lung cancer is the most deadly cancer disease with an estimated 27% of all cancer deaths , . a large part of patients with lung cancer undergoes radiotherapy . tracking tumor motion poses a significant challenge for precise dose delivery in lung cancer radiotherapy , due to respiratory motion of up to 3.5 cm for primary lung tumors . if the patient s breathing motion is not correctly predicted , tumor miss might occur , or sensitive normal tissue might be undesirably exposed resulting in unwanted treatment toxicity . advanced technologies of radiotherapy , intensity modulated radiotherapy and image guided radiotherapy , may offer the potential of precise radiation dose delivery for moving objects . however , they still need an additional function to predict the precise position of the tumor against subtle variations in real - time , . radiation dose is typically delivered in 3 to 5 fractions over 5 to 12 days for early stage lung cancer using stereotactic radiotherapy or 30 to 33 fractions over 6 to 7 weeks for more advanced disease with each fraction lasting between 10 and 45 minutes . the patient s breathing motions during these fractions are broadly divided into two categories  : 1 ) intra - fractional and 2 ) inter - fractional variations . intra - fraction motion indicates changes where the patient is undergoing the radiation therapy , which turns up on a time scale of seconds to minutes , , . each individual shows different breathing patterns . on the other hand , inter - fractional variation is typically shown in a time scale of minutes to hours or a day - to - day level , , . inter - fractional motion is distinguishable from intra - fractional movement because the inter - fractional variation covers even baseline shifts and weight gain or loss , . however , most studies of breathing prediction so far have focused on respiratory motions within the single treatment session , i.e. , intra - fractional variation . recently , several studies  have pointed out the difference between intra - fractional and inter - fractional movements and have discussed the importance of inter - fractional variation in radiation treatment or related imaging techniques . table 1 summarizes the comparison between intra- and inter - fractional movements.table 1comparison between intra- and inter - fractional variations.variation typeintra - fractioninter - fractiontime of occurrenceduring a single fraction , between different fractions , , , time scaleseconds to minutes hours or day - to - day level , , motion coverageinternal organ motion , breathing , swallowing , position changes of patients , patient weight gain / loss , internal organ motion , breathing , swallowing ,   prediction methods for intra - fractional variation have been addressed in many studies ,  , , , ,  as illustrated in table 2 . however , inter - fractional variation has not been actively studied as much as intra - fractional motion yet despite its necessity in radiotherapy , , , . intra- and inter - fractional variation of breathing motion can raise many challenges for respiratory prediction thirdly , the novel method should be able to handle any unpredictable breathing variation.table 2previous prediction methods for intra- and inter - fractional variations.methoddescriptiondrawbackvariationmargin-based  compensated locational changes of the tumor in a primitive way , adding extra margins high possibility of over / under - dose since the margin is determined by motion range of the tumor without knowing its variationintra-/inter - fractionlinear predictive model ( lp ) ,  estimated the future state based on functions comprised of linear combination of input data , proper coefficients , and constants inferior prediction accuracy for breathing signals with a long latency poor performance improvement by its exclusive usage assumption that the nonlinear respiratory movement is linearintra-/inter - fractionadaptive filter ( af ) , , ,  ,  combined modified lps and additional filters that adjust coefficients of lps no guarantee of its superb performance in most cases because it highly depends on adaptation intervalsintra - fractionkalman filter ( kf ) , , ,  efficient recurrent filter which has been utilized in various forms : kalman constant velocity , kalman constant acceleration , an interacting multiple model , and hybrid implementation based on the extended kf ( hekf) only adaptable to linear or nearly linear estimation high computation complexity of kf - based models combined with other prediction toolsintra - fractionartificial neural network ( nn)-based , , , , , , , ,  , ,  showed outstanding accuracy for irregular patterns and abrupt changes, extended approaches : back propagation nn , feed - forward nn , recursive nn , wavelet nn , customized prediction with multiple patient interactions using nn ( cnn ) , and hekf long calculation time for prediction parameters and resultsintra - fractioncubic model  estimated respiratory variance by using a third - order polynomial equation same drawback of low accuracy as lp because the cubic model is also one of the mathematic approaches like lpinter - fractionstochastic fluence map optimization ( fmo ) model  extended deterministic fmo model , which assumes that a patient is static solved observed problems by employing convex penalty functions and numerous scenarios to characterize inter - fractional uncertainties unpredictable method for other disregarded scenariosinter - fraction in this paper , we propose a new prediction approach for intra- and inter - fraction variations , called intra- and inter - fractional variation prediction using fuzzy deep learning ( iifdl ) . the proposed iifdl clusters the respiratory movements based on breathing similarities and estimates patients breathing motion using the proposed fuzzy deep learning ( fdl ) . to reduce the computation time , first , this is the first analytical study for modeling multiple patients breathing data based on both intra- and inter - fractional variations . secondly , the proposed method has a clinical impact for enhanced adjustment of margin size because it achieves high prediction accuracy for respiratory motion , even for inter - fractional variation . thirdly , this study shows the clinical possibility of real - time prediction by largely shortening computing time . furthermore , the training process can be shortened , by training breathing signals with similar patterns together in the proposed iifdl . the proposed fdl is a combination of fuzzy logic and a nn with more than two hidden layers , i.e. deep learning network . due to the nn architecture of fdl , it has a self - learning feature , setting network parameters by training itself according to input and desired output values . fdl also has a fuzzy logic feature of reasoning capability for uncertainty . in fdl , a few fuzzy parameters , i.e. prediction parameters of fdl , determine weight values between nodes in the network , and weight values are considered as the prediction parameters in other methods . consequently , the number of prediction parameters is much less than that of other mutated nn methods and parametric nonlinear models . this reduces the computation time substantially and makes suitable for to real - time and nonlinear estimation . 1 exemplifies a simple architecture of fdl , including layer 1 through layer 4 in the hidden layers . the functions of four hidden layers can be summarized as follows : layer 1 provides membership functions which are determined by a membership function ( mf ) parameter set \documentclass[12pt]{minimal } 
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 1)patient clustering : patients breathing feature metrics are computed from the respiratory signals , and then patients are clustered according to their breathing feature similarities.2)prediction using fdl : for each patient group , the training procedure of the hybrid learning algorithm is conducted , and then breathing signals with intra - fractional variation or inter - fractional variation are predicted using fdl . patient clustering : patients breathing feature metrics are computed from the respiratory signals , and then patients are clustered according to their breathing feature similarities . prediction using fdl : for each patient group , the training procedure of the hybrid learning algorithm is conducted , and then breathing signals with intra - fractional variation or inter - fractional variation are predicted using fdl . we describe the specific clustering procedure in subsection \documentclass[12pt]{minimal } 
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 } { } $ c_{final}$ 
 \end{document } classes depending on selected principal features of y. after multiple patients are clustered , we can train patients data for each group . for intra - fractional variation , fdl trains parameters based on input data in a single session and fdl predicts breathing motion by training the fdl network for multiple datasets of previous sessions . here , datasets of inter - fractional variation already include the patient s intra - fractional variation , as described in section i. training datasets consist of the initial data and the target data . we train the datasets with the hybrid learning algorithm . during the training procedure , two prediction parameter sets of fdl , i.e. , mf parameter set \documentclass[12pt]{minimal } 
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 \end{document } and lr parameter set r , are obtained and applied to the proposed fdl . for estimating intra- and inter - fractional variation from the cyberknife data , fdl has a similar structure to fig . 1 , the input datasets consist of three - dimensional ( 3d ) coordinates for each channel . thus , we designed the proposed prediction method to have three fdls for each \documentclass[12pt]{minimal } 
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 } { } \begin{equation * } o_{1,i } = \begin{cases } { \mu _ { a_{i } } \left ( { { i_{1 } } } \right ) = 1 / { \left [ { { 1+\left | { { { \left ( { { i - m_{i,3 } } } \right ) } / { m_{i,1 } } } } \right |^{2m_{i,2 } } } } \right ] } , } \\ \qquad \qquad \qquad \qquad \qquad \qquad \qquad { 1\le i\le 3 } \\ { \mu _ { b_{i-3 } } \left ( { { i_{2 } } } \right ) = 1 / { \left [ { { 1+\left | { { { \left ( { { i - m_{i,3 } } } \right ) } / { m_{i,1 } } } } \right |^{2m_{i,2 } } } } \right ] } , } \\ { \mu _ { c_{i-6 } } \left ( { { i_{3 } } } \right ) = 1 / { \left [ { { 1+\left | { { { \left ( { { i - m_{i,3 } } } \right ) } / { m_{i,1 } } } } \right |^{2m_{i,2 } } } } \right ] } , } \\ \qquad \qquad \qquad \qquad \qquad \qquad \qquad { 7\le i\le 9 } \\ \end{cases}\quad \end{equation*}\end{document } where \documentclass[12pt]{minimal } 
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 } { } $ m_{i,3}$ 
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 } { } $ o_{\mathrm { 3},i}$ 
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 } { } \begin{align } o_{2,i}=&{w}_{i } = \mu _ { a_{k } } \left ( { { i_{1 } } } \right ) \mu _ { b_{l } } \left ( { { i_{2 } } } \right ) \mu _ { c_{m } } \left ( { { i_{3 } } } \right ) , ~~ 1\le i\le 27 \\ o_{3,i}=&\frac { w_{i}}{\sum \limits _ { j } { w_{j}}}\left ( { { r_{i,1 } i_{1 } \!+\!r_{i,2 } i_{2 } \!+\!r_{i,3 } i_{3 } + r_{i,4 } } } \right ) , ~~ 1\le i\le 27\qquad \notag \\ { } \end{align } 
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 } { } $ r_{i,3}$ 
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 } { } $ r$ 
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 } { } \begin{equation * } o_{4,1 } = f=\sum \limits _ { i } { \frac { w_{i}}{\sum \limits _ { j } { w_{j}}}f_{i } } = \frac { \sum \limits _ { i } { w_{i } f_{i}}}{\sum \limits _ { i } { w_{i } } } \end{equation*}\end{document } the equation ( 12 ) produces a single coordinate of the predicted respiratory signal , i.e. , \documentclass[12pt]{minimal } 
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 } { } $ z$ 
 \end{document } coordinates , so that we can derive estimated 3d coordinates of breathing signals from those fdls . we describe the experimental data for intra- and inter - fraction motion , in subsection \documentclass[12pt]{minimal } 
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 } { } $ c$ 
 \end{document}. breathing data of 130 patients were collected in georgetown university medical center using the cyberknife synchrony ( accuray inc . the collected data contained no personally identifiable information , and the research study was approved by the georgetown university irb . during data acquisition , three sensors were attached around a target position on the patient s body . individual patient s database contains datasets recorded through three channels by led sensors and cameras . each database contains a record time , 3d coordinates , and rotation data of three channels . the intra - fractional variation dataset had 130 databases , and the inter - fractional variation dataset consisted of 32 databases with at least 1-hour time difference in - between . each database contains a record time , 3d coordinates , and rotation data of three channels . the intra - fractional variation dataset had 130 databases , and the inter - fractional variation dataset consisted of 32 databases with at least 1-hour time difference in - between . sampling frequencies for patients variation data were 5.20 , 8.67 , and 26hz , corresponding to the measurement intervals , 192.30 , 115.38 , and 38.46ms . each database contains calibrated datasets of a record time , 3d coordinates , and rotational data of three channels . during the training procedure , we randomly extracted 1000 samples for each patient . the obtained samples regarding the measurement intervals were about 0.63min for 38.46ms , 1.92min for 115.38ms , and 3.2min for 192.30ms . table 4 shows experimental data of intra- and inter - fractional variation . in the intra - fractional variation dataset , all of 130 databases were used , and training and test data were randomly selected within 1-hour time range . in the inter - fractional variation dataset , however , we selected 32 databases . training and test data were selected with at least 1-hour time difference in - between them for the inter - fractional variation dataset . this time scale is not on the day - to - day level as the standard definition of the inter - fractional variation , but it meets the inter - fractional time scale condition of . actual inter - fractional motion data might be larger than data we chose because changes occurred in fractions on different days such as weight gain or loss were not contained in experimental data.table 4experimental data.data typeintra - fractional variationinter - fractional variationpatient # 13032measurement intervals ( ms)38.46 , 115.38 , and 192.30inputsestimated tumor locationoutputsnext tumor position in the current fractiontraining dataprevious tumor location data in the current fractiontumor location data in the previous fractionstest datacurrent tumor location data in the current fractioncurrent tumor location data in the current fraction we present the patient clustering results with the calculated criterion function values \documentclass[12pt]{minimal } 
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 \end{document}. therefore , cyberknife patient databases were grouped into 11 classes using the proposed iifdl , and the clustering results for intra- and inter - fractional variation data are presented in table 5.table 5patient database clustering.class number1234567891011total # of data - basesintra - fractional variation183522726192118130inter - fractional variation1110156n / a2n / a1532 in table 5 , 130 databases of the intra - fractional variation and 32 databases of the inter - fractional variation were grouped into 11 and 9 classes , respectively . each class showed the similar breathing features regardless of the variation type . in the intra - fractional variation , some classes ( e.g. class 1 , 4 , 7 , 9 , and 10 ) have only one or two patients . they are most likely considered as the irregular respiratory signals , due to their less feature similarities with other patients breathing signals . class 2 and 8 for the inter - fractional variation also have highly few patients , but we do not consider these classes as the irregular breathing signals . it is difficult to judge the scarcity of class 2 and 8 based on the few number of intra - fractional variation databases , also these two classes were already considered as regular breathing groups for the intra - fractional variation . in this subsection , we compare the prediction performance of the proposed iifdl with existing methods . especially , previous methods for the inter - fractional movement are mathematical models depending on predefined scenarios of patients variation , without the self - learning feature . the prediction performance of these methods is susceptible to how many potential scenarios were considered . in other words , there is a practical limitation to get decent performance results in the experiment with those mathematical models . accordingly , we chose the existing methods for intra - fractional prediction , cnn and hekf , as the comparison targets , and we applied the selected methods to the case of the inter - fractional variation . the predictors used in cnn and hekf are nn and a combination of nn and kf , respectively , as mentioned in section i. thus , these methods have the self - learning feature . furthermore , cnn is the prediction approach designed for multiple patients motion like the proposed iifdl . we evaluate the prediction performance of iifdl using by the following three criteria : root - mean - square error ( rmse ) , overshoot , and prediction time . 5 shows prediction results of two databases by iifdl , cnn , and hekf , with 115.38ms interval as a median of [ 38.46 , 192.30ms ] . 5 ( a ) and 5 ( b ) present the prediction results of the intra - and inter - fractional variation datasets . here , a horizontal axis is the time index extracted from cyberknife data . a black line is a measurement , a red line with a  \documentclass[12pt]{minimal } 
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 \end{document} marker represents the estimation results of hekf . also , two green dotted lines are upper and lower boundaries of target data , respectively . figure 5.prediction results for ( a ) intra- and ( b ) inter - fractional variation by iifdl , cnn , and hekf : ( a ) db47 and ( b ) db121 with 115.38ms interval . the estimated values of the proposed iifdl were closer to the target values , i.e. measurements , than those of cnn and hekf . prediction results for ( a ) intra- and ( b ) inter - fractional variation by iifdl , cnn , and hekf : ( a ) db47 and ( b ) db121 with 115.38ms interval . the estimated values of the proposed iifdl were closer to the target values , i.e. measurements , than those of cnn and hekf . 5 , the estimated points of the proposed method iifdl were closer to the target values than those of cnn and hekf . in fig . 5 , many points of cnn were distributed near or out of the boundaries , and most of the points of hekf were out of the range between upper and lower boundaries . however , the predicted values of iifdl were within the boundaries in most cases . the rmse comparison of the intra - fractional variation of each patients class showed that the proposed iifdl , cnn , and hekf had the similar rmse values overall , and iifdl outperformed cnn and hekf particularly in class 4 considered as irregular breathing signals . for the inter - fractional variation of each patients class , the experimental result also validated that the proposed iifdl is less vulnerable to the breathing irregularity . in table 6 , we summarized the average rmse and standard deviation values of iifdl , cnn , and hekf for each different measurement interval . based on those results , we also derived improvement rate of iifdl , determined by the following formula : ( rmse average of cnn / hekf - rmse average of iifdl)/rmse average of cnn / hekf \documentclass[12pt]{minimal } 
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 \end{document } ( average of cnn / hekf - average of iifdl ) / average of cnn / hekf * 100% . for given the measurement intervals of the intra - fractional variation in table 6 , the rmse results presented that all the average rmse and standard deviation values of iifdl were lower than those of cnn and hekf , except the interval of 192.30ms . although iifdl was worse than hekf in comparison on the average rmse result for the time interval of 192.30ms , the average rmse of iifdl was 0.03 mm larger than that of hekf , which is a relatively small difference . with decreased time interval from 192.30 to 38.46ms , the proposed iifdl had the more improvement rate from 11.81 to 90.54% for cnn and 6.86 to 54.36% for hekf . in the total results , the proposed method had the standard deviation of 0.46 mm , whereas cnn and hekf had fluctuating rmse values with the standard deviation of 6.16 mm and 0.92 mm . in comparison to the existing methods , the proposed iifdl improved 38.27% and 21.69% of the average rmse values , for each cnn and hekf , in the experiment of the intra - fractional variation . as show in table 6 , the experimental results for the inter - fractional variation represent that all rmse values of iifdl were lower than those of cnn and hekf . the proposed iifdl improved rmse more when the time interval was smaller , which is the same as the experimental results of the intra - factional variation . the proposed iifdl with the overall standard deviation of 1.02 mm showed higher error stability than cnn and hekf with the overall standard deviation of 3.86 mm and 3.53 mm . moreover , iifdl enhanced 59.02% and 60.44% of rmse in comparison to cnn and hekf as shown in table 6 . therefore , we can expect that the proposed method contributes to the radiotherapy by providing higher prediction accuracy and error stability . the prediction overshoot rate is also one of the criteria that enable to assess prediction accuracy of rmse , and it can be defined as a ratio of the estimated points are out of the boundary ranges to the total ones , here the range was determined by the 95% prediction interval of target data . 6 presents the overshoot results by iifdl , cnn , and hekf for the intra - fractional variation . the measurement interval was 115.38ms , which is a middle interval of [ 38.46 , 192.30ms ] . a horizontal axis is the patient database number , and a red , blue , and orange bar indicate the overshoot value of iifdl , cnn , and hekf , respectively . the measurement interval is 115.38ms , which is a middle interval [ 38.46 , 192.30ms ] . the proposed iifdl had less variation of the error values only up to 9.1% , but cnn and hekf showed occasionally huge overshoot results almost 100% . the measurement interval is 115.38ms , which is a middle interval [ 38.46 , 192.30ms ] . the proposed iifdl had less variation of the error values only up to 9.1% , but cnn and hekf showed occasionally huge overshoot results almost 100% . 6 , the proposed iifdl had less variation of the error values only up to 9.1% , but cnn and hekf showed occasionally huge overshoot results almost 100% . in the same vein with the experiment of rmse , the proposed method improved overshoot performance with higher stability in databases we utilized . in fig . 7 , we show the overshoot results of iifdl , cnn , and hekf for the inter - fractional variation to demonstrate the stability of the proposed iifdl . the measurement interval is 115.38ms , which is a middle interval [ 38.46 , 192.30ms ] . however , cnn and hekf had large overshoot results up to 100% and wider variance of the overshoot rates than the proposed iifdl . the measurement interval is 115.38ms , which is a middle interval [ 38.46 , 192.30ms ] . however , cnn and hekf had large overshoot results up to 100% and wider variance of the overshoot rates than the proposed iifdl . there was no overshoot value in class 10 . as the experimental results of intra - fractional variation , cnn and hekf had wider variance of the overshoot rates than the proposed iifdl . 7 , the existing methods , cnn and hekf had large overshoot results up to 100% . however , the maximum overshoot value of the proposed iifdl was 8.4% . in table 7 , we summarized average overshoot rates and their standard deviation values of iifdl , cnn , and hekf for each measurement interval.table 7overshoot comparison.variationintra-fractional variation ( % ) inter - fractional variation ( % ) measurement interval ( ms)38.46115.38192.30average38.46115.38192.30averageiifdl4.652.443.902.123.692.294.082.284.202.533.722.333.552.273.822.38imp . rate over cnn 57.9763.7479.0066.9085.6783.6171.8180.37imp . rate ) \documentclass[12pt]{minimal } 
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 \end{document } ( average of cnn / hekf - average of iifdl ) / average of cnn / hekf * 100% . as shown in table 7 , all average overshoot rates of the proposed iifdl are considerably lower than those of cnn and hekf , in both experimental results for the intra- and inter - fractional variation . furthermore , standard deviation values of the overshoot rate had remarkable differences in between iifdl and two other methods . for the intra - fractional variation , the total standard deviation values of iifdl , cnn , and hekf were 2.28% , 26.78% , and 28.26% , respectively . overall results for the intra - fractional variation showed that the proposed method improves the overshoot percentage by 66.90% for cnn and 74.96% for hekf . for the inter - fractional variation , also , iifdl markedly reduced not only the average overshoot percentage but also the standard deviation . the overall improvement rates of iifdl was 80.37% for cnn and 86.17% for hekf in the experiment for the inter - fractional variation . to evaluate and compare effects on the computational complexity by the proposed iifdl , we measured average cpu time of each prediction method using a pc with intel core i7 3.07 ghz and 16.0 gb ram . table 8 compares the computing time of iifdl , cnn , and hekf for each measurement interval used in the experiment , where time difference represents the difference of the computing time between the previous methods and iifdl.table 8computing time comparison.variationintra-fractional variation ( ms)inter - fractional variation ( ms)measurement interval ( ms)38.46115.38192.30average38.46115.38192.30averageiifdl1.324.911.615.061.705.071.545.011.324.911.615.061.705.071.545.01time diff . from cnn 252.60250.99254.74252.78253.16249.94251.32251.47time diff from hekf 251.76251.47252.82252.02250.72253.36249.85251.31atime difference ( time diff . ) \documentclass[12pt]{minimal } 
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 \end{document } computing time average of cnn / hekf - computing time average of iifdl . in the experimental results for the intra - fractional variation of table 8 , iifdl had the average computing time of 1.54ms and the standard deviation of 5.01ms , for all databases and intervals . the average computing time and the standard deviation were 254.32ms and 11.68ms for cnn and 253.56ms and 10.74ms for hekf . thus , the total average of the time difference reduced by iifdl was 252.78ms for cnn and 252.02ms for hekf . for the inter - fractional variation , the average computing time of the proposed iifdl was 1.54ms and its standard deviation was 5.01ms throughput all databases and measurement intervals . the average computing time and its standards deviation were 253.01ms and 9.17ms for cnn , and 252.85ms and 6.17ms for hekf . in the experiment for the inter - fractional variation , the total average of the time difference reduced by iifdl was 251.47ms for cnn and 251.31ms for hekf . as we mentioned in section ii , the proposed fdl , requires less prediction parameters than cnn and hekf . accordingly , the proposed iifdl could reduce the computing time immensely as shown in the experimental results in table 8 . moreover , iifdl and cnn train the multiple breathing signals simultaneously based on the respiratory feature similarities . for instance , there were 35 intra - fractional variation databases of patients in class 2 , and hekf needed to train the respiratory signals 35 times more than iifdl and cnn , to acquire the prediction results . thus , the proposed iifdl is expected to improve the prediction speed maintaining the prediction accuracy during the treatment session in the clinical perspective . table 9 compares the two kinds of variation regarding rmse , overshoot , and computing time.table 9experimental result comparison of intra- and inter - fractional variations.variationintra-fractional variationinter - fractional variationrmseiifdl average ( mm)0.330.38cnn average ( mm)0.970.98hekf average ( mm)0.421.01improvement rate ( cnn ( % ) /hekf ( % ) ) 38.27/21.6959.02/60.44overshootiifdl average ( % ) 4.083.82cnn average ( % ) 13.1421.54hekf average ( % ) 16.6229.89improvement rate ( cnn ( % ) /hekf ( % ) ) 66.90/74.9680.37/86.17computing time ( ms)iifdl average1.541.54cnn average254.32253.01hekf average253.56252.85time difference ( cnn / hekf)252.78/252.02251.47/251.31 for rmse and overshoot of the previous methods cnn and hekf , results of the inter - fraction variation were worse than those of the intra - fractional variation as shown in table 9 . this is because the respiration variability for the inter - fraction is larger than that for the intra - fraction . on the other hand , iifdl showed similar rmse and overshoot results for both intra- and inter - fractional variation . due to the reasoning capability of iifdl for uncertainty , the proposed iifdl achieved the similar level of the prediction results with the intra - fractional variation in the experiment for the inter - fractional variation . the proposed iifdl reduced it less than 2ms , which were over 250ms in the previous methods , cnn and hekf . additionally , this implies that iifdl can be used in real - time applications as the proposed method can estimate the next respiratory signal before it comes . specifically , the next breathing signal will come with the interval of 38.46ms to 192.30ms , and iifdl can calculate the estimated value within 2ms on average that is before termination of the time interval . we provide more comparison with other previous methods , , , , ,   in table 10 , to verify the accuracy performance of iifdl . the previous methods in table 10 were referred to in section i. as shown in table 10 , the proposed iifdl had the lowest error results among 9 methods . however , comparability is limited as experiments were not conducted in the identical environment . table 10error comparison with previous methods.methodiifdlcnn hekf af , siso af / miso af kf , nn , lp cubic intra - fractional variation ( mm)0.330.920.58<2.01.58 / 1.71<2.5<2.51.2n / ainter - fractional variation ( mm)0.380.981.01n / an / an / an / a4.64.7 in a curative setting , high radiation doses need to be delivered with high precision , and safety margines need to be added to the target to ensure sufficient dose coverage . however , safety margins and resulting side effects of radiotherapy compromise the ability to deliver tumoricidal treatment doses . as a result , local tumor reccurences occur in 30% of conventionally fractionated treatments   and less than 10% of stereotactic applications . respiratory tumor motion range and consistency vary with patient , within one fraction and between repeated fractions with change in tumor motion range > 3 mm in 20% of fractions . in addition to addressing intra - fractional variation , this paper also investigated prediction for inter - fractional variation that might be larger than intra - fractional variation and therefore more challenging to address . compared to currently applied population - averaged margins between 3 and 10 mm in motion - inclusive treatment , margins can be significantly reduced according to the residual prediction error for the individual patient using motion - tracking and iifdl . the proposed iifdl can contribute to treatment planning to improve delivery accuracy , by adjusting the treatment field position according to the predicted intra- and inter - fractional variation . based on the experimental results above , we have validated that the proposed iifdl can estimate the next breathing signal before the next incoming signal arrives . therefore , iifdl is expected to achieve real time prediction in a stream computing environment if the prediction system tolerates measurement delay of respiratory signal . future studies may seek to identify correlations between tumor location in the lung , as well as patient - related parameters and comorbidities and predicted intra- and inter - fractional variation to even further improve prediction accuracy . in addition , further study can be conducted on prediction with other machine learning methods to improve prediction accuracy of tumor motion , which have not been introduced yet for estimating intra- and inter - fractional variation , such as support vector machines , . based on this algorithm , we also proposed the specific estimation method for intra- and inter - fractional variation of multiple patients , called iifdl . our approach has three main contributions to prediction of patients motion during a single treatment session and between different fractional sessions . first , the proposed method is the first study on the modeling of both intra- and inter - fractional variation for multiple patients respiratory data , collected from the cyberknife facility . second , the proposed iifdl might enhance tumor tracking techniques due to its high prediction accuracy . third , the proposed fdl , the predictor used in iifdl , has a much shorter computation time than other methods , so that the proposed iifdl shows the optimistic perspective on real - time prediction . the experimental results validated that the rmse value of the proposed iifdl was improved by 38.27% of cnn and 21.69% of hekf for the intra - fractional variation . for the inter - fractional variation , iifdr improved the average rmse values by 59.02% for cnn and 60.44% for hekf . the iifdl also improved the prediction overshoot by 66.90% for cnn and 74.96% for hekf for the intra - fractional variation . in a case of the inter - fractional variation , for the average computing time , the previous methods spent over 250ms for computation , but the proposed iifdl consumed less than 2ms . the outcomes of rmse and prediction overshoot demonstrate that the proposed method has more of a superb prediction performance than existing approaches . particularly , computation time results showed that iifdl can be considered as a suitable tool for real - time estimation .
tumor movements should be accurately predicted to improve delivery accuracy and reduce unnecessary radiation exposure to healthy tissue during radiotherapy . 
 the tumor movements pertaining to respiration are divided into intra - fractional variation occurring in a single treatment session and inter - fractional variation arising between different sessions . 
 most studies of patients respiration movements deal with intra - fractional variation . 
 previous studies on inter - fractional variation are hardly mathematized and can not predict movements well due to inconstant variation . 
 moreover , the computation time of the prediction should be reduced . to overcome these limitations 
 , we propose a new predictor for intra- and inter - fractional data variation , called intra- and inter - fraction fuzzy deep learning ( iifdl ) , where fdl , equipped with breathing clustering , predicts the movement accurately and decreases the computation time . through the experimental results 
 , we validated that the iifdl improved root - mean - square error ( rmse ) by 29.98% and prediction overshoot by 70.93% , compared with existing methods . 
 the results also showed that the iifdl enhanced the average rmse and overshoot by 59.73% and 83.27% , respectively . 
 in addition , the average computation time of iifdl was 1.54 ms for both intra- and inter - fractional variation , which was much smaller than the existing methods . 
 therefore , the proposed iifdl might achieve real - time estimation as well as better tracking techniques in radiotherapy .