The role of oscillatory theory in brain function: Deep Brain Stimulation as a treatment for Parkinson's Disease (see the web page www.systemsofparkinsons.org for details).
Model identification loop (including model discrimination, optimal experimental design and parameter estimation), simulation, state identification and predictive control of distributed processes.
Abstract: This work presents a methodology which exploits the underlying biochemical structure of bioprocesses to estimate concentrations in aerobic fermenters from oxygen measurements. Although a number of estimators have been proposed over the years in the literature, the methodology proposed in this work is able to operate in transient conditions while does not require the knowledge of the growth kinetics. In addition, it can be also applied to fermenters where the spatial distribution of the concentrations is relevant. In this case, we propose a systematic approach to optimally locate the sensors based on the use of reduced order models. This method allows the reconstruction of the oxygen concentrations from a limited number of sensors. Finally, the methodology proposed will be illustrated on a horizontal tubular reactor for the production of gluconic acid by free-growth of Aspergillus niger.
Abstract: In many cases, it is difficult to derive a precise mathematical model, based on first principles, for a given process. Besides, the computation of the solution of models obtained through this methodology may require a large computational effort making them useless for real time tasks like control or optimization. Neurofuzzy modelling, which permits an easy way to derive successful models, is a good alternative which can be employed to overcome such limitations.
In this paper, together with the neurofuzzy modelling, several strategies based on non-linear predictive control are presented. The low computational cost associated with neurofuzzy models and controllers makes them suitable candidates to be implemented into industrial Programmable Logic Controllers (PLC). Both the model and controllers are validated and implemented in a pilot plant for the thermal sterilization of solid canned food in steam retorts and based on the results, a comparison between the different predictive control strategies is presented.
Abstract: In this work a library of operation units for the simulation, optimisation and control of thermal processes in the food industry is presented. Food processing plants are good examples of hybrid systems where continuous dynamics are coupled with discrete events. The library was developed in EcosimPro since it is able to efficiently handle hybrid systems. In addition, it includes a user friendly graphical interface (Ecodiagram) which makes mathematical models accessible to non expert users. The paradigm of object oriented programming (OOP), which includes features such as the inheritance, abstraction or encapsulation, was employed to construct such models in EcosimPro. The library can be employed, for instance, to analyse the effect of alternative production technologies or to design new operation policies in the event of fluctuating supply conditions. Although this work is focused on processes of the canned food industry, new units can be added in order to simulate other processes such as pasteurization or drying without the need of modifying the existing components. The models have been validated using a pilot plant installed at the IIM-CSIC although they can be applied to other plants with different specifications. Finally, some advantages of the library are illustrated through a number of case studies. Copyright (C) 2008 CEA-IFAC.
Abstract: Reaction-Difusion (RD) mechanisms can describe many biological phenomena such
as neuron firing in the brain, the heartbeat, cellular organization activities or even
biological disorders such as fibrillation. The FitzHugh-Nagumo (FHN) model is a
particular case of RD systems. It is able to capture the key features of many biolog-
ical processes and since it is relatively simple it has been widely employed during
recent years. Some examples of its predictive capabilities include the representation
of the normal behaviour of some physiological phenomena, related to a travelling
plane wave, as well as biological disorders associated with spiral or irregular fronts.
The objective of this work is to design a control law able to stabilize complex be-
haviours (travelling plane wave) in biological systems using the FHN system model
as the case study. Since, in biological systems there usually exists a lack of detailed
information on the system structure, our control law will be designed to be robust,
i.e., in such a way that these problems do not a®ect to its stability properties.
To this purpose, we will extend results in ¯nite dimensional robust control theory
to RD systems by means of order reduction techniques, in particular the Proper
Orthogonal Decomposition method.
Abstract: In the paper, a class of bioprocesses with fully unknown kinetics is considered. Indirect adaptive control algorithm where the process kinetics is presented as unknown time-varying parameter is derived. A general procedure for optimal tuning of kinetic estimator design parameters is proposed by stability analysis of the control scheme. Theoretical results are verified by simulations of the control scheme of continuous fermentation of gluconic acid production by Aspergillus niger. In the conclusion, some other applications of proposed procedure are discussed. 169; 2007 Elsevier Ltd. All rights reserved.
Abstract: The dissipative nature of spatially distributed process systems is exploited to develop
efficient exponential state observers based on a low-dimensional dynamic representation
of the original set of partial differential equations. The suggested approach combines
standard observer design techniques for reactors, where the reaction rates are
unknown with efficient model reduction methodologies based on projection of the original
concentration and temperature fields on low-dimensional subspaces capturing the
slow dynamics of the process. The global exponential stability of the resulting observer
is derived combining classical Lyapunov analysis with a transformation that allows us
to obtain a diffusion system from a diffusion-convection system. In addition, aspects
related to the location of sensors and their influence on the ability to reconstruct the
necessary fields to feed the observer will also be considered.
Abstract: There are many distributed processes in the chemical industry as it is the case of tubular reactors in which the parameters or the structure of the reaction terms are only a rough approximation of reality. In order to efficiently control this kind of systems, it is important to take into account this lack of detailed information (robustness). In this work, we make use of the classical theory on the robust nonlinear control for finite dimensional systems and extend it to distributed process systems by taking advantage of the special nature of dissipative systems. In this way, theoretical issues related to the nonlinearity of the diffusion terms and inhomogeneous boundary conditions are handled by means of the Kirchhoff and state transformations, respectively. In addition, and for practical reasons, the problem of controller saturation is considered. The different aspects of the methodology will be illustrated through a number of computational experiments concerning non-isothermal tubular reactors with convection and/or diffusion terms. 169; 2007 Elsevier Ltd. All rights reserved.
Abstract: In this article, we develop a systematic approach for efficient field reconstruction in distributed process systems from a limited number of measurements. The approach generalizes previous methods for sensor placement so as to be able to handle field reconstruction problems in arbitrary spatial domains where complex nonlinear phenomena take place. Pattern formation in fluid dynamics or diffusion-reaction systems are examples exhibiting complex nonlinear distributed behaviors, especially when taking place in arbitrary 2D or 3D domains. Our approach exploits the dissipative nature of the diffusion-convection process and the underlying algebraic structure of the finite element method to efficiently construct field representations in terms of globally defined basis functions and to optimally select the placement of sensors. The results will be illustrated on a fluid dynamic process: the Rayleigh-Be?nard problem. 169; 2007 American Chemical Society.
Abstract: Many phenomena such as neuron firing in the brain, the travelling waves which produce the heartbeat, arrythmia and fibrillation in the heart, catalytic reactions or cellular organization activities, among others, can be described by a unifying paradigm based on a class of nonlinear reaction-diffusion mechanisms. The FitzHugh-Nagumo (FHN) model is a simplified version of such class which is known to capture most of the qualitative dynamic features found in the spatiotemporal signals. In this paper, we take advantage of the dissipative nature of diffusion-reaction systems and results in finite dimensional nonlinear control theory to develop a class of nonlinear feedback controllers which is able to ensure stabilization of moving fronts for the FHN system, despite structural or parametric uncertainty. In the context of heart or neuron activity, this class of control laws is expected to prevent cardiac or neurological disorders connected with spatiotemporal wave disruptions. In the same way, biochemical or cellular organization related with certain functional aspects of life could also be influenced or controlled by the same feedback logic. The stability and robustness properties of the controller will be proved theoretically and illustrated on simulation experiments. 169; 2005 Elsevier Ltd. All rights reserved.
Abstract: In this work we present the development of an efficient model-based real time dynamic
optimization (DO) architecture for the control of distributed parameter systems (DPS).
The approach takes advantage of the dissipative nature of this class of systems to obtain
reduced order models (ROM) which are then used by the optimization modules to
compute in real time the optimal operation policy. The DO module is based on the
combination of the control vector parameterization (CVP) approach and a suitable NLP
solver selected among several local and global possibilities.
Abstract: The understanding of neurodegeneration of the Substantia nigra (SN), the hallmark of Parkinson's Disease (PD) is limited. The majority of studies conducted focus on isolated sub-components of the relevant pathogenic pathways. However, this isolated approach may be inadequate to describe the pathogenesis. A systems approach employing in-silico modelling facilitates the linking of diverse sub-components, which is often impossible in-vitro or in-vivo. Using energy flow as a unifying basis [1], an attempt is made to relate various pathological markers of PD. SN neurons function on a tight energy budget, owing to a high level
of arborization and pacemaking activity. This involves the L-type calcium channel [4], and imposes long-term accumulation of calcium within SN organelles. The fate of intra-cellular calcium ions in particular is examined since they strain the energy budget and in turn slow down a few non-critical metabolic activities. Excessive mitochondrial calcium accumulation triggers a cascade of events that leads to a positive feedback loop which proves fatal to SN neurons. Lewy Bodies (LB) are generally considered as an aftermath of such events. However, we hypothesize the process of brillation (that leads to the formation of LB) in itself is a signi cant player in SN degeneration. This may occur via coalescence of the rapid calcium buffer calbindin, from the cellular pool with -synuclein brils. Increased mortality among SN neurons with low expression of calbindin [2] and a synergistic assosciation of calbindin and -synuclein genes [3] support this hypothesis. A model developed on this basis supports the view that brillation and subsequent transient absence of buer can trigger SN apoptotic loss.
Abstract: In recent years, Markov processes have been widely used to describe opening probabilities
of ion-channels. This approach can be readily combined with thermodynamics to obtain a
model without employing abstract concepts such as in the commonly used Hodgkin-Huxley
formalism. However in these Markov models, the number of important states is often am-
biguous and overestimating this number creates unnecessary computational complexities as
well as identi ability problems.
In this work, we propose a simple expression that represents the conductance of voltage
regulated ion-channel gating in a functional cell. The model is developed with a mechanistic
motivation based on concepts in elementary thermodynamics applied to protein Markov
models. In order to obtain a low order identi able model preserving the physical meaning,
the existence of a unique simple path of transition from every stable ion-channel state to the
open state is assumed. Under this supposition that seems reasonable with respect to protein
conformational dynamics, a general mechanistic expression is obtained that depends on the
number of channel states. Interestingly, using data available from a number of sources in the
literature the open probability of ion-channel stationary conductance of several channel types
can be accurately described using a maximum of three states. For such a model, parameters
are found to be structurally identi able and easily determinable from experimental data.
The model as such may be further extended to incorporate the dynamic behaviour of the
system.
The model has the advantage of having its basis on the biophysical mechanism and that
the resulting identi able model structure overcomes the problems with over-parameterised
Markov models. Such approaches are relevant to understand neuronal behaviour at the
systems level. The model may be regarded as a rst step in producing a robust model for
ion-channel gating, including environmental eects such as transitions in the lipid bi-layer
and couplings to neighbouring channels.
Abstract: The degeneration of dopaminergic (DA) neurons in the Substantia Nigra pars compacta (SNc) is a hallmark of idiopathic Parkinson's disease (PD). However, resolving the degeneration mechanisms which target these neurons is not simple. For example, it is well known that DA neurons in the SNc deteriorate with age and are prone to die in PD, but there is no clear picture of what causes this or other related processes.
Fortunately, some clues have come to light in recent epidemiologic studies. The latest work show how hypertensive drugs that block L-type calcium channels in the brain also considerably reduce the incidence of PD [2]. Following this insight, experiments with in vivo and in vitro models of PD have shown that SNc DA neurons rely on L-type Cav 1.3 channels to sustain their autonomous pacemaking. Significantly for PD, this reliance upon calcium channels for pacemaking increases with age [1]. This linkage strongly suggests that the control of calcium homeostasis, which is fundamental for the normal function of any cell, may be especially compromised in ageing SNc neurons. Unfortunately, calcium signalling involves the interplay of multiple intracellular organelles and it becomes extremely difficult to design experiments to estimate the energy cost of calcium regulation and to associate it with levels of predisposition to PD. In this communication, we propose that the control of calcium homeostasis and the degeneration of aged DA SNc neurons may be better understood from a systems perspective. To this end, we describe the development of a mathematical model of whole cell dynamics with which we are able to reproduce all relevant pathological features. In order to maintain the physiological meaning, and avoid technical issues of system identifiability, a modular approach was used during model development. Model modules representing different components - such as ion channels and pumps - were separately developed and calibrated with available data specific to SNc cells. finally, each module can be integrated in a model framework for the whole cell and in a form that is capable of predicting ATP consumption, in the form of an energy budget, for both healthy and compromised cells.
In future works, the model will be further extended to explore positive feedback loops due to calcium stress. One interesting example is the feedback mechanism that includes: mitochondria stress, production of reactive oxygen species, misfolding of α-synuclein, and where the extension includes calcium cell specific mechanisms such as sequestration of calbindin and increase of calcium cytoplasm.
[1] C. Chan, J. Guzman, E. Ilijic, J. Mercer, C. Rick, T. Tkatch, G. Meredith, and D. Surmeier. 'Rejuvenation' protects neurons in mouse models of Parkinson's disease. Nature, 447(7148):1081-1086, 2007.
[2] B. Ritz, S. L. Rhodes, L. Qian, E. Schernhammer, J. H. Olsen, and S. Friis. L-Type Calcium Channel Blockers and Parkinson Disease in Denmark. Annals of Neurology, 67(5):600-606, 2010.
Abstract: Closed-loop control systems can often be made unstable or oscillatory by the introduction of time delays.
We hypothesize that deep brain stimulation (DBS) ameliorates essential and Parkinsonian tremor
by reducing time delays in the feedback paths of the motor control system, thus stabilizing the system.
The mechanism we posit for this reduction in feedback delay is partial blockade of axonal pathways by
antidromic activation, with the blockade being less complete for axons with higher propagation velocities.
The inverse relationship between blockade effectiveness and propagation velocity is due to the
blocking pulses clearing the axon faster when their velocity is higher, leaving a larger fraction of the
time during which activity is not blocked. This hypothesis, whose plausibility we demonstrate using
a simple computational model, accounts for a variety of experimental results, and makes a number of
strong testable predictions.
Abstract: This work presents the theoretical design and the experimental validation of a real time optimisation logic for distributed parameter systems. This logic consists of a hierarchy of two layers. The upper layer is responsible of obtaining the optimal control profile by a suitable combination of the control vector parameterisation approach with a hybrid globallocal optimiser and the use of reduced models for distributed parameter systems. The lower layer corresponds to a PID controller designed in the framework of Internal Model Control to keep tracking capabilities at short time scales. This logic was applied to the real time optimisation of the thermal processing of packaged foods in batch retorts
at the pilot plant available at the IIM-CSIC. The objective was to maximise food product quality while satisfying safety
constraints. The proposed scheme was able to optimally operate
the system under standard plant perturbations and under a
pressure drop.
Abstract: The electrical stimulation of the brain for the treatment of neuropsychiatric disorders has a
long history that goes back to the early 1950s. Specifically it was first used for the treatment of
tremor in Parkinsons Disease (PD) in 1968. However it was not until the work of Limousin and
coauthors that deep brain stimulation (DBS) was commonly accepted as a therapeutic procedure
for PD. Since then, there have been significant advances in our understanding of DBS. Yet, some
fundamental questions about the basic mechanisms remain.
A current hypothesis is that DBS acts via stimulation-induced modulation of pathological
network activity. In PD this pathological behaviour is a consequence of the reduction of the
dopamine supply to the striatum reducing the inhibition of the indirect circuit and, therefore,
causing the pathway to be highly excited. According to the stimulation-induced modulation
hypothesis, DBS would modulate this pathological activity by interfering with the interneuronal
communication, specifically by breaking the abnormal patterns of synchrony.
This thesis is supported by experimental findings which suggest that neurons in the beta band
are inhibited by the stimulus. These experimental findings have inspired several computational
studies. Notably, Tass and co-workers have proposed various pulse-based methods for desyn-
chronizing a population of coupled oscillators. To evaluate the efficacy of these methods, the said
authors employed an extended version of the standard Kuramoto model, which incorporated the
effect of the stimulus. Their findings single out the so called double-pulse stimulation technique
as the most effective method for achieving desynchronization.
At the workshop, we will present a survey of recent experimental and theoretical work related to
the desynchronization hypothesis. We will also present some preliminary results of a computational
study of DBS of the Subthalamus Nucleus with applications to PD.
Abstract: A novel chemical reactor, the Open Plate Reactor, is being develop by Alfa Laval AB. It combine good mixing with high heat transfer capacity. In this reactor highly exothermic reactions can be produced using more concentrated reactants. A nonlinear model predictive control is proposed to maximize the reaction yield under hard input and state constraints. A reduced order model is proposed to decrease the optimization time, so we can implement it online. The approach takes advantage of the use of global spatial basis functions and uses the proper orthogonal decomposition (POD), to approximate the system by a low-dimensional set of ordinaries di®erential equations (ODEs). Simulations show a high reaction yield and ensure that the temperature inside the reactor do not exceed the safety limit.
Abstract: In this work, the dissipative nature of spatially distributed bioprocess systems is exploited to develop efficient state observers based on a low dimensional dynamic representation of the original set of partial differential equations. The approach we suggest combines standard observer design techniques for bioreactors with efficient model reduction methodologies based on projection of the original concentration fields on low dimensional subspaces capturing the slow dynamics of the process. Aspects related with the location of sensors and their influence on the ability to reconstruct concentration fields will also be considered. Finally, the different aspects of the methodology, as well as the efficiency of the resulting observers will be illustrated on a case study of industrial interest, namely a tubular bioreactor producing gluconic acid by Aspergillus Niger. 169; 2005 IEEE.
Abstract: Many of the processes in the food and biotechnology industries are operated in
batch or semi-continuous modes thus being dynamic in nature. In addition some
relevant state variables, or even manipulable variables (controls), depend not only
on time but on position, i.e. distributed process systems (DPSs).
This PhD work has been aimed at the development of real time optimisation
(RTO) schemes suitable for the control of food and biotechnology industries related
processes. The proposed schemes are based on the harmonious combination of the
following elements: process measurements and observers, a reliable model and the
necessary simulation techniques, together with a suitable optimisation approach
and a feedback logic.
Abstract: Tomando como metáfora el neuston, que define la comunidad organismos que viven asociados a la superficie, en la interfase agua-aire, este proyecto explora la interfase ciencia-arte, suscitando un diálogo en el entorno del mar y de las ciencias marinas en Galicia. El Proyecto Neuston, propuesto como un experimento transdisciplinar, establece la colaboración entre quince cientÃficos del IIM y quince artistas plásticos o literatos. Tomando como punto de partida una publicación cientÃfica, el investigador expone al artista un aspecto concreto de su trabajo, que sirve de inicio a un diálogo a partir del cual el artista realiza su propuesta. Los resultados del proyecto se recogieron en un libro (Varios autores, 2009) y se mostraron en una exposición (Museo do Mar de Galicia, Vigo, del 13/03/09 al 21/06/09).
