**2. Material and methods**

The database utilized in this chapter consists of 10 patients treated with real-time compensation of tumor motion by means of the Synchrony® respiratory tracking module, as available in the Cyberknife® system. This system provides tumor tracking relying on external/internal correlation model between the motion of external infrared markers and of clips implanted near thoracic tumors. In this system, the correlation model will be constructed at the beginning of each treatment session and will be updated over the course of treatment. **Figure 4** depicts three-mentioned steps as model configuration, model performance, and model update during treatment. The model is built by means of training data set before starting the treatment. Training data include 3D external markers motion as model input and internal implanted clip as model output. When the model is made, it can be applied to estimate tumor motion as a function of time during the treatment. The model can also be updated and re-built as needed during the treatment with X-ray imaging representing the internal marker location. For model performance, the only input data including external markers motion are given, and the output is tumor motion estimation. The utilized model in this flowchart is based on fuzzy logic inference system that is robust enough for tumor motion prediction based on our previous studies [34–38].

Markers motion data set represents the position information of each marker as function of time. This data set is saved in matrix form for model construction and performance. **Figure 5** shows a matrix with n rows and nine columns including x, y, and z of three utilized external markers located on rib cage and abdomen regions. For model construction and performance, the motion data set should be firstly clustered. Motion data set is firstly arranged at two input and output matrices.

Motion Challenge of Thoracic Tumors at Radiotherapy by Introducing an Available Compensation Strategy http://dx.doi.org/10.5772/67444 271

**Figure 4.** A block diagram of a correlation model including its construction, performance and update.

is traced by means of specific external markers placed on thorax region (rib cage and abdomen) of patient body and recorded by some monitoring systems such as infrared optical tracking (OTS) or laser-based systems. In contrast, the internal tumor motion is tracked using implanted internal clips inside or near the tumor volume and is visualized using orthogonal X-ray imaging system in snapshot mode. The generated correlation model can estimate the tumor motion from external markers data as input when internal marker data are out of access. The end result is a nonlinear mapping from the motion data of external markers as input to an output, which is the estimate of tumor position versus time. Recently, several respiratory motion prediction models have been developed in different mathematical approaches [34–37]. Since the breathing phenomena have inherently high uncertainty and therefore cause a significant variability in input/output data set, a mathematical model with highest accuracy may

correlate input data with tumor motion estimation with less uncertainty error [8].

errors of target localization was calculated using available statistical metrics [15].

enough for tumor motion prediction based on our previous studies [34–38].

**2. Material and methods**

270 Radiotherapy

and output matrices.

Since explaining all proposed strategies concerning tumor motion management is very extensive, we concentrated on external surrogate's radiotherapy in this chapter as clinical available strategy. Therefore, in this chapter, we quantitatively investigate the effect of motion error of thoracic tumors on treatment process at external surrogate's radiotherapy. To do this, the motion information of a group of real patients treated with Cyberknife Synchrony system (from Georgetown University Hospital) was taken into account, and the amount of possible

The database utilized in this chapter consists of 10 patients treated with real-time compensation of tumor motion by means of the Synchrony® respiratory tracking module, as available in the Cyberknife® system. This system provides tumor tracking relying on external/internal correlation model between the motion of external infrared markers and of clips implanted near thoracic tumors. In this system, the correlation model will be constructed at the beginning of each treatment session and will be updated over the course of treatment. **Figure 4** depicts three-mentioned steps as model configuration, model performance, and model update during treatment. The model is built by means of training data set before starting the treatment. Training data include 3D external markers motion as model input and internal implanted clip as model output. When the model is made, it can be applied to estimate tumor motion as a function of time during the treatment. The model can also be updated and re-built as needed during the treatment with X-ray imaging representing the internal marker location. For model performance, the only input data including external markers motion are given, and the output is tumor motion estimation. The utilized model in this flowchart is based on fuzzy logic inference system that is robust

Markers motion data set represents the position information of each marker as function of time. This data set is saved in matrix form for model construction and performance. **Figure 5** shows a matrix with n rows and nine columns including x, y, and z of three utilized external markers located on rib cage and abdomen regions. For model construction and performance, the motion data set should be firstly clustered. Motion data set is firstly arranged at two input As mentioned before, the utilized correlation model is on the basis of fuzzy logic concept. In fuzzy logic, linguistic variables represent operating parameters to apply a more human-like way of thinking. Fuzzy logic works by means of if-then rule-based approach to solve a problem rather than attempting to model a system mathematically. Recently, the main features of fuzzy logic theory make it highly applicable in many systematic designs in order to obtain a better performance when data analysis is too complex or impractical for conventional mathematical models. Since breathing motion variability is remarkable, fuzzy logic-based correlation model may robust and can practically be applied on a real patient data set. In fuzzy logic-based systems, membership functions represent the magnitude of participation of each input, graphically. The proposed fuzzy correlation model involves data clustering for membership function generation, as inputs for fuzzy inference system section. Data clustering analysis is the organization of a collection of data set into clusters based on similarity. In the implemented fuzzy logic algorithm, data from all three external markers arranged in an input matrix with nine columns, and data

**Figure 5.** X, Y and Z motion direction of three external markers inside matrix with n rows and nine columns.

from internal marker set in an output matrix with 1 column are clustered initially. Sugeno and Mamdani types of fuzzy inference systems configured by (1) data fuzzification, (2) *if-then* rules induction, (3) application of implication method, (4) output aggregation, and (5) defuzzification steps, utilized due to its specific effects on model performance. The proposed correlation model was developed in MatLab (The MathWorks Inc., Natick, MA) using the embedded toolboxes of fuzzy logic. **Figure 6** shows nine data points (small spots) of motion data set of one external marker clustered at three groups (large spots). The cluster centers (large spots) were distributed as an available mathematical method that works on the basis of data points' spatial distribution density. After data clustering, membership functions will be obtained using the information of clusters center. The mathematical information of these functions is used for defining the parameters of learning based inference system as correlation model.

**Figure 6.** Nine data points (small spots) of motion data set of an external marker with three clusters (large spots).

For real-time tumor tracking, the correlation models should be executed without a significant delay such that on-time compensation strategy should be applied against tumor motion. Therefore, the execute time of each correlation model that strongly depends on the utilized mathematical procedures should be taken into account for clinical application.

#### **3. Results**

In order to show quantitatively the challenging issues of targeting accuracy concerning thoracic tumor, its motion and correlation model output of one lung patient were shown graphically. Moreover, root means square error (RMSE) was utilized as mathematic tool, and the average of RMSE over total patients used in this work was reported. **Table 1** illustrates the


from internal marker set in an output matrix with 1 column are clustered initially. Sugeno and Mamdani types of fuzzy inference systems configured by (1) data fuzzification, (2) *if-then* rules induction, (3) application of implication method, (4) output aggregation, and (5) defuzzification steps, utilized due to its specific effects on model performance. The proposed correlation model was developed in MatLab (The MathWorks Inc., Natick, MA) using the embedded toolboxes of fuzzy logic. **Figure 6** shows nine data points (small spots) of motion data set of one external marker clustered at three groups (large spots). The cluster centers (large spots) were distributed as an available mathematical method that works on the basis of data points' spatial distribution density. After data clustering, membership functions will be obtained using the information of clusters center. The mathematical information of these functions is used for defining the param-

For real-time tumor tracking, the correlation models should be executed without a significant delay such that on-time compensation strategy should be applied against tumor motion. Therefore, the execute time of each correlation model that strongly depends on the utilized

**Figure 6.** Nine data points (small spots) of motion data set of an external marker with three clusters (large spots).

In order to show quantitatively the challenging issues of targeting accuracy concerning thoracic tumor, its motion and correlation model output of one lung patient were shown graphically. Moreover, root means square error (RMSE) was utilized as mathematic tool, and the average of RMSE over total patients used in this work was reported. **Table 1** illustrates the

mathematical procedures should be taken into account for clinical application.

**3. Results**

272 Radiotherapy

eters of learning based inference system as correlation model.

**Table 1.** Motion features of tumors and external markers of selected patients with their treatment time.

motion information of 3D external markers and implanted clip inside tumor volume for 10 patients plus treatment time for each patient.

As seen in **Table 1**, tumors type include lung liver, pancreas, and chest wall. In this table, LLL, RLL, and RUL indicate left lower lung, right lower lung, and right upper lung, correspondingly. The average 3D RMSE over this patient group is 0.99 mm.

**Figure 7** shows tumor motion in anterior posterior (AP), superior inferior (SI), and left right (LR) directions obtained from stereoscopic X-ray imaging regarding with correlation model output for a lung cancer patient. As seen in this figure, remarkable error belongs to tumor motion tracking at SI direction versus two other directions while the minimum similarity was happened in this direction. At both SI and LR directions, minimum targeting error is happening at middle part of total treatment time.

**Figure 8** shows the tumor motion tracking of one patient with liver cancer over few minutes of treatment time on anterior posterior (AP) directions. The stereoscopic X-ray imaging points indicated by dark spots in these figures represent the exact position of tumor location at that time.

As seen in this figure, breathing condition is almost normal and tumor tracking is going well with least uncertainty error, and there is a close correlation among model output and real

**Figure 7.** Lung tumor motion in anterior posterior (AP), superior inferior (SI) and left right (LR) directions obtained from stereoscopic X-ray Imaging in comparison with correlation model output.

**Figure 8.** Motion prediction of a liver tumor by means of fuzzy-based correlation model over treatment time. Dark spots taken by stereoscopic system represent the exact position of the tumor.

position of tumor. For this patient, the calculated root mean square error (RMSE) is 1.7-mm 3D that represents tumor motion tracking is performing as well by means of utilized fuzzybased prediction model. As noncontrol patient with large error, **Figure 9** represents targeting error of one worse patient with pancreas cancer with abnormal breathing motion variation at LR direction. As seen in this figure, tumor motion tracking is with large error; while at some times, the distance between imaging data point and the output of correlation model is significant. For example, third imaging point is far away from model output that represents motion tracking is not going well. This is nonnegligible targeting error that should be considered to be minimized.

**Figure 9.** Motion prediction of a pancreas tumor by means of fuzzy-based correlation model over treatment time. Dark spots taken by stereoscopic system represent the exact position of tumor.

### **4. Discussion**

**Figure 8.** Motion prediction of a liver tumor by means of fuzzy-based correlation model over treatment time. Dark spots

**Figure 7.** Lung tumor motion in anterior posterior (AP), superior inferior (SI) and left right (LR) directions obtained from

taken by stereoscopic system represent the exact position of the tumor.

stereoscopic X-ray Imaging in comparison with correlation model output.

274 Radiotherapy

Cancer disease is one of the most common reasons of death at worldwide. A number of treatments for cancer include surgery, chemotherapy, and radiotherapy. Radiation therapy is one of the most common treatments for some cancer cells. It uses X-rays, gamma rays, electron beams, or protons and heavy ions to physically and chemically damage DNA of cancer cells. Radiation can be given alone or used with other treatment modalities, such as surgery or chemotherapy. In principal, at radiation therapy, several strategies can be utilized to deliver high doses of radiation to the cancer cells as target while delivering minimum dose to the surrounding healthy tissues at the same time. The goal of radiation treatment is to damage cancer cells, with as little harm as possible to nearby healthy cells. By the way, nearby normal cells may also be affected by radiation, but they will recover and go back to work normal. Unlike chemotherapy, which exposes the whole body to cancer-fighting drugs, in most cases, radiation therapy is a local treatment.

In this chapter, we focused on radiation treatment of moving thoracic tumors located in thorax region of patient body and move mainly due to respiration. This motion will be problematic for tumor localization and its aligning against therapeutic beam. In old strategies, tumor volume at its total moving space entitled internal tumor volume was considered as target for irradiation. In this strategy, a remarkable dose is received by nearby normal tissues that may cause serious side effects. Then, several efforts were done for tumor motion error compensation as motion-gated radiotherapy or real-time tumor-tracking radiotherapy. At both latter strategies, tumor motion information should be extracted as a function of time during irradiation. In this chapter, we quantitatively assess the effect of tumor motion and possible drawbacks and errors at external surrogate's radiotherapy. For this aim, tumor motion information of a real patient treated with Cyberknife Synchrony system was taken into account. A fuzzy logicbased correlation model was developed to track tumor motion using motion data set of rib cage and abdomen region of patient. Final results represent graphically the amount of tumor motion estimated by utilized model on 3D with a calculated targeting error. In order to reduce such errors, more robust prediction models should be implemented. Moreover, the accuracy of model learning and its configuration at pretreatment step before therapeutic irradiation may reduce estimation error. At external beam radiotherapy of dynamic tumors, another issue that must be considered is due to patient displacement or inter-fractional motion error between each fractions of treatment process. In the modern radiotherapy, the success degree of a treatment strongly depends on the compensation of both inter- and intra-fraction motion errors.
