Chaotic Convolutional Long Short-Term Memory Network for

Respiratory Motion Prediction

Narges Ghasemi

1,2 a

, Shahabedin Nabavi

1 b

, Mohsen Ebrahimi Moghaddam

1 c

and Yasser Shekofteh

1 d

Faculty of Computer Science and Engineering, Shahid Beheshti University, Tehran, Iran

Department of Computer Science, Viterbi School of Engineering, University of Southern California, U.S.A.

Keywords:

Convolutional Long Short-Term Memory, Deep Neural Network, Lung Motion, Radiotherapy, Respiratory

Motion Prediction.

Abstract:

One of the challenges of treating lung tumors in radiation therapy is the patient’s respiratory movements

during the treatment, which lead to tumor motion. The goal of respiratory motion prediction is to predict

the movements of lung tissues and lung tumors during the breathing cycle. Predicting respiratory movements

allows radiation to be directed only at the tumor, minimizing exposure to healthy tissue and reducing the risk

of side effects. Using 4D CT images, we can ﬁnd the next position of the lung tumor and make a 4D radiation

therapy plan. As obtaining 4D CT scans is harmful to the patient due to radiation, the aim of this study is to

construct a 4D CT during a respiratory cycle using only a 3D image. In this paper, a Chaotic Convolutional

Long Short-Term Memory network is proposed, which utilizes chaotic features in respiratory signals to predict

pulmonary movements more accurately. The innovation of this method is paying attention to chaotic features

of respiratory signals, which leads to better interpretability of the presented model. The obtained results show

that the proposed method has a higher learning speed and better performance compared to previous models,

which generate 4D CT scans.

1 INTRODUCTION

Cancer Statistics 2022 reports that lung cancer re-

mains the foremost cause of cancer-related mortality

(Siegel et al., 2022), underlining the pressing need

for precise and effective treatments. Radiation ther-

apy, which employs high-energy rays to destroy can-

cer cells and shrink tumors, is a fundamental part of

lung cancer treatment. However, a signiﬁcant chal-

lenge arises during the delivery of radiation therapy:

as patients breathe, the consequent movement of tu-

mors leads to inadvertent exposure of healthy tissue

to therapeutic rays. This not only increases the risk of

secondary cancers but also complicates the effective

targeting of lung tumors.

Respiratory motion prediction aims to predict how

lung tissues and lung tumors will move during breath-

ing. By integrating these predictions into treatment

https://orcid.org/0009-0006-6673-7760

https://orcid.org/0000-0001-7240-0239

https://orcid.org/0000-0002-7391-508X

https://orcid.org/0000-0002-6733-3702

planning, the precision in targeting tumors can be

signiﬁcantly enhanced. Radiation therapists are then

able to tailor the treatment plan to synchronize with

the tumor’s movement, ensuring that the radiation is

delivered effectively to the intended target. The abil-

ity to concentrate radiation on the tumor, while limit-

ing exposure to healthy tissue, is crucial for reducing

side effects. This precision is especially important be-

cause radiation therapy, if not meticulously targeted,

can inadvertently harm nearby healthy tissues.

Efﬁcient delivery of radiation, guided by accurate

prediction of pulmonary movements, can shorten the

duration of treatment sessions. This is of particular

importance for patients who face challenges enduring

lengthy treatments. Moreover, by precisely predicting

the movement of lung tissues, radiation therapists can

reduce the need for multiple treatment sessions that

may arise from initial targeting inaccuracies. This not

only improves the efﬁcacy of the therapy but also sig-

niﬁcantly enhances patient comfort by lessening the

overall treatment burden.

A series of three-dimensional Computed Tomog-

raphy (CT) scan images of the lung during the phases

Ghasemi, N., Nabavi, S., Moghaddam, M. and Shekofteh, Y.

Chaotic Convolutional Long Short-Term Memory Network for Respiratory Motion Prediction.

DOI: 10.5220/0012732600003720

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 4th International Conference on Image Processing and Vision Engineering (IMPROVE 2024), pages 99-106

ISBN: 978-989-758-693-4; ISSN: 2795-4943

of the respiratory cycle constitute a four-dimensional

(4D) CT scan. Essentially, a 4D CT scan compiles

multiple three-dimensional CT scans, each capturing

a different phase of respiration, to provide a time-

sequenced view of the lungs. This imaging technique

allows clinicians to observe the internal dynamics of

the body over time, which is invaluable in planning

treatment by considering the shape and movement of

the tumor and surrounding organs during the breath-

ing cycle. 4D CT scan images are a valuable tool for

estimating uncertainties related to respiratory move-

ments (Rehailia-Blanchard et al., 2019). In this pa-

per, we aim to propose a respiratory motion predic-

tion deep learning model that considers the inherent

characteristics of respiratory signals to predict future

slices of a lung CT volume based on the current slices

in the breathing cycle.

The contributions of this study are:

- A convolutional LSTM network architecture is

proposed in this study for respiratory motion predic-

tion to predict future slices in the breathing cycle us-

ing current slices. Using this method and 4D CT im-

ages as ground truth, the proposed model predicts the

slices of the next respiratory phase volume and com-

pares it with its corresponding slice.

- A chaotic feature extractor (CFE) and a chaotic

activation function (CAF) are used to improve the pre-

diction procedure and increase the accuracy of radia-

tion therapy. A chaotic convolutional LSTM model is

proposed to this end.

The rest of this article is organized as follows.

Section 2 reviews related studies. Section 3 describes

the proposed method. The results of the experiments

are presented in Section 4. Section 5 discusses the re-

sults obtained, followed by the conclusion in Section

2 RELATED WORKS

Accurate respiratory motion prediction is crucial for

effective radiation treatment planning. Traditional

methods, such as those using external surrogates

marked on the chest or abdomen, have laid the

groundwork for capturing respiratory patterns. These

methods include predictive techniques based on the

autoregressive moving average method (McCall and

Jeraj, 2007), Kalman ﬁlter-based approaches (Lee

et al., 2011; Bukhari and Hong, 2014), and kernel es-

timation methods (Ruan, 2010). While valuable for

their non-invasiveness, they fall short in detailing the

complex internal organ motions that are vital for pre-

cision in modern medical imaging techniques.

With the advent of machine learning, more so-

phisticated approaches have emerged to surmount the

limitations of traditional methods. Techniques rang-

ing from Adaptive Neuro-Fuzzy Inference Systems

(Rostampour et al., 2018) to Artiﬁcial Neural Net-

works (ANNs) (Sun et al., 2017), and further to Re-

current Neural Networks (RNNs) (Kai et al., 2018),

have been explored for their capacity to factor in the

temporal dependencies missing from ANNs. The

evolution of RNNs into Long Short-Term Memory

(LSTMs) networks has speciﬁcally addressed the gra-

dient vanishing and explosion challenges characteris-

tic of earlier RNNs. In the domain of respiratory mo-

tion prediction, these LSTM networks, particularly

when trained on 4D CT imaging data, have shown

promise in enhancing prediction accuracy for treat-

ment planning (Lin et al., 2019). Additionally, re-

search has highlighted the potential of Conditional

Generative Adversarial Networks (CGANs), such as

the work of (Isola et al., 2017), originally designed

for image-to-image translation, in next frame predic-

tion tasks, including applications in respiratory mo-

tion prediction for medical imaging.

In the work of (Nabavi et al., 2020), the

ConvLSTM-based PredNet model, initially presented

in (Lotter et al., 2016) for predicting successive

frames in video sequences, has been adapted for fore-

casting subsequent slices in medical imaging. This

model leverages the existing slices as inputs to antic-

ipate future slices in a sequence. Additionally, work

of (Ghasemi and Samadi Miandoab, 2022) employs

parallelized ConvLSTM layers to enhance feature ex-

traction from the data slices, improving the predictive

capabilities of the model. Our study seeks to bridge

this gap by introducing a novel chaotic feature ex-

tractor (CFE) and a chaotic activation function (CAF)

within the ConvLSTM framework. These additions

are speciﬁcally designed to grapple with the unpre-

dictable, chaotic nature of respiratory movement. By

doing so, our model ventures beyond existing models,

leveraging the chaotic dynamics of respiratory mo-

tion to potentially elevate the accuracy of predictions

and adaptability to the unique breathing patterns of

patients.

3 METHOD

The Method section is organized into three primary

parts. First, we lay out the problem formulation. The

second part details the proposed method, and the ﬁ-

nal part describes the implementation details and set-

tings, offering insight into how the model is applied

and tested.

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3.1 Problem Formulation

In this study, we approach the prediction of respira-

tory motion using 4D CT data to infer the future state

of lung CT volumes. We seek to calculate the lung

CT volume at a future time point t + ∆t based on the

current volume at time t. Our model works by pre-

dicting each corresponding slice of the future CT vol-

ume, ˆs

t+∆t

, from the current CT volume slice, s

, and

then reconstructing the complete future volume

t+∆t

The prediction for each slice at a given time step t and

slice s

is formulated as:

ˆs

+∆t

= f (s

) (1)

where f denotes the motion prediction model.

3.2 Proposed Method

The input of the model is the current CT volume, and

we aim to predict the CT volume at the next time step.

These volumes are sliced, and the input of the model

is a slice of the current volume, aiming to predict the

corresponding slice in the next time step. Initially,

a chaotic feature extractor generates a feature map

with dimensions similar to the input image. This fea-

ture map is then concatenated with the input image,

followed by a convolution operation that reduces the

channel size to one, merging the information of the

image and the chaotic features. ConvLSTM blocks,

interlaced with chaotic activation functions, further

extract features, and a ﬁnal convolution block gener-

ates the predicted future slice. Batch Normalization is

applied between ConvLSTM blocks to enhance train-

ing speed. The architecture of the proposed frame-

work is illustrated in Figure 1.

Chaos is characterized by seemingly irregular,

unpredictable long-term, and non-periodic behavior

within a deterministic system. Research of (Michalski

et al., 2014) has demonstrated that respiratory signals

exhibit complex nonlinear dynamics and chaotic be-

havior. To explore this chaotic behavior in lung CT

scans, a 2D discrete cosine transform (2D DCT) is

computed on the input image. The image is then tra-

versed in a zigzag pattern from the bottom right to the

top left, forming a 1D vector. This vector is subjected

to a chaos test (Gottwald and Melbourne, 2004), ver-

ifying its chaotic properties.

3.2.1 Chaotic Feature Extractor

Artiﬁcial intelligence has achieved remarkable suc-

cess in practical applications, yet it often lacks a

close representation of the chaotic ﬁring properties

observed in biological neurons. This limitation has

spurred the development of neuron architectures that

embody intrinsic chaos, as seen in biological systems.

In (Harikrishnan and Nagaraj, 2019; Balakrishnan

et al., 2019), a single-layer chaos-inspired neuronal

architecture for classiﬁcation problems is proposed.

In our research, the Generalized Lur

oth Series (GLS)

neurons form the input layer, consisting of n neurons

, G

, ..., G

, where n is the length of the vectorized

input image, and the pixel values are normalized to

the interval [0,1].

The GLS neuron is described by a 1-D piecewise

linear chaotic map T : [0, 1) → [0, 1), given by:

T (x) =

(

if 0 ≤ x < b

1−x

1−b

if b ≤ x < 1

(2)

where x lies in the range [0,1). The parameter b is a

crucial component of the GLS map, inﬂuencing the

neuron’s chaotic behavior. In this study, the value of

b was determined through empirical testing. Various

values were trialed, and the optimal b was selected

based on the performance of the model.

Each GLS neuron starts with an initial neural ac-

tivity q, representing the initial value for the chaotic

map. These neurons then ﬁre chaotically in response

to a stimulus, a real number between 0 and 1. The

ﬁring time—or the number of iterations required for

the neuron’s output to fall within an epsilon neighbor-

hood of the pixel’s initial value—is used as the chaotic

feature for that particular pixel. The concept of Topo-

logical Transitivity (TT) ensures that this process will

converge, meaning that ﬁring will eventually cease,

as demonstrated in (Harikrishnan and Nagaraj, 2019;

Balakrishnan et al., 2019).

The features extracted by this method, now in vec-

tor form, are then reshaped to match the input image’s

dimensions and concatenated back to the input image

for further processing.

3.2.2 Convolutional Long Short-Term Memory

The 4D CT captures the movement of the organs and

tumor over time. It consists of a sequence of 3D CTs.

In order to take advantage of the temporal dependency

between images, we can use long short-term memory

that is created to predict time series. The main draw-

back of long short-term memory is not paying atten-

tion to the spatial characteristics of the data because

it loses the spatial properties by vectorizing the data.

This problem can be overcome by using convolutional

long short-term memory, which is designed for spa-

tiotemporal sequence forecasting problems (Shi et al.,

2015).

Chaotic Convolutional Long Short-Term Memory Network for Respiratory Motion Prediction

101

Figure 1: The architecture of the Chaotic Convolutional LSTM Network (CCLSTMNet).

3.2.3 Chaotic Activation Function

In recent studies, oscillatory activation functions have

shown promise in improving the gradient process

and minimizing the network size (Noel et al., 2021).

Traditional activation functions such as the sigmoid,

rectiﬁed linear unit (ReLU), and hyperbolic tangent

(Tanh) come with their respective beneﬁts and draw-

backs. The vanishing gradient problem is a challenge

for sigmoid and Tanh functions, slowing the learn-

ing process, whereas ReLU can result in dead neurons

when many neurons’ activation values are zero.

A chaos-based activation function was proposed

to better mirror the neuronal structure of the brain,

incorporating the sigmoid function with the logistic

map to induce chaos (Reid and Ferens, 2021). The lo-

gistic map is utilized for its capacity to create chaotic

behavior.

The sigmoid function, bounded between zero and

one, ensures the logistic map’s input remains within

the required range, deﬁned as follows:

Sigmoid(x) =

1 + e

−x

(3)

Subsequently, the output of the sigmoid function

serves as the input to the logistic map:

LogisticMap(x) = r · x · (1 − x) (4)

where r is the excitatory rate of a neuron. This com-

posite function constitutes the chaos-based activation

function, instilling a chaotic dynamic in the network’s

function.

3.3 Implementation Details

The code implementation was performed using the

Keras library in Python, with the computational envi-

ronment provided by Google Colaboratory Pro (Co-

lab Pro), a cloud-based Jupyter Notebook service. A

batch size of one was utilized. We started with a learn-

ing rate of 0.001, implementing a reduction strategy

when the loss ceased improving for a duration of ﬁve

epochs. The neural network was trained using the

Mean Squared Error (MSE) loss function to minimize

the difference between the predicted outputs and the

ground truth data. The optimization of the network

weights was conducted using the Adam optimizer.

Considering computational efﬁciency, the input

images were resized to a resolution of 160× 160. The

’leave one patient out’ cross-validation method was

employed for model evaluation. This involved using

data from one patient as the test set and the rest for

training, iterating through each patient. The initial

neural activity for the GLS neurons was set at 0.7,

with the parameter b in the GLS map from Equation

2 set to 0.467.

4 EXPERIMENTAL RESULTS

In this section, we present the experimental setup used

to evaluate the respiratory motion prediction frame-

work, with comparisons to state-of-the-art methods.

To examine how each component contributes to the

framework’s overall performance, a set of experi-

ments is presented. We achieve this by conducting an

ablation study and experiments focusing on individ-

ual components such as chaotic feature extraction and

chaotic activation function. Additionally, we compare

our method with other approaches that generate im-

ages.

4.1 Experimental Designs

In our study, we employed the CREATIS dataset,

which consists of ten 3D volumes per patient, rep-

resenting distinct phases of the respiratory cycle for

six patients. The imaging was conducted with a 16

Slice Brilliance CT Big Bore Oncology™ conﬁgura-

tion from Philips (Vandemeulebroucke et al., 2007).

Axially sliced volumes were saved as reference im-

ages. The number of images in axial view for each

patient is outlined in Table 1. In total, 10090 CT slices

were compiled for the six patients. To manage com-

putation costs, these slices were resized to 160 × 160

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in the preprocessing phase.

Table 1: Number of slices per volume.

Patient Number of slices per volume

Patient 1 141

Patient 2 169

Patient 3 170

Patient 4 187

Patient 5 181

Patient 6 161

The leave-one-patient-out (LOPO) cross-

validation method was applied to evaluate the

model’s robustness, with a training set composed of

the data from ﬁve patients and the sixth patient’s data

serving as the test set. This procedure was cycled

through each patient to complete the validation

process.

In this paper, we employ three evaluation met-

rics to assess the performance of our proposed model:

Root Mean Squared Error (RMSE), Structural Simi-

larity Index (SSIM), and Peak Signal-to-Noise Ratio

(PSNR).

This metric measures the difference between pre-

dicted and actual values. When applied to image pro-

cessing, it measures how closely a predicted image

matches the original image. A lower RMSE indicates

less error between the predicted and original images,

which means the predicted image is more accurate.

RMSE is calculated using Equation 5:

RMSE(x, y) =

∑

i=1

∑

j=1

(x(i, j)− y(i, j))

(5)

where x and y represent the ground truth and the pre-

dicted images, respectively, with M representing the

number of rows and N representing the number of

columns in each image.

SSIM measures the similarity between two images

by comparing their structural information, luminance,

and contrast. It provides a score ranging from -1 to 1,

with a higher score indicating greater similarity be-

tween the predicted and original images. SSIM is de-

ﬁned as per Equation 6:

SSIM(x, y) =

(2µ

+ c

)(2σ

+ c

)

(µ

+ µ

+ c

)(σ

+ σ

+ c

)

(6)

where µ

and µ

are the average pixel values of images

x and y, σ

and σ

are the variances of x and y, and σ

is the covariance of the images. The constants c

and

are small stabilizers to prevent division by zero.

PSNR is another measure of image quality evalu-

ation, which quantiﬁes the quality of a reconstructed

image or video by comparing it to the original, undis-

torted version. A higher PSNR value suggests less

distortion. PSNR is obtained from Equation 7:

PSNR(x, y) = 10log



MAX

MSE(x, y)



(7)

where MAX

is the maximum possible pixel value of

the image, and MSE is the mean squared error as cal-

culated in Equation 8.

MSE(x, y) =

∑

i=1

∑

j=1

(x(i, j)− y(i, j))

(8)

4.2 Results

In Table 2, we present the quantitative results obtained

from the Chaotic ConvLSTM network for each pa-

tient in terms of RMSE, SSIM, and PSNR. Also, the

weighted average of these results is presented. Fig-

ure 2 shows the RMSE and SSIM between ground

truth and predicted slices across the different patients.

Figure 3 shows some examples of the model out-

put, ground truth, and their difference during the ten

phases.

Table 3 shows the comparison results of the res-

piratory motion prediction algorithms using ConvL-

STM and CGAN on the CREATIS dataset. Compared

to other algorithms, the proposed strategy accuracy

has been improved, and the training time has been re-

duced.

4.3 Ablation Study

In order to better understand the role and contribution

of each module in our framework, an ablation study

was performed. Different conﬁgurations of the pro-

posed model have been deployed. The baseline ver-

sion of the model includes a sequence of ConvLSTM

with a chaotic activation function and a CNN module.

This means that the model attempts to learn how to

generate volumes directly by generating slices with-

out considering chaotic features. Table 4 shows the

results of the ablation study, evaluating each conﬁgu-

ration based on the quantitative metrics.

5 DISCUSSION

In this paper, we introduced a Chaotic ConvLSTM

network designed for predicting 3D CT scan slices

from preceding scans. The innovation of this model

lies in harnessing chaotic features inherent in respi-

ratory signals, leading to notable enhancements in

learning speed and prediction accuracy compared to

existing methods. Such improvements underscore the

Chaotic Convolutional Long Short-Term Memory Network for Respiratory Motion Prediction

103

Table 2: Quantitative metrics result.

Patient RMSE SSIM PSNR

Patient 1 experiment 4 × 10

−3

0.995 48.09

Patient 2 experiment 5 × 10

−3

0.994 44.93

Patient 3 experiment 8 × 10

−3

0.988 41.49

Patient 4 experiment 7 × 10

−3

0.992 43.13

Patient 5 experiment 5 × 10

−3

0.993 45.17

Patient 6 experiment 5 × 10

−3

0.993 45.53

Weighted average 6 × 10

−3

± 1 × 10

−3

0.993 ± 0.002 44.60 ± 1.6

(a) (b)

Figure 2: (a) RMSE values obtained for 6 patients. (b) SSIM values obtained for 6 patients.

(a) Reference slices.

(b) Predicted slices.

slices.

Figure 3: The predicted pulmonary motion. The ﬁrst row

represents the reference slices; the second row represents

the predicted slices, and the third row represents the differ-

ence between the reference image and the predicted image.

model’s potential for clinical application, particularly

in optimizing radiation therapy through respiratory

motion prediction.

Given the chaotic nature of respiratory signals, our

approach employs chaotic feature extraction, mim-

icking the complex ﬁring patterns observed in neural

structures. This strategy not only reﬁnes the predic-

tion process but also contributes to the precision of

radiation therapy, potentially increasing its efﬁcacy.

The process of generating images, a core compo-

nent of our method, is inherently non-invasive. By

predicting 4D CT scans within a respiratory cycle, our

approach offers detailed insights into organ motion,

encompassing anatomical details and tissue charac-

teristics beyond mere motion tracking. This wealth

of information holds signiﬁcant promise for enhanc-

ing treatment planning and diagnostic accuracy.

Recent advances in medical imaging technolo-

gies have signiﬁcantly broadened our capabilities in

diagnosing and treating complex health conditions.

Among these, 4D CT imaging stands out for its com-

prehensive visualization of organ and tissue dynam-

ics. Nonetheless, the application of 4D CT imaging is

not without its drawbacks, notably the high radiation

exposure required and the potential for image distor-

tion due to the compilation of multiple CT scans over

time.

Our proposed Chaotic ConvLSTM network

presents a viable alternative, especially in settings

lacking advanced 4D CT imaging capabilities. Its

ability to simulate 4D imaging from a single 3D

CT scan could substantially reduce radiation expo-

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104

Table 3: Performance comparison of video next frame prediction models on a 4D MRI video.

Model RMSE SSIM

cGAN(Isola et al., 2017) 0.015 0.937

ConvLSTM(Nabavi et al., 2020) 0.009 0.943

ConvLSTM(Ghasemi and Samadi Miandoab, 2022) 0.012 0.988

Proposed Method 0.006 ± 0.001 0.993 ± 0.002

Table 4: Quantitative metrics comparison between different conﬁgurations.

Model RMSE (×10

−3

) SSIM

ConvLSTM 744 ± 163 0.959

Baseline (ConvLSTM + CAF) 653 ± 152 0.992 ± 0.002

Proposed (ConvLSTM + CAF + CFE) 626 ± 141 0.993 ± 0.002

sure and eliminate the distortions and artifacts typical

of traditional 4D CT reconstructions. These advan-

tages are particularly appealing for radiotherapy cen-

ters with limited access to cutting-edge imaging tech-

nology, offering a cost-effective yet efﬁcient solution.

Furthermore, the comparative analysis of error

rates and the ﬁdelity of generated images to their

ground truth counterparts conﬁrm the superiority of

our model over traditional ConvLSTM-based ap-

proaches. This efﬁcacy stems from our model’s

unique integration of chaotic dynamics, enhancing its

ability to predict pulmonary motion with remarkable

accuracy.

In light of these ﬁndings, our work contributes to

the ongoing evolution of medical imaging and pre-

dictive modeling. By leveraging the chaotic pat-

terns inherent in biological systems, we offer a novel

perspective on motion prediction that could signiﬁ-

cantly impact the ﬁeld of radiation therapy and be-

yond. Future work will aim to expand the application

of chaotic feature extraction and explore its potential

in other areas of medical imaging and treatment plan-

ning, paving the way for broader clinical adoption.

6 CONCLUSIONS

In this study, we developed and presented a novel

Chaotic Convolutional LSTM Network aimed at en-

hancing the accuracy of respiratory motion prediction

for radiation therapy planning. This method predicts

each subsequent CT slice based on the preceding one.

This approach, tested on the CREATIS dataset, un-

derscores the method’s superiority over traditional 4D

CT-generating techniques by offering signiﬁcant im-

provements in prediction accuracy.

The promising outcomes of this research highlight

not just the methodological advancements but also

the potential for substantial clinical impact, particu-

larly in the ﬁeld of radiation therapy where precise

tumor targeting is critical. The reduced error rates and

the method’s non-invasive nature represent signiﬁcant

steps forward in the pursuit of safer, more effective

treatment strategies.

Looking ahead, our research opens several av-

enues for further investigation and application. A

key direction for future work involves validating the

proposed Chaotic ConvLSTM network against dy-

namic breathing lung phantoms, a crucial step to-

wards conﬁrming its applicability and effectiveness in

real-world clinical settings. Additionally, exploring

the integration of this network into existing radiation

therapy planning systems could provide actionable in-

sights into its operational beneﬁts and challenges.

The successful application of chaotic character-

istics in respiratory motion prediction underscores a

promising path for future investigations. We plan

to explore the potential of the Chaotic ConvLSTM

network in modeling physiological processes with

similar chaotic dynamics. This exploration aims to

broaden the utility of our approach, offering a com-

prehensive tool for analyzing and predicting complex

physiological behaviors that exhibit chaotic proper-

ties. By focusing on these areas, we intend to deepen

our understanding of chaotic phenomena in biology

and their implications for medical imaging and diag-

nostics.

In conclusion, the Chaotic ConvLSTM network

represents an advancement in the predictive model-

ing of respiratory motion. Its development not only

contributes to the body of knowledge in medical

imaging and computational biology but also sets the

stage for groundbreaking applications in personalized

medicine and advanced healthcare delivery.

ACKNOWLEDGEMENTS

The authors are grateful to L

eon B

erard Cancer Cen-

ter and CREATIS Laboratory, Lyon, for sharing their

Chaotic Convolutional Long Short-Term Memory Network for Respiratory Motion Prediction

105

imaging data.

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