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On the ModElling of micro-robots in the Gut: a non-smooth dynamics Approach

Periodic Reporting for period 1 - OMEGA (On the ModElling of micro-robots in the Gut: a non-smooth dynamics Approach)

Reporting period: 2021-10-01 to 2023-09-30

Bowel cancer has the highest global mortality rates among other forms of cancer. According to Digestive Cancers Europe, bowel cancer is the second deadliest cancer, approximately 170,000 people dying every year, in the European Union. Survival rates vary across European countries due to national variations in healthcare and locally provided treatment strategies. Although early cancer detection can significantly improve patients’ outcomes, most of the patients were detected at a late stage. If more patients are diagnosed at an early stage (from the current 13% to 50%), 130,000 more lives could be saved per year and more than €3b in healthcare budget can be saved. Thus, in order to fulfil the Sustainable Development Goal of Good Health and Well-Being identified by the United Nations, significantly improve the survival rates, and reduce the heavy burden of bowel cancer on patients, the healthcare systems and the wider economy, more effective screening techniques and programmes for early detection must be in place in all countries in Europe.

Lower gastrointestinal (GI) endoscopies, which examine the colon for detection of premalignant and malignant changes through visualisation of the colonic mucosa, comprise more than 50% of the demand for endoscopies. Despite major advances in image acquisition and processing over recent decades, the basic design and ergonomics of endoscopes have barely changed in more than 40 years. It is less reliable for small pedunculated polyps and for sessile serrated lesions which are not easily visualised. Endoscopy remains challenging for both clinicians and patients. Some GI patients experience significant pain during procedures, which require a team of clinicians to sedate and monitor patients, and to maintain and decontaminate increasingly complex and expensive devices. For clinicians to acquire safely the required expertise and practice, lengthy training periods (2-5 years) and highly developed professional regulatory frameworks are required. Therefore, in GI endoscopic practice, there is an urgent need for new modalities that are safe, painless, accurate and reliable, which requires minimal training for practitioners.

This fellowship seeks to develop a new mathematical tool for analysing the sensing capability of micro-robots to aid the detection of hard-to-visualise bowel lesions. In the long term, this work aims to initiate a new modality for bowel cancer screening, delivering an efficient minimally invasive procedure for patients.

After an in-depth study of the robot-tumour interactions, the findings reveal significant changes in robot's dynamics when the robot encounters different circular folds and tumours. Such a correlation between the dynamical characteristics of the robot and the tumour’s mechanical properties proves the potential of utilising a vibrational capsule robot for early detection of bowel cancer.
The fellow initially studied the locomotion of a capsule robot self-propelling in the small intestine. While considering the lining of the small intestine that consists of a series of circular folds in different sizes, dynamics and locomotion of the robot when encountering various types of circular folds were investigated, and locomotion control for the capsule robot moving in the small intestine was proposed. In particular, the work provides detailed one- and two-parameter bifurcation analyses of the capsule–fold dynamics under four different fold cases. To perform such a bifurcation analysis, the contact force of capsule–fold interaction was firstly approximated as a piecewise smooth nonlinear restoring force via interpolation. Then bifurcation analysis was conducted by using the GPU parallel computing and path-following techniques.

Considering the anatomy of small intestine involving lesions, circular folds and tumours are the major sources resisting the locomotion of capsule robot. By mimicking the small-bowel tumours as cone folds, the fellow then carried out a comparative study on the dynamics of the capsule robot in contact with different circular and cone folds. With the aid of GPU parallel computing and path-following techniques, extensive bifurcation and basin stability analyses are performed to identify different capsule-fold interactions and unravel the parametric influences on the robot, such as fold shape, Young’s modulus and robot’s control parameters (e.g. excitation period and amplitude). It was found that fold shape and Young’s modulus may only affect capsule’s dynamics significantly when robot’s excitation period is large. Two essential locomotion modes, a period-one motion with capsule-fold contact in the small region of excitation amplitude and a fold crossing motion in the large region of excitation amplitude, dominating the dynamics of the robot regardless of fold shape and Young’s modulus were observed. In addition, the instability mechanism of this period-one motion was revealed. The numerical study done by the fellow provides a solid basis for the locomotion control of the robot when encountering different types of circular folds and small-bowel tumours. It also offers the potential of utilising robot’s dynamics for bowel cancer detection.

The fellow was also involved in the study of an experimental rig with two-sided constraint and bidirectional drift, which is the prototype of the capsule robot in centimetre scale. The fellow carried out parameter identification for the experimental rig by using the simulated annealing algorithm. The experimental work particularly focused on observing several types of bifurcations which are common in the capsule-tumour contact model. It was found that with a higher excitation frequency and amplitude, the vibro-impact dynamics on both ends of the constraints could result in a large amount of uncertainties, thus bi-stable and chaotic motions are likely to be observed. While being unstable, the system runs with a relatively high energy efficiency in this configuration.
This work has presented an in-depth analyses on the robot–tumour dynamics under different mechanical properties, such as Young's modulus of the tumour which is a key biomarker for identifying cancerous lesion, uncovering the instability mechanisms of periodic motions of the robot. Such results can provide essential guidance for the locomotion control of the capsule robot in the lower gastrointestinal environment. On the other hand, this work also presented robot's stability analysis to further characterise the robot-tumour dynamics from a global perspective. More importantly, the robot's stability analysis also reveals a significant change in robot's dynamics when the robot encounters different circular folds and tumours. Indeed, such a correlation between the dynamical characteristics and the fold’s mechanical properties has proved the potential of utilising robot's dynamics for early detection of bowel cancer.
Capsule robot in contact with circular fold and tumour