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Biological systems

Biological systems offer prominent examples of large-scale networked systems for which fundamental modelling, analysis and control problems are still unsolved. In biology there are multiple sources of complexity that hamper the applicability of techniques developed for monolithic and centralized systems. Next we provide a description of the main conceptual challenges we plan to address in the collaborative framework of the HYCON2 project.

Complexity-aware data-based modelling

The availability of biological data with various degrees of precision and resolution on different aspects of cellular functioning has fostered research on methods for data-based modelling of biological processes. However, experience on dynamic modelling of biochemical processes suggests that, in order to work, standard identification techniques need to be tailored in order to cope with the features of the biological system under study and the available data. Research on identification algorithms for networked systems is still in its infancy and will be considered within the project framework.

A further level of complexity is due the stochastic nature of biochemical reactions underlying cell behaviours. When molecules come in low copy numbers it is not appropriate to abstract them into deterministic concentrations and therefore one has to develop appropriate modelling frameworks for identification that comprise and complement concentration-based models (e.g. based on ordinary differential equations) and particle-based stochastic models. Stochastic variability it is also the main factor responsible for cell-to-cell variations in gene expression.

At the highest level of complexity, one must take into account that proteins move and interact within a 3D space. In this context, the main challenge is to develop stochastic models that are rich enough to capture the spatiotemporal kinetics of molecules and simple enough to be used in identification experiments based on Fluorescence Recovery After Photobleaching (FRAP) data.

Structured modelling for biological systems: hierarchies and emergent behaviours

In the context of systems biology, both continuous and discrete models for biochemical networks and pathways have been proposed. Continuous models based on ordinary differential equations provide a detailed description on the dynamics of biological pathways but lead to cell-level, models that are overly complex for simulation and analysis purposes. Discrete models, like boolean networks or finite state machines have a simple mathematical form that is appealing for describing processes at the cell level but in general there is no guarantee that these models are consistent with ODE-based representations. The development of methods for constructing a hierarchy of discrete abstractions in which models at a given level include the essential dynamic properties of models at lower levels is still a major challenge. More specifically, the main goals are (i) to develop a precise definition of 'essential dynamic property' of a pathway (ii) to understand the influence of the spatial discretization when abstracting continuous dynamics into discrete ones and (iii) to devise discretization scheme that are optimal with respect to the size and accuracy of the abstracted models.

Another approach to deal with the complexity of intracellular networks is modularization, i.e. the identification of simpler subnetworks devoted to specific functions. A key problem in modelling biological processes is to understand how macroscopic robust behaviours stem out of random interaction at the molecular level. While in many cases cells try to keep random fluctuations under control to make their functioning more predictable, there are key processes, like DNA replication in eukaryots, that involve considerable randomness. At present, the potential advantages stochasticity may offer in complex interaction networks are very poorly understood and need to be analyzed using rigorous frameworks such as stochastic optimal control and game theory for complex systems.

Additional sources of complexity enter the game when moving from single cells to cell populations or tissues. As an example, a largely unexplored topic is to understand how genetic programs of individual cells, intercellular signalling mechanisms and mechanical forces contribute in determining the morphogenesis of tissues such as the epithelium of the Drosophila embryo.

The interplay of robustness and network topology in biochemical networks

Robustness and sensitivity analysis of biochemical reaction networks has so far almost exclusively focused on parametric aspects, i.e. how perturbation in kinetic parameters impacts on the network functioning. Little attention has been devoted to an equally fundamental problem: how uncertainties and changes in the network topology affect the network behaviour. Understanding the role of network topology help identify network fragilities, elucidate the sources of abnormal states and determine strategies to fight disease states that have developed some form of robustness.

Distributed control of cell populations

Besides considering modelling and analysis issue for cells, research in systems and synthetic biology is shifting towards to goal of controlling the behaviour of cell populations. A prominent example is the induced synchronization of cells in a robust fashion. Synthesis of control schemes for cells can be foreseen thanks to the availability of experimental techniques such as microfluidic devices that allow one to measure gene expression in single cells while regulating precisely the cellular environment. While detailed models allow for the accurate simulation of biological systems, they are probably far too complex for designing control strategies. This raises the issue of deriving design-oriented models retaining only the most relevant features of the more complex ones. An even more challenging goal will be to equip cell populations with distributed regulators mapped into biochemical networks for realizing desired collective behaviours such as the production of a protein in a synchronized fashion.

Medical systems

The term “Electrical stimulation” encompasses a broad array of electrical treatments targeting at therapeutic alteration of the function of the central, peripheral and autonomicnervous systems by means of implanted devices. The most common approach is to apply electrical currents to the neural tissue in order to control the movement of muscles or to activate parts of the sensory system. In particular, two functionally different approaches can be distinguished: neuromodulation and functional electrical stimulation (FES).

Functional electrical stimulation is directed towards the restoration of motor function and implanted devices are used to generate electrical impulses to activate muscles in patients with paralysis from neurological disorders. In neuromodulation (which includes brain, spinal cord and peripheral nerve stimulation), the electrical stimulation is used to modify the activity in specific circuits of the central nervous system. Neuromodulation has been proven to be successful for the management of persistent pain and motor disorders, to alleviate symptoms related to Parkinson’s disease and more recently to treat psychiatric disorders and epileptic seizures.

Stimulation patterns which are currently used in medical practice are under open loop control and a deep understanding of the mechanisms involved in electrical stimulation is still missing. Therefore one of the main objectives is to elucidate these mechanisms and consists, firstly, in the development of adequate models of neuronal activity (with corresponding numerical simulation tools) and of propagation of electrical stimulus produced by electrodes in the brains; secondly, in the design of stimulation sequences based on these models. In the latter case one aims both at determining adequate parameters for open-loop stimulation (frequency, amplitude, pulse width, waveform, and size of the stimulating electrodes) and at developing new closed-loop stimulation techniques using measurements produced by the same electrodes, thus making stimulation methods more adapted to human physiology and more individualized.

Such complex systems need advanced control theory tools coupled with understanding of the underlying neurophysiological processes and calls for the joint efforts of neurologists and mathematicians/engineers via the validation of mathematical models by experimental data. We also expect that development and validation of the new techniques will pave the way to the application of electrical stimulation in new clinically-relevant applications.
Next we describe specific applications of electrical stimulation that will be considered within the framework of HYCON2.

Electrostimulation for restoration of vestibular functions

Preliminary results achieved in animals indicate that it is possible to use implantable electrodes to restore balance. However, the potentials and limits of this approach are still not clear. Particularly interesting is the possibility of using multi-site electrodes to improve the efficacy of the neuroprosthesis. The ultimate goal will be the development and test in human disabled subjects of an implantable system for the restoration of vestibular functions.

Neurotechnologies for promotion and recovering of locomotion

It has been shown that after the interruption of all supraspinal inputs in adult rats, epidural electrical stimulation applied to specific spinal segments can induce locomotion. When combined with pharmacology and neurorehabilitative locomotor training, such electrical stimulations promoted the recovery of stepping patterns that was nearly indistinguishable from non-disabled locomotion. The main goals will be 1) to develop spinal cord electrode arrays; 2) to establish efficient multisite spinal cord stimulation patterns to reanimate the paralyzed limbs of spinal rats; 3) to extract useful information from cortical recordings to modulate stimulations of spinal circuits in promoting locomotion. Another aim will be to ensure the coordinated integration of these innovative neurotechnologies in clinically-relevant experimental applications.

Robotic assistance/electrical stimulation for paralyzed people

To support movements of paralyzed people functional electrical stimulation of muscles and robotic assistance might be combined with the aim to restore lost motor functions while exploiting the neuro-muscular system of the patient at a maximum. Complex tasks such as walking and grasping require different control strategies for both actuations systems depending on the current stage of the movement. The latter is often described by a state machine. To control the system, different sensors (inertial sensors, force sensors, bio-impedance) and human-machine interfaces (electromyography to detect residual muscle activity, brain computer interface etc.) can be used. At the moment robotic assistance systems and electrical stimulation are mostly applied independently to the patient. In rare cases, combinations have been reported using simple position / velocity control of the robotic devices while electrical stimulation is under open-loop control.

Deep brain stimulation for Parkinson decease

Deep brain stimulation consists in an electrical stimulation of deep brain structures, such as the internal segment of the globus pallidus (GPi) or the subthalamic nucleus (STN). Since its invention, in the late eighties, it has become an efficient and widely accepted symptomatic treatment of Parkinson decease. In recent years it was proposed that closed-loop algorithms may give novel DBS waveforms more effective than their high-frequency counterparts. Methods from nonlinear dynamics, statistical physics and optimal control allowed the development of novel stimulation techniques which specifically counteract pathologic synchrony. We aim at developing new stimulation methods using both micro- and macroscopic level models of neuronal activities.  The expected results, by combining modelling and control expertise for this purpose, will provide insights into new stimulation waveforms for open-loop stimulation and will allow the development of a new generation of closed-loop stimulation (based on averaged measurements of neuronal activity) thus providing interesting optimization of the current clinical techniques.  This research will be ultimately oriented towards the development of a prototype and its clinical trial.