A real-time optimal inverse planning for Gamma Knife radiosurgery by convex optimization: description of the system and first dosimetry data

OBJECTIVE The authors developed a new, real-time interactive inverse planning approach, based on a fully convex framework, to be used for Gamma Knife radiosurgery. METHODS The convex framework is based on the precomputation of a dictionary composed of the individual dose distributions of all possible shots, considering all their possible locations, sizes, and shapes inside the target volume. The convex problem is solved to determine the plan, i.e., which shots and with which weights, that will actually be used, considering a sparsity constraint on the shots to fulfill the constraints while minimizing the beam-on time. The system is called IntuitivePlan and allows data to be transferred from generated dose plans into the Gamma Knife treatment planning software for further dosimetry evaluation. RESULTS The system has been very efficiently implemented, and an optimal plan is usually obtained in less than 1 to 2 minutes, depending on the complexity of the problem, on a desktop computer or in only a few minutes on a high-end laptop. Dosimetry data from 5 cases, 2 meningiomas and 3 vestibular schwannomas, were generated with IntuitivePlan. Results of evaluation of the dosimetry characteristics are very satisfactory and adequate in terms of conformity, selectivity, gradient, protection of organs at risk, and treatment time. CONCLUSIONS The possibility of using optimal, interactive real-time inverse planning in conjunction with the Leksell Gamma Knife opens new perspectives in radiosurgery, especially considering the potential use of the full capabilities of the latest generations of the Leksell Gamma Knife. This approach gives new users the possibility of using the system for easier and quicker access to good-quality plans with a shorter technical training period and opens avenues for new planning strategies for expert users. The use of a convex optimization approach allows an optimal plan to be provided in a very short processing time. This way, innovative graphical user interfaces can be developed, allowing the user to interact directly with the planning system to graphically define the desired dose map and to modify on-the-fly the dose map by moving, in a very user-friendly manner, the isodose surfaces of an initial plan. Further independent quantitative prospective evaluation comparing inverse planned and forward planned cases is warranted to validate this novel and promising treatment planning approach.

A Data-Driven Frequency-Domain Approach for Robust Controller Design via Convex Optimization

Achille Nicoletti

The objective of this dissertation is to develop data-driven frequency-domain methods for designing robust controllers through the use of convex optimization algorithms. Many of today's industrial processes are becoming more complex, and modeling accurate physical models for these plants using first principles may be impossible. With the increased developments in the computing world, large amounts of measured data can be easily collected and stored for processing purposes. Data can also be collected and used in an on-line fashion. Thus it would be very sensible to make full use of this data for controller design, performance evaluation, and stability analysis. The design methods imposed in this work ensure that the dynamics of a system are captured in an experiment and avoids the problem of unmodeled dynamics associated with parametric models. The devised methods consider robust designs for both linear-time-invariant (LTI) single-input-single-output (SISO) systems and certain classes of nonlinear systems. In this dissertation, a data-driven approach using the frequency response function of a system is proposed for designing robust controllers with H∞ performance. Necessary and sufficient conditions are derived for obtaining H∞ performance while guaranteeing the closed-loop stability of a system. A convex optimization algorithm is implemented to obtain the controller parameters which ensure system robustness; the controller is robust with respect to the frequency-dependent uncertainties of the frequency response function. For a certain class of nonlinearities, the proposed method can be used to obtain a best-linear-approximation with an associated frequency dependent uncertainty to guarantee the stability and performance for the underlying linear system that is subject to nonlinear distortions. The concepts behind these design methods are then used to devise necessary and sufficient conditions for ensuring the closed-loop stability of systems with sector-bounded nonlinearities. The conditions are simple convex feasibility constraints which can be used to stabilize systems with multi-model uncertainty. Additionally, a method is proposed for obtaining H∞ performance for an approximate model (i.e., describing function) of a sector-bounded nonlinearity. This work also proposes several data-driven methods for designing robust fixed-structure controllers with H∞ performance. One method considers the solution to a non-convex problem, while another method convexifies the problem and implements an iterative algorithm to obtain the local solution (which can also consider H2 performance). The effectiveness of the proposed method(s) is illustrated by considering several case studies that require robust controllers for achieving the desired performance. The main applicative work in this dissertation is with respect to a power converter control system at the European Organization for Nuclear Research (CERN) (which is used to control the current in a magnet to produce the desired field in controlling particle trajectories in accelerators). The proposed design methods are implemented in order to satisfy the challenging performance specifications set by the application while guaranteeing the system stability and robustness using data-driven design strategies.

EPFL2018

Kinetic hard-modelling and spectral validation of rank-deficient spectroscopic data

Julien Léo Billeter, Konrad Hungerbühler

In recent years, chemometric methods for the analysis of multivariate kinetic data have considerably progressed. Kinetic hard-modelling is one of these methods that is based on the rate law and used to determine the kinetic parameters (e.g. rate constants) of chemical reactions by non-linear optimisation. Applied to spectroscopy, kinetic hard-modelling relies on Beer’s law to decompose the time and wavelength resolved data into the concentration profiles and the molar spectra of the pure components. In direct implicit kinetic hardmodelling, the concentration profiles are obtained by numerical integration of the rate laws and pure spectra are linearly estimated at each iteration using the pseudo-inverse of the concentration matrix [1]. Direct implicit kinetic hard-modelling of spectroscopic data allows the validation of the kinetic mechanism by comparing the estimated component spectra with independently measured ones. A severe drawback, however, is that this implicit method fails when concentrations profiles are linearly dependent, as the pseudo-inverse and thus the component spectra cannot be computed. Different Strategies have been proposed as a remedy to this rank deficiency problem, such as (1) defining some absorbing species as uncoloured, (2) providing some component spectra for the analysis, (3) dosing one or more species or (4) analysing simultaneously several experiments recorded under different initial concentrations (3-way analysis). In absence of a systematic method, the appropriate species to be included in these four Strategies are selected by experience or trial and error. Spectral validation of the kinetic mechanism can also be difficult when Strategy (1) is employed, as the fitted component spectra are complex linear combinations of the true pure spectra. We have recently proposed a systematic method for the experimental and data analytical design of kinetic data measured by spectroscopy that allows identifying the species to be incorporated in Strategies (1) – (4) and calculating the linear combinations of the true pure spectra when Strategy (1) is used, an important step for spectral validation [2]. This systematic method is based on a time-invariant matrix that avoids the numerical integration of the time-variant concentration profiles and allows the experimental design of chemical reactions, even if the associated rate constants are not yet known, i.e. before optimisation. This time-invariant matrix uses the entire set of kinetic reactions and only requires a reduction to independent reactions if linear combinations of the true pure spectra are desired (Strategy 1). For this, a method has also been developed. In this presentation, the systematic method of species selection is presented using simulated data and, from this, appropriate experimental designs (Strategies) are suggested. The method is also presented using experimental results obtained from the reaction of benzophenone with phenylhydrazine in THF (under catalysis of acetic acid), for which the postulated kinetic mechanism has been successfully validated via the comparison between fitted and measured component spectra in mid-IR and UV-vis [3]. [1] M. Maeder, A.D. Zuberbühler, Anal. Chem., 62 (1990), 2220-2224. [2] J. Billeter, Y.M. Neuhold, K. Hungerbühler, Chemom. Intell. Lab. Syst., 95 (2009), 170-187. [3] J. Billeter, Y.M. Neuhold, K. Hungerbühler, Chemom. Intell. Lab. Syst., 98 (2009), 213-226.

2009

A Linearly Convergent Algorithm for Decentralized Optimization: Sending Less Bits for Free!

Martin Jaggi, Anastasiia Koloskova

Decentralized optimization methods enable on-device training of machine learning models without a central coordinator. In many scenarios communication between devices is energy demanding and time consuming and forms the bottleneck of the entire system. We propose a new randomized first-order method which tackles the communication bottleneck by applying randomized compression operators to the communicated messages. By combining our scheme with a new variance reduction technique that progressively throughout the iterations reduces the adverse effect of the injected quantization noise, we obtain a scheme that converges linearly on strongly convex decentralized problems while using compressed communication only. We prove that our method can solve the problems without any increase in the number of communications compared to the baseline which does not perform any communication compression while still allowing for a significant compression factor which depends on the conditioning of the problem and the topology of the network. We confirm our theoretical findings in numerical experiments.