Saleh A, Lotfavar A. Genetic algorithm-based optimal computed torque control of a vision-based tracker robot: Simulation and experiment. Engineering Applications of Artificial Intelligence 2018;67:24-38. Zare S, Tavakolpour-Saleh A, Binazadeh T. Passivity based-control technique incorporating genetic algorithm for design of a free piston Stirling engine. Renewable Energy Focus 2019;28:66-77. Rutter EM, Stepien TL, Anderies BJ, Plasencia JD, Woolf EC, Scheck AC, et al. Mathematical Analysis of Glioma Growth in a Murine Model. Sci Rep 2017;7(1):2508-. Swanson KR, Rostomily RC, Alvord EC, Jr. A mathematical modelling tool for predicting survival of individual patients following resection of glioblastoma: a proof of principle. Br J Cancer 2008;98(1):113-9.

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Manuscript Title: A novel in silico platform for fully automatic personalized brain tumor growth

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Mojtaba Hajishamsaei: Conceptualization, Methodology, Software, Validation, Writing - Original Draft, Visualization. Ahmadreza Pishevar: Conceptualization, Methodology, Validation, Supervision, Project administration. Omid Bavi: Formal analysis, Validation, Visualization, Writing - Review & Editing. Majid Soltani: Validation, Writing - Review & Editing, Supervision, Project administration.

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