Advanced Monte Carlo Methods for Medical Physics – MoCaMed

The approach of the MoCaMed project involved exploring innovative and recent methods in the fields of Quasi-Monte Carlo (QMC) and Artificial Intelligence (AI), particularly through deep learning (DL). These fields open new avenues for improving Monte Carlo Simulation (MCS).

The principle of QMC, used in rendering for computer graphics, involves altering how the simulation samples particles to improve their distribution. This more regular distribution naturally reduces the noise in the observables obtained from the simulation. For equivalent quality, it is thus possible to reduce the number of particles used and thereby decrease the computation time. This approach can only be used on observables where the distribution of the result has an impact, such as a medical image or a dose map in radiotherapy. This mechanism is highly complex because the adaptation of sampling is not done during the generation of particles but on their impacts in the environment after their trajectory. This necessitates a deep modification of the MCS, particularly the random generation processes used to determine the physical interactions with matter.

Machine learning (DL), on the other hand, allows learning complex tasks from large amounts of data. The idea here is to generate a large number of MCS simulations to subsequently learn how the simulation works. Of course, the complete simulation cannot be predicted by DL in a generic way, but our approach consisted of replacing certain parts of the simulation, which are time-consuming, with DL elements. The main advantage is that predicting a result with DL is much faster than simulating the transport and interactions of particles in the medium. For example, this can be used to transport particles more quickly through the patient's body or to rapidly produce the distribution of energy deposited by the particles in the tissues.

For the first time, the use of quasi-random sequences (QMC) has been explored to accelerate Monte Carlo simulations (MCS) in the medical field. This study involved modifying the random number generators used in the simulations. The results obtained show a significant improvement in convergence rates in simple cases, with increases of up to 50%. However, a substantial limitation was identified when applying this method to more realistic scenarios, where the dimensionality of MCS in medical physics proves to be too high. Indeed, the high consumption of random numbers, due to the many interactions in matter, makes the effective deployment of QMC methods practically impossible. This very important result was identified for the first time in this context.

In the field of artificial intelligence, and more particularly deep learning, various methods have been developed to optimize simulation times in medical imaging. For example, an innovative approach involved generating particles emanating directly from the patient without simulating their transport inside, which increases the simulation speed up to 20 times. This method was evaluated in the context of realistic medical applications in single-photon emission computed tomography (SPECT). In this same context, the use of deep learning was employed to quickly generate particles from radioactive sources inside the human body, thus reducing computation times by up to 100 times.

Furthermore, other models have been explored to accelerate the calculation of doses deposited by particles in the patient, particularly in the context of radiotherapy. A first strategy involved predicting the dose deposition based on the patient's specific anatomy and the energies of the incident particles. This method significantly reduced computation time, with an acceleration factor of 100. Another innovative solution uses deep learning to reconstruct high-resolution dose maps from low-resolution dose maps (with few particles). This approach achieved an acceleration factor of 300, thus opening new perspectives for faster and more precise simulations in radiotherapy. The results using these acceleration methods have an average error of around 5% compared to a classical simulation, which is approximately the same level of uncertainty typically used in MCS in this application context.

Some of these methods have been integrated and shared with the community through the latest version of the open-source MCS software for medical physics, OpenGATE 10.

The prospects of this project include several main areas. First, we plan to test the robustness and generalization of our methods on various medical applications to validate their effectiveness and adaptability. Next, we will continue to use deep learning to replace parts of Monte Carlo simulations, which has already shown promising results in terms of reducing computation times.

Another research area will involve exploring approaches similar to quasi-Monte Carlo to reduce the dimensionality of problems, which is crucial for improving the efficiency of simulations in realistic scenarios. Finally, we will integrate the validated elements into the OpenGATE platform, allowing the scientific community to benefit from these advancements and apply them in their own research and clinical practices. These steps are essential for advancing the field of medical physics and improving patient care.

Monte Carlo (MC) simulation in medical physics is extensively used during research and development of nuclear imaging systems and treatment planning systems in radiotherapy. All imaging system rely on MC simulation to design, control, optimize, but also to perform research in image reconstruction. All treatment planning systems use MC to characterize photon/particle beams, to compute Dose Point Kernels for analytical dose engines, or directly absorbed dose in patients. However, the increasing need for detailed and accurate simulations, especially considering recent imaging detectors and new radiotherapy protocols, still leads to long simulation times. Variance Reduction Techniques (VRT) have been developed for years but are still restricted to specific applications. Fast GPU particle tracking methods have also been investigated but turned out to be difficult to maintain and generalize. Hence, there are still important needs to improve MC efficiency both in imaging and radiotherapy simulation.

Recent developments on asymptotic VRT such as Quasi-Monte Carlo (QMC) and Artificial Intelligence (AI) open new ways to improve MC. QMC approaches, mostly developed in the field of Computer Graphics, improve MC efficiency by considering samples that are as uniformly distributed as possible. Regarding AI methods in MC, recent approaches showed the feasibility to learn particles response function of SPECT head detector and dose distribution in particle therapy. However, these methods are still limited to some specific applications and do not revolutionize the basis of MC simulation for medical physics.

The ambition of the MoCaMed project is to design, develop and evaluate advanced Monte Carlo sampling and Deep Learning methods to improve MC simulations in medical physics. To achieve such advances, three main foundations of MC simulations will be revisited through three main objectives, from theoretical problems to realistic example applications (imaging and dosimetry) while building the necessary software infrastructure for hosting future developments. The first objective will study the adaptation of QMC and Optimal Transport techniques that have been studied in Computer Graphics to medical physics applications. The foreseen outcome will be new ways to represent and sample distribution probabilities. The second objective is to develop alternative methods to conventional particle tracking within phantom and detector head in order to speed up the MC simulations, based on GAN and neural networks. The third objective will propose fast and accurate predictions of dose distributions by combining MC and AI, and in particular, Deep Learning approaches. Two models will be proposed, one for photons and one for electrons. Finally, all developments will be integrated into the open-source GATE software, one of the main open-source platforms for advanced medical physics simulation in nuclear medicine and particle therapy, together with complete realistic demonstrators (SPECT simulation of molecular therapy treatment, prostate low-dose-rate brachytherapy, and hypo-fractioned external beam radiotherapy).

This consortium gathers researchers from LaTIM, CREATIS and LIRIS laboratories (INSERM, CNRS), experienced in Computer Graphics, AI and simulations in medical physics. All developed methods and results will be openly available for researchers and industrials and will serve as a basis of future developments. Sharing accessible and efficient new MC methods will also foster future common projects with research groups and companies (such as Philips, GE, Siemens, Elekta, IBA with which we are regularly collaborating). Finally, while we focus here on medical physics applications, improved Monte Carlo algorithms may also be useful in other domains such as computer vision or finance.