**Modeling of the Temperature Field in the Magnetic Hyperthermia Hyperthermia**

**Modeling of the Temperature Field in the Magnetic**

DOI: 10.5772/intechopen.71364

Iordana Astefanoaei and Alexandru Stancu

[23] Holman JP. Heat Transfer. 7th ed. New York, NY: Mc Graw-Hill Book Company; 1990

2009;46:358-366. DOI: 10.1016/j.commatsci.2009.03.020

Publishing Corp; 1980. 197 p. DOI: 007084740-5

304 Numerical Simulations in Engineering and Science

[24] Ferreira IL, Voller VR, Nestler B, Garcia A. Two-dimensional numerical model for the analysis of macrosegregation during solidification. Computational Materials Science.

[25] Melaaen MC. Calculation of fluid flows with staggered and nonstaggered curvilinear nonorthogonal grids—The theory. Numerical Heat Transfer-Part B. 1992;21:1-19

[26] Patankar VS. Numerical Heat and Fluid Flow. 2nd ed. Washington, DC: Hemisphere

Iordana Astefanoaei and Alexandru Stancu Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.71364

### **Abstract**

The numerical and/or analytical modeling of the temperature field developed by the magnetic systems in the external alternating magnetic fields is essential in the Magnetic Hyperthermia. Optimization of the all parameters involved in the burning process of the malignant tissues can be realized more efficiently using a mathematical model. The analytical models can be used for the validation of any numerical complex models of the heating processes. This work focuses on the parameters which influences the therapeutic temperature field developed by the magnetic systems within the malignant tissues when the magnetic field is applied. An analytical model was developed to predict and control the bioheat transport within a malignant tissue. This model was compared with a numerical model which was developed in the same conditions of the thermal analysis. Infusion of a diluted suspension of magnetic nanoparticles (MNP) into liver tissue was modeled using the Darcy's equation. The MNP concentration and the temperature field were computed for different parameters as: (i) ferrofluid infusion rates, (ii) particle zeta potential and (iii) magnetic field parameters. The convection-diffusion-deposition of the particles within tissues was considered in this analysis. This study indicates the essential role of these parameters to predict accurately the hyperthermic temperature field. The model presented in this paper predicts the optimum MNP dosage and the temperature at every point within the malignant tissue.

**Keywords:** finite element method (FEM), Magnetic Hyperthermia, modeling of the temperature field, magnetite nanoparticles


**2. Materials and Methods**

## *2.1. Methodology*

The application of machine learning regression methods to predict the dynamics of a rolling bearing cage requires data representing the correlation between the varied parameters and the calculated cage dynamics. The starting point was the multi-body simulation model defined in the software Caba3D [22,23]. The calculation parameters of the model such as initial and boundary conditions, friction models, and elastic modeling of the cage are described in Section 2.2. The geometry of the cage as well as the bearing load and rotational speed were modified with the help of a comprehensive simulation plan using the design of experiment, see Section 2.3. A Latin hypercube sampling was used to ensure that the varied parameters are distributed uniformly in the entire mathematical space defined by previously specified boundaries [24]. The limits of the simulation plan were chosen so that the operating conditions prevailing in reality are mainly covered. On the basis of the uniformly distributed parameter values in the simulation plan, the correlations between the parameters can be efficiently learned by the algorithm. After performing the calculations, the simulation results were used to determine the input and output parameters and thus the data sets for machine learning, see Section 2.4. Characteristic values such as the Cage Dynamics Indicator (CDI) defined by Schwarz et al. [21] were derived from the calculated time series, which can be used for the assessment of the cage dynamics and as target values for machine learning. Artificial neural networks (ANN) [25], random forest (RF) [26], and XGBoost [27] were applied to predict the target variables based on the varied calculation parameters, see Section 2.5. The optimization of the hyperparameters of the used algorithms was performed as part of the training process using an evolutionary algorithm (EA) [28]. Finally, the predictions of the optimized models for test data sets were compared so that the most suitable algorithm could be selected. Figure 1 illustrates the procedure for generating a regression model for the prediction of characteristic values representing cage dynamics.

**Figure 1.** Procedure in this study, starting with the dynamics simulation and the design of experiments, followed by the creation of a database, the training of the machine learning models, and analysis of the predictions.


**3.1 Landslide inventory**

Landslide inventory is the base for landslide hazard zonation mapping [5, 28, 33, 35, 42]. A clear understanding of landslide conditions and a more detailed assessment of the landslide hazard of the area concerned are essential to make a systematic landslide inventory. The landslide inventory map depicts the location and characteristics of prior landslides. The geologic, topographic, and climatic conditions that are overcome at the site give an important indication regarding the causes and triggering mechanisms of the past slope failures. Hence, landslide inventory mapping provides helpful insight regarding the potential for future landslide occurrences. Based on relevant literature, historical sources, and classical field survey and mapping, landslide inventory on sliding processes was compiled. The inventory includes 46 different types of mass movements from the past and present that are dispersed throughout the area. The landslide inventories (**Figure 5a**) were collected through the direct field survey method. The density of landslides is very high in the central part of the area which is covered by highly weathered basalt.

*Landslide Assessment and Hazard Zonation in the Birbir Mariam District, Gamo Highlands… DOI: http://dx.doi.org/10.5772/intechopen.108122*

#### **Figure 5.**

*a. Landslide inventory map of Birbir Mariam district, b. slope geo-material map of Birbir Mariam district.*

#### **Figure 6.**

*Landslide causative factor maps, a. groundwater condition manifestation, b. land use land cover, c. slope morphometry, and d. relative relief.*

### **3.2 Landslide causative factors**

Intrinsic factors are the inherent or static causative parameters that define the favorable or unfavorable stability conditions within the slope [4, 11]. The main landslide causative factors selected for the Birbir Mariam area are summarized in **Table 1** and their brief descriptions are presented hereunder.

### *3.2.1 Groundwater condition*

Groundwater has a major influence on slope stability. In hilly terrains, groundwater does not follow a consistent pattern and is generally channeled along rock structural discontinuities. It is difficult and time-consuming to assess the behavior of groundwater in hilly terrains over large areas. Groundwater surface indicators (**Figure 6a**) such as damp, wet, dripping, and flowing provide valuable information on the stability of hill slopes and are helpful for the rating [4].


**Set-Valued Analysis**

Editors

**Anca Croitoru Anna Rita Sambucini Bianca Satco**

MDPI • Basel • Beijing • Wuhan • Barcelona • Belgrade • Manchester • Tokyo • Cluj • Tianjin

*Editors* Anca Croitoru University "Alexandru Ioan Cuza" of Iasi Romania

Anna Rita Sambucini University of Perugia 1 Italy

Bianca Satco University of Suceava Romania

*Editorial Office* MDPI St. Alban-Anlage 66 4052 Basel, Switzerland

This is a reprint of articles from the Special Issue published online in the open access journal *Mathematics* (ISSN 2227-7390) (available at: https://www.mdpi.com/journal/mathematics/special issues/Set Valued Analysis).

For citation purposes, cite each article independently as indicated on the article page online and as indicated below:

LastName, A.A.; LastName, B.B.; LastName, C.C. Article Title. *Journal Name* **Year**, *Volume Number*, Page Range.

**ISBN 978-3-0365-0784-2 (Hbk) ISBN 978-3-0365-0785-9 (PDF)**

© 2021 by the authors. Articles in this book are Open Access and distributed under the Creative Commons Attribution (CC BY) license, which allows users to download, copy and build upon published articles, as long as the author and publisher are properly credited, which ensures maximum dissemination and a wider impact of our publications.

The book as a whole is distributed by MDPI under the terms and conditions of the Creative Commons license CC BY-NC-ND.


**5.3 Acyclovir, valacyclovir and other antiretroviral drugs**

Oral antivirals are not a regular treatment modality, but isolated case report about improvement in wart lesion after oral treatment with acyclovir [112], valacyclovir are there. Plantar wart is cleared completely with 1 gm valacyclovir for 60 days [113]. Improvements of wart with intravenous cidofovir in one HIV seropositive patient with complete clearance are available [114].  The observations are not powerful enough to assume causality (instead of a simple casual or placebo effect).


**And Finally**

As discussed in this chapter, cultural planning processes are messy by nature and there is no toolkit or route map that can be rolled out and replicated. Meller [34] some time ago criticised the vagueness in the Geddes' legacy and it remains unclear how to translate that knowledge and passion into reality within a top down planning framework so that local people and heritage assets, including tangible infrastructure and intangible histories can reliably have power and voice in the planning process. We argue that, rather than imposing a toolkit, there is a need for better articulation of these messy unpredictable processes. And perhaps, the messiness is exactly the crunch point here. There are ingredients, there are underpinning values, but no toolkit because each situation is, of necessity, unpredictable and requires responsiveness to the heritage, the creativity, the people (and their imagination). In other words, the unique DNA and local circumstances of each place are all part of the plan. In fact, they *are* the plan: to be unveiled.


**14.5 Ease of sharing**

The modern digital education system is completely different from the old-fashioned old education system, which mainly relied on students keeping large, handwritten notebooks filled with knowledge that they learned from their teachers in class or through intensive research in the library. Students may now save a ton of time and effort by easily archiving and sharing material with just a click.


**3.1 Time-domain features results**

The multiple and binary classification results of 25 feature vectors extracted from SSVEP signals using time-domain properties are given below, respectively.

*Evaluating Steady-State Visually Evoked Potentials-Based Brain-Computer Interface System… DOI: http://dx.doi.org/10.5772/intechopen.98335*

#### **Figure 17.**

*Percentage of classifier where the best result is the most often obtained as a result of running the algorithms 2,520 times in total (for Haar wavelet function).*

#### **Table 2.**

*Results of multiple classification for time-domain features.*

#### **Table 3.**

*Results of multiple classification for frequency-domain features.*

#### **Table 4.**

*Multiple classification results of wavelet features.*

#### **Table 5.**

*Classification results of the most successful frequency pairs of the Haar mother wavelet.*

### *3.1.1 Multiple classification results*

Presented in **Table 2** are accuracy results for multiple classification. In regard to these results, the highest performance was shown by the Ensemble Learning classifier with 52.40%.

### *3.1.2 Binary classification results*

According to the binary classification results shown in **Figure 2**, the best performance was obtained with an accuracy value of 91.68% in 6–10 Hz frequency pairs based on the average of the subjects. Simultaneously, when the subjects are considered separately, a classification performance up to 100% were obtained. In addition, there is no definitive finding related to the increase in the accuracy value parallel to the difference between frequencies for the time-domain.

The results of classifiers to be expressed in the pie chart in **Figure 3** are the number of hits of the classifiers obtained. These numbers were obtained by running all algorithms 2,520 times in total. The best classification performance is shown by the Ensemble learning classifier.

#### **3.2 Frequency-domain features results**

For the frequency-domain characteristics used in the problem of determining seven different frequencies, firstly, spectrum analysis was performed to detect the stimulus frequencies more clearly than the signal. This analysis is often used to obtain frequency information in evoked SSVEP responses. The power spectrum of SSVEP

### *Evaluating Steady-State Visually Evoked Potentials-Based Brain-Computer Interface System… DOI: http://dx.doi.org/10.5772/intechopen.98335*

signals was determined by FFT using MATLAB software to calculate its power, entropy, and variance for each band in the frequency range corresponding to the frequencies. For this purpose, the signal received FFT is divided into EEG bands (delta, theta, alpha, beta, gamma), and energy, entropy, and variance values of each band are calculated. A total of 15 feature vectors are generated.

#### *3.2.1 Multiple classification results*

According to the multiple classification results of the seven frequencies presented in **Table 3**, it was determined that the best performance was in the Ensemble Learning classifier with an accuracy value of 57.10%. Another remarkable finding here is that the results of the classifier from all individuals are the same. This shows us that, like the time-domain, the Ensemble Learning classifier performs better than others. In addition, when multiple classification results of frequency-domain features are compared with multiple classification results of time-domain features, it has been determined that there is an increase of 4.70% on an individual basis and 3.18% on average.

#### *3.2.2 Selected three class classification results*

In this part, three frequencies (6 Hz - 8.2 Hz - 10 Hz), which are considered to increase the classification performance, were chosen among the seven frequencies present in the data set, during the feature extraction phase. The reason for choosing these frequencies are the results of the study done in Ref. [12, 13, 20].

According to the results obtained (**Figure 4**), the highest classification performance for the first participant was 83.30% in the Ensemble Learning classifier, the highest 100% classification performance for the second participant was in the KNN and SVM classifiers, and 88.90% for the third participant in the KNN classifier. Finally, in the fourth participant, it was seen again in the Ensemble Learning classifier with 77.80%.

When the results are evaluated considering the classifiers, the performance of the six different classifiers was calculated by taking the average of the four participants and the highest performance was found in the Ensemble Learning classifier with an accuracy of 79.73%.

#### *3.2.3 Binary classification results*

Considering the averages of the binary classification results of frequency features, the performances obtained vary between the lowest 70.85% and the highest 100%. Accordingly, the highest performance was determined with 100% accuracy value in 7.5–10 frequency pairs.

When the results are evaluated in terms of classifiers, it is clearly seen in **Figure 6** that the classifier with the highest accuracy rate is the Ensemble Learning classifier. Runner-up classifier is the SVM classifier. Other classifiers following Ensemble Learning and SVM were identified as KNN, Logistic Regression and Naive Bayes classifiers, in order. It is also seen that no successful results have been obtained in the LDA and Decision Tree classifiers.

#### **3.3 Wavelet transform features results**

This section aims to analyze three crucial features, such as energy, variance, and entropy, which are frequently used in DWT studies, have been extracted from the

bands (delta, theta, alpha, beta, and gamma) of the EEG signal. These features were generated for six different mother wavelets (Haar, db4, sym4, coif1, bior3.5, rbio2.8) commonly used in the literature. The results of each were evaluated in detail for multiple, binary, and three selected frequencies.

## *3.3.1 Multiple classification results*

On the basis of mother wavelet selection, the results in (**Table 4**), reveal that Bior3.5 and Coif1 mother wavelets were relatively successful, although there is no dominant wavelet type. Experimenting with a larger sample size (number of subjects), in order to generalize, can help obtain more precise results.

In contrast to the mother wavelet selection, when the classifiers are evaluated, the success of Ensemble learning and LDA classifiers is clearly seen.

### *3.3.2 Classification results for three selected frequencies*

In this analysis, as in the classification of frequency-domain features (Section 3.2.2), multiple classification was made by selecting 3 selected frequencies (6 Hz - 8.2 Hz – 10 Hz) where the differences between the frequencies were higher among the seven frequencies. However, unlike the analysis made in the frequency-domain, the selected features are classified and evaluated both they are used together, that is, when energy, variance and entropy features are used as a single feature vector (all features together, and they are used as separate features. Thus, detailed information about the power, irregularity and bias of the signal was obtained. At the same time, it is learned how to use these three features, which have the indispensable properties of the signal, more effectively. And the contribution of these features, which are frequently used in the literature, as a new form of features is wanted to be shown.

In **Figure 7**, the ACC values obtained by classification of the energy, entropy, and variance features extracted using each wavelet family are presented. Mean, minimum and maximum values of the classification results were also shown. According to these results, the values given by the Haar wavelet function for energy, entropy, and variance feature groups, which yield more successful results than other wavelet functions, were 75.85%, 73.08%, and 73.75%, respectively. There were no major differences between the mean values of the features extracted based on the Haar wavelet. However, it was seen that the entropy feature group had a 100% success rate compared to the others.

In **Figure 8**, the extracted features based on wavelet were used as a feature set, and the successful performances of the wavelet families were compared in this way. It was seen that the most successful wavelet family was the Haar wavelet function. The ranking of success in other wavelet families has not changed.  It was seen that some mother wavelet performances increased when compared with the ACC values in which the features in **Figure 7** were handled separately. Mean values of coif1, db4, and sym4 mother wavelet functions increased.

As a result of the classification processes performed separately for each subject, when the performances of both feature groups were examined, the most successful wavelet function was found as the Haar wavelet. When the average accuracy values of the feature groups are examined, the results in the case that the three features are used *Evaluating Steady-State Visually Evoked Potentials-Based Brain-Computer Interface System… DOI: http://dx.doi.org/10.5772/intechopen.98335*

as a single feature vector gave higher results for all wavelet functions than the other feature group. Although there is no dominant result in the comparison of energy, entropy, and variance features among themselves, the highest result was seen in the entropy feature in Subject 3 with 100%.

The results of classifiers to be expressed in the pie chart in **Figure 9** are the number of hits of the classifiers obtained. With reference to results obtained, it is obvious that the most successful and also the most frequent classifier in the classification was obtained as the Ensemble classifier.

#### *3.3.3 Binary classification results*

In this analysis, feature vectors are treated as a single feature vector and individual (separate) feature vectors, similar to those in Section 3.2.3. The resulting feature vectors were then evaluated by binary classification in order to analyze frequencies in detail. As the results of the experimental design, the classification performances are obtained for:

Each feature (energy, entropy, variance and all features together) extracted using each wavelet family. All values of the classification results are presented in **Figures 10**–**15** for each mother wavelet, respectively.

According to these results, features obtained from the Haar wavelet function yielded higher accuracies than those obtained from the other wavelet functions. Maximum accuracy performances were obtained in the frequency pairs "6–10", "6.5–8.2", "6.5–10" in the Haar wavelet (**Table 5**). When the features are evaluated, it is realized that the "All features together" feature generally has better results for all mother wavelet functions.

And another researched hypothesis results are presented in **Figure 16** for each mother wavelet, respectively. The purpose here is to show the change in the accuracy value according to the increase in the difference between the frequencies.

Finally, classification results obtained are presented in **Figure 17**. Since the classification results of all the features ranking are similar for all the wavelet functions, the classification result of the "All features together" for Haar wavelet function is presented. According to these results, the most successful classifier was obtained as the Ensemble classifier.