Method for simulating physiological neural signals

Abstract

The invention relates to a method for simulating physiological neural signals which originate from the lumbar spinal cord and in particular are transmitted to motoneurons, wherein: a simulation model comprises a plurality of populations of neurons which are interconnected so as to excite or inhibit one another; during simulation, a stimulus signal is diverted via a first population of interneurons; and the first population has no input value which is dependent on other populations.

Description

[0001] Methods for simulating physiological neuronal signals

[0002] The invention relates to a method for simulating physiological neuronal signals originating from the lumbar spinal cord, in particular those transmitted to motor neurons, wherein a simulation model comprises several populations of neurons that are connected to one another in an excitatory or inhibitory manner. Furthermore, the invention relates to a data processing system comprising means for executing said method and a computer program product comprising instructions that, when executed by a computer, cause the computer to execute said method. In particular, the invention relates to a method for determining an electrical signal for treating a neurological dysfunction in a patient, wherein said method is used to simulate physiological neuronal signals.

[0003] As early as 1911, the experiments of Thomas Graham Brown [Brown, TG (1911). The intrinsic factors in the act of progression in the mammal. Proc. R. Soc. Lond. B, 84(572), 308-319.] revealed that the basic pattern of walking can be generated by the spinal cord without descending activation from the cortex.

[0004] Brown also defined a general theory of the basic circuitry of a central pattern generator in 1914 [Brown, TG (1914). On the nature of the fundamental activity of the nervous centres; together with an analysis of the conditioning of rhythmic activity in progression, and a theory of the evolution of function in the nervous system. The Journal of physiology, 48(1), 18-46.] and used the term half-center for the first time.

[0005] In 1961, Wilson [Wilson, DM (1961). The central nervous control of flight in a locust. Journal of Experimental Biology, 38(2), 471-490. Walker, M. (2017). Why we sleep: Unlocking the power of sleep and dreams. Simon and Schuster.] provided evidence of a central pattern generator (CPG) in his experiments by isolating the locust's nervous system. The isolated nervous system was capable of producing patterns similar to the locust's flight. Graham's ideas were later taken up by Lundberg [Lundberg, A. (1981). Regulatory Functions of the CNS. Motion and Organization Principles.], in whose description of the flexion reflex, spinal interneurons play an influence and serve as a basic function for controlling the movement pattern of mammals.

[0006] Later, evidence was provided by studies on many vertebrates, including the lamprey, a vertebrate fish that Sten Grillner and colleagues [Grillner, S., Wallen, P., Brodin, L., & Lansner, A. (1991). Neuronal network generating locomotor behavior in lamprey: circuitry, transmitters, membrane properties, and simulation. Annual review of neuroscience, 14(1), 169-199.] used as the basis for their experiments and simulations.

[0007] The models of Sten Grillner and colleagues describe the oscillating behavior of an agonist versus antagonist, meaning that two motor neuron pools are alternately stimulated by the pattern generator. While the agonist is active, the antagonist is inhibited. Therefore, the activation of an agonist requires a half-center, as mentioned above. To simulate the lamprey, several half-centers were connected in series, which activate one after the other [Grillner, S. (2006). Biological pattern generation: the cellular and computational logic of networks in motion. Neuron, 52(5), 751-766.; Grillner, S. (2011). Control of locomotion in bipeds, tetrapods, and fish. Comprehensive Physiology, 1179-1236.].

[0008] Ein ähnliches Modell verwendeten Rybak und Kollegen [Rybak, I. A., Shevtsova, N. A., Lafreniere-Roula, M., & McCrea, D. A. (2006). Modelling spinal circuitry involved in locomotor pattern generation: insights from deletions during fictive locomotion. The Journal of physiology, 577(2), 617-639.; Rybak, I. A., Dougherty, K. J., & Shevtsova, N. A. (2015). Organization of the mammalian locomotor CPG: review of computational model and circuit architectures based on genetically identified spinal interneurons. eNeuro, 2(5), ENEURO-0069.; Danner, S. M., Shevtsova, N. A., Frigon, A., & Rybak, I. A. (2017). Computational modeling of spinal circuits controlling limb coordination and gaits in quadrupeds. Elife, 6, 031050.; Shevtsova, N. A., Hamade, K., Chakrabarty, S., Markin, S. N., Prilutsky, B. I., & Rybak, I. A. (2016). Modeling the Organization of Spinal Cord Neural Circuits Controlling Two-Joint Muscles. In Neuromechanical Modeling of Posture and Locomotion (pp. 121-162).Springer, New York, NY.] to model such a half-center. This model is derived from studies of respiratory muscles. These studies identified ion channels in the associated neuron pools that exhibit very high time constants – the persistent sodium channels (NaP), which are used to generate rhythms [Paul, JR, DeWoskin, D., McMeekin, LJ, Cowell, RM, Forger, DB, & Gamble, KL (2016). Regulation of persistent sodium currents by glycogen synthase kinase 3 encodes daily rhythms of neuronal excitability. Nature communications, 7, 13470.].

[0009] It is an object of the present invention to improve the above models and provide the most realistic (and accurate) simulation possible of the neural processes relevant to muscle movements in humans and animals. The simulation thus has the sole (reasonably assumed) purpose of reproducing the physiological neural signals observed and measured in a patient that are crucial for a movement, and, if necessary, to supplement the body's own signals with electrical stimulation, or to pre-test the effects of such supplements, the signals and patterns of which can be determined using the simulation. This should ultimately enable or at least improve the treatment of motor dysfunction, for example.

[0010] This object is achieved by the invention defined in the claims.

[0011] It has been found that an essential component of a realistic simulation is that, within the simulation, a stimulus signal is redirected via a first population of interneurons, where the first population has no input value dependent on other populations.

[0012] A method for simulating physiological neuronal signals as described above and further explained below with more specific examples and optional variants can be used in particular in the context of a method for determining an electrical signal for treating a neurological dysfunction in a patient. Based on measured physiological neuronal signals from the patient, the simulation model is adapted to replicate these physiological neuronal signals. Using the adapted simulation model, an external electrical signal is simulated, and the parameters of the electrical signal are adjusted such that the simulated physiological neuronal signals approximate a signal curve without dysfunction. The adjustment can, for example, consist of a change in a static electrical potential.Alternatively, the frequency and amplitude of a periodic stimulus signal can be changed. The comparison with the signal curve without dysfunction can have a tolerance range. For example, this can be a purely qualitative comparison or a distance from an ideal curve. An adjustment is already accepted if the difference between the output signal achieved by the simulation and the original output signal is greater than the difference between the output signal achieved by the simulation and an ideal output signal.

[0013] The above method for detecting an electrical signal can be used, for example, to treat a patient's neurological dysfunction in the musculoskeletal system, particularly in the lumbar spinal cord. For this purpose, the detected electrical signal can be applied via electrodes to the patient's body, e.g., to individual limbs.

[0014] Below we explain some optional features that further contribute to a realistic simulation.

[0015] The first population can have an inhibitory effect on a second population of neurons, where the second population belongs to a central pattern generator, to which at least a third population of neurons belongs in the simulation model. The central pattern generator thus comprises at least two – simulated – populations of neurons, the second and third populations. The different populations together form an oscillating system whose dynamic behavior ultimately determines the course of the generated pattern and thus the generated output signal.

[0016] For example, the second population can have an excitatory effect on the third population and, conversely, the third population can have an inhibitory effect on the second population with a delay.

[0017] In the simplest case, the delay in question can be defined and parameterized by a time constant (T), where the time constant (T) can be between 0.1 and 30 milliseconds, in particular between 0.1 and 20 milliseconds. The time constant can, for example, be considered as a constant for an exponential decay of the activation of a simulation population.

[0018] The populations belonging to the central pattern generator can be selected so that they predominantly excite each other. This means that, measured by the number of connections, there are predominantly more excitatory connections than inhibitory connections between the populations.

[0019] The central pattern generator can include at least a fourth population of neurons in the simulation model, wherein preferably the fourth population has a mutually excitatory effect on the second population and the fourth population has an excitatory effect on the third population and is conversely inhibited by the third population with a delay. These mutual effects between the populations, be they excitatory or inhibitory, can each be individually associated with delays, each parameterized with its own time constant. The fourth population enhances the self-excitation within the pattern generator. The inhibition (or inhibition) of both the second and fourth populations by the third population is broken by the stimulus signal, which can be a constant stimulus, for example. As a result, the system, i.e. the central pattern generator, is excited sufficiently quickly to trigger an oscillation.

[0020] According to a further embodiment, at least a fifth population of neurons in the simulation model can belong to the central pattern generator, wherein the fifth population is a self-exciting population, wherein the fifth population preferably has an excitatory effect on the second population. This allows the inhibitory effect of the first population on the second population to be periodically compensated. As a result, an approximately linear response of the pattern generator to the stimulus signal is achieved. Specifically, in this embodiment, a proportional relationship (at least within a working range) between the magnitude of a constant stimulus signal and the output frequency can be achieved.

[0021] In all of the above variants, a simulated physiological neural signal can be formed by an output value of the central pattern generator, whereby this output value is preferably compared with a measured physiological neural signal in order to adapt the simulation model. In particular, the amplitude and frequency of the output signal are evaluated. Depending on the desired or expected neurological response, the measured physiological neural signal can be too low (if no signal should actually be triggered at the relevant location) or too low (if the measured signal should be more prominent than other measured signals). Therefore, a simulation configuration that reproduces the measured behavior can be searched for by changing the parameters of the simulation model and the stimulus signal.Subsequently, by changing the stimulus, an attempt can be made to bring the simulation's output signal closer to the desired output signal. The parameters of this change provide information about a possible alleviation of the observed dysfunction.

[0022] For example, in the above configuration of the pattern generator, an output value of the fourth population can be used as the output value of the central pattern generator.

[0023] To further improve control of the amplitude of the output signal, it can alternatively be provided that at least a sixth population of neurons in the simulation model belongs to the central pattern generator, whereby the sixth population is excited by the fourth population and an output value of the sixth population is used as the output value of the central pattern generator. To control the output signal, a further external stimulus can be simulated on the sixth population.

[0024] Instead of directly stimulating the sixth population, the central pattern generator can alternatively include at least a seventh population of neurons in the simulation model, with the seventh population having an inhibitory effect on the sixth population. Similar to the stimulus applied to the first population, which inhibits the second population, the stimulus applied to the seventh population can ultimately have an inhibitory effect on the sixth population, with the timing used for effects between populations in the simulation.

[0025] In a further refinement of the simulation, slower effects on the dynamics of the system can be accounted for, for example, by influencing the interaction between the populations through moderation parameters. Each population is assigned a moderation parameter, with the moderation parameters themselves following a temporal evolution that depends on the excitation of the respective population. In this way, the effect of the glial system observed in nature on the interactions between neurons can be accounted for in a simplified and effective manner.

[0026] The invention will be further explained below using particularly preferred embodiments, to which it is not intended to be limited, and with reference to the drawings. In detail:

[0027] Fig. i shows a graphical representation of a metamodel;

[0028] Fig. 2 shows exemplary parameters in the metamodel for defining an external disturbance signal;

[0029] Fig. 3 shows a pattern generator (“half-center”) according to Rybak;

[0030] Fig. 4 shows a first embodiment of a pattern generator of the type in question here and the output signal obtained thereby;

[0031] Fig. 5 shows the transfer function used in the example according to Fig. 4;

[0032] Fig. 6 shows a second embodiment of a pattern generator of the type in question here and the output signal obtained thereby;

[0033] Fig. 7 shows a third embodiment of a pattern generator of the type in question here and the output signal obtained thereby;

[0034] Fig. 8 shows a complete simulation model based on the pattern generator with agonist and antagonist shown in Fig. 4;

[0035] Fig. 9 shows the result of the simulation in the form of the generated output signals of the model shown in Fig. 8;

[0036] Fig. 10 shows a fourth embodiment of the pattern generator and Fig. n shows the corresponding output signals.

[0037] To accomplish the task of simulating a flexible model, for example, of the spinal cord and its various properties, it is useful to use a simulation environment in the form of standard software that is as flexible and powerful as possible. The selected standard software should, in particular, be able to (numerically) solve the differential equations underlying the model and thus execute the simulation. For the following examples, the simulation environment in the software product "MATLAB" from MathWorks was used in the form of a specially developed and publicly available toolbox [Anzinger, M. (2005). Toolbox for simulating inhomogeneous populations. Application in the field of neuron populations. Diploma thesis at the Medical University of Vienna, 1-83.]. The components of this toolbox referenced below form part of the present disclosure.

[0038] The graphical notation of the simulation model used in all figures will first be shown using a simple example and the corresponding program code.

[0039] Figure 1 shows an example of a graphical representation of a metamodel. The model contains two objects, each with four populations. Each object contains a 4x4 matrix in the background, representing the internal connections and a vector of equal length for the internal time constant. An ellipse defines a negative synaptic connection, and an arrow a positive one. The curved lines Verb.i and Verb.2 define a single synaptic connection with a latency of 10 ms (milliseconds).

[0040] The corresponding program code, based on the toolbox referenced above, is:

[0041] % struct net Metamodel=createModel ( ) ;

[0042] % neces sary time constants tau_Obj 1 = [ 20 , 10 , 20 , 10 ] ; tau_Obj 2 = [ 20 , 10 , 20 , 10 ] ;

[0043] REVISED SHEET (RULE 91) ISA / EP % own weight matrix wMat = [0 0 0 0;

[0044] -1 0 1 -1;

[0045] -1 1 0 -1;

[0046] 0 1 1 0 ] ;

[0047] % Add object 1 and 2 to metamodel with matrix and time constants;

[0048] [Metamodel, Ob l] = addPO (Metamodel , tau_Ob l, 'wMatrix', wMat) ;

[0049] [Metamodel, Ob 2] = addPO (Metamodel , tau_Ob 2, 'wMatrix', wMat) ;

[0050] % Add Connection_l and 2 to Metamodel with weight 1 and latency 10ms

[0051] Metamodel = connectPO (Metamodel ,

[0052] ' src ' , Ob 1. node { 3} , ' dest ' , Ob 2. node { 4} , ' weight ' , 1 , 'delay', 10) ;

[0053] Metamodel = connectPO (Metamodel ,

[0054] ' src ' , Ob 2. node { 3} , ' dest ' , Ob 1. node { 4} , ' weight ' , 1 , 'delay', 10) ;

[0055] The functions addPO and connnectPO fill the metamodel with the information.

[0056] The stimulus is part of the metamodel. It defines the external disturbances in the system. In the graphical metamodel, we can easily represent this as a signal generator. This generator must then provide the disturbance signal in a time-accurate manner for the entire time period to be simulated. To do this, it uses information about the signal shape, the target population, the time period to be simulated, and information about the solver's time discretization.

[0057] The discretization is calculated here with a constant step size. The disturbance signal can therefore be precalculated at the beginning of the simulation and made available to the model at the correct time during runtime. Fig. 2 shows example parameters in the metamodel for defining an external disturbance signal. Forehead.in specifies the respective disturbance variable. The StimuliVector parameter provides the disturbance function with the correct time discretization to the model at runtime. The Time parameter specifies the time at which the disturbance variable is applied to the model. The Node parameter denotes the target population in the model. The corresponding program code is:

[0058] % generate a rectangle with pulse length of 600ms

[0059] % and an amplitude of 0.65.

[0060] Sl=ones (1, 600 / dt) *0.65; % add the stimulus S 1 to the metamodel % at time 100 ms .

[0061] Metamodel = addStimulus ( net , pendulum . node { 1} , S l , 100 ) ;

[0062] The integrator forms the heart of the simulation. The relevant information for the simulated neural system is passed on here. The parameters of the integrator used here are the time span to be simulated tspan and the corresponding step size dt, the metamodel metaModel, the system of differential equations used for a single homogeneous population which is stored in the solver parameter and finally the transfer function which is specified by the sigm parameter. dt=0 . 1 ; % fixed integrator step size in ms tspan=100 ; % time span to be calculated in ms result = runModel (Metamodel , dt , tspan, ' solver ' , ' S2 ​​' , ' si gm ' , @ si gm ) ;

[0063] For the solver itself, the 4th order Runge-Kutta method is used.

[0064] To illustrate the state of the art and for comparison, Fig. 3 shows a pattern generator (“half-center”) according to Rybak [McCrea, DA, & Rybak, IA (2008). Organization of mammalian locomotor rhythm and pattern generation. Brain research reviews, 57(1), 134-146.] in the graphical notation used here. Red circles are excitatory interneurons (populations), blue circles are inhibitory interneurons. Circle E represents the extensor motoneurons and circle F the flexor motoneurons. A half-center according to Rybak has the capability of alternating oscillation of flexor and extensor. Oscillation of a single motoneuron pool is not possible. The neurons of a population are modeled according to the Hodgkin-Huxley style and consist of approximately 20 - 100 individually modeled neurons.

[0065] As an example from functional electrical stimulation, it is worth mentioning that a constant stimulus (constant frequency and constant amplitude) applied to the afferent signals of the lumbar spinal cord was able to trigger the walking pattern of a patient with complete paraplegia. However, applying a constant stimulus in functional electrical stimulation is much more likely to inhibit unwanted movement patterns than to activate them.

[0066] In the models of Rybak and colleagues, a constant stimulus is applied to both motor units of the half-center, providing the necessary excitation to generate an oscillation. Increasing the amplitude of this stimulus also increases the frequency of the oscillation. If stimuli of different strengths are applied to both motor units, the active time shifts proportionally from agonist to antagonist and vice versa - Fig. 3.

[0067] Fig. 4 shows a simulation and, in particular, a pattern generator of the type under consideration here. The left part shows the pattern generator according to the graphical notation above; the right part shows its response to changes in the stimulus signal. For this purpose, a stimulus is applied to population 5 (the first population), which is varied over a certain value. Each change is shown in a waterfall plot. The stimulus is varied from 0 - +1. B: A strong linearization of the system across the stimulus can be seen, which results from the introduction of the additional interneuron (first population). The transfer characteristic of the sigmoidal function is mapped over the pulse width. The pulse is completely inhibited at a stimulus strength of approximately 0.6.

[0068] The sigmoidal function is derived from a stimulus value of 0 - 0.6. This is primarily due to the transfer function used in Fig. 5. With an input of 0.6, this already produces an output of 0.9. This means that to expand the control range to an input of 0.1 - 0.9, the transfer function would have to have a flatter curve. If the transfer function is changed, however, the weights in the model must also be adjusted.

[0069] The corresponding program code of this simulation is:

[0070] % struct net net=createModel ( ) ;

[0071] % necessary time constants for models 1 and 2. ptau=[l, 20, 3, 30, 3] ; % for model S2

[0072] % ptau=[0.22, 0.72] ; % for model SI

[0073] % own weight matrix wMat= [ 3.3 0 0 0 0;

[0074] 1 0 2.2 -1.8 -1;

[0075] 0 1.8 0 -1.2 0;

[0076] 0 1 1 0 0

[0077] 0 0 0 0 0] ; y= [ 0.2 , 0 , 0 , 0 , 0 ] ;

[0078] [net P] =addPO (net, ptau, 'wMatrix', wMat, 'inityl', y) ;

[0079] % create stimuli dt=0.1; % stepwidth of the integrator tspan=1000; % total time span stimStart=l 00 ;

[0080] BERICHTIGTES BLATT (REGEL 91) ISA / EP tStim=tspan-stimStart ;

[0081] S2=one % rectangle figure elf; while S2<0.99 net . cntStimulus=O ; net = addStimulus (net, P.node{5}, S2, 10) ;

[0082] % start simulation

[0083] R = runModel (net, dt, tspan, 'solver', 'S2', 'sigm', @ s i gm2 ) ; hold on; x=R.PO(l) . yl (3, : ) ; y=R . t ; z=ones ( 1 , length (R.t) ) *S2 (1) ; plot3 (y, z, x) ;

[0084] S2=S2+0.01; end; view ( 0 , 20 ) ;

[0085] According to another embodiment, an additional population is introduced into our model, which is used solely to control the amplitude. This population is assigned a weight <1 to reduce the resulting amplitude. The height is then controlled with an additional stimulus.

[0086] Population 6 was inserted into our model, which is excited by Population 3 with a weight of 0.5. The output of Population 6 is now visible in Fig. 6. The blue line shows the output without any additional stimulus. A constant stimulus was then applied to Population 6 over the entire time period, starting with a strength of 0.05 to 0.35 in 0.01 steps. It can be seen that the amplitude increased as the stimulus increased. A slight increase in the bias is visible. However, if the stimulus were increased further, the bias would increase accordingly. The amplitude can therefore only be controlled within a small range of the input signal.

[0087] To circumvent this problem, instead of applying a stimulus to the output, it is assumed that the stimulus already has a maximum amplitude at the beginning and that its amplitude is controlled by an inhibitory interneuron. This corresponds to the third embodiment shown in Fig. 7. It can be seen that the amplitude can be controlled over the entire range. The bias error from before no longer occurs.

[0088] REVISED SHEET (RULE 91) ISA / EP To describe a half-center, one uses an agonist and its corresponding antagonist. Conventional medicine assumes that the motor neurons of the antagonist are inhibited when the antagonist is stretched by activating the agonist. In fact, with every movement, the antagonist is also activated to stabilize the respective joint. This is also clearly visible in the respective muscle recordings of non-impaired individuals and is important for correctly interpreting the respective activation patterns.

[0089] To model the interplay of agonist and antagonist, we use a pattern generator model as shown in Fig. 4 for each muscle group. If the first muscle group—we call it the agonist—is active, it inhibits the second muscle group—we call it the antagonist—via a lateral connection (Fig. 8). Here is the corresponding simulation code:

[0090] % struct net net=createModel ( ) ;

[0091] % necessary time constants for models 1 and 2. ptau=[l, 20, 3, 30, 3] ; % für Modell S2

[0092] % own weight matrix wMat= [ 3.3 0 0 0 0 ;

[0093] 1 0 2.2 -1.8 -1;

[0094] 0 1.8 0 -1.2 0;

[0095] 0 1 1 0 0;

[0096] 0 0 0 0 0] ; yAg= [0.2, 0.1, 0, 0, 0 ] ; yAn= [0.2, 0., 0, 0.2, 0 ] ;

[0097] % Collect Populatios to the net

[0098] [net Agon] =addPO (net , ptau, 'wMatrix', wMat, ' inityl ' , yAg) ;

[0099] [net Antagon] =addPO (net , ptau, 'wMatrix', wMat, 'inityl', yAn) ; ilateral connections - Afferenzen net = connectPO (net ,

[0100] ' src ' , Agon . node { 3} , ' dest ' , Antagon . node { 4} , ' weight ',0.9) ; net = connectPO (net ,

[0101] ' src ' , Antagon . node { 3} , ' dest ' , Agon . node { 4} , ' weight ',0.9) ;

[0102] % create stimuli dt=0.1; % stepwidth of the integrator tspan=1000; % total time span stimStart=100; tStim=tspan-stimStart ; S l=ones ( 1 , 1 / dt ) ; % Dirac Impuls (with 1 ms length) S2=ones ( 1 , tStim / dt ) * 0 . ; % rectangle S4=ones ( 1 , tStim / dt ) * 0 . ; % rectangle figure ( 1 ) ; elf ; while S2<0 . 99 net . cntStimulus=O ; net = addStimulus (net , Agon . node { 5} , S2 , 0 ) ; net = addStimulus (net , Antagon . node { 5} , S2 , 0 ) ; % start simulation R = runModel (net , dt , tspan, ' solver ' , ' S2 ' , ' sigm' , @ s 1 m2 ) ; hold on; x=R . PO ( l ) . yl ( 3 , : ) ; y=R . t ; z=ones ( 1 , length ( plot3 ( y, z , x, ' b ' ) x=R . PO ( 2 ) . yl ( 3 , : y=R . t ; z=ones ( 1 , length ( plot3 ( y, z , x, ' r ' ) S2=S2+ 0 . 01 ; end;

[0103] As long as the agonist in Population 3 is active, it inhibits the entire antagonist muscle group via the lateral connection to Population 4. Once the active period is over and the agonist is sufficiently inhibited, the antagonist gains the upper hand and becomes active. The agonist is then inhibited via the lateral connection to Population 4. The duration of the pulse is controlled independently for each group via stimulus Sti and stimulus St2. The result of the simulation in the form of the generated output signals is shown in Fig. 9. Blue lines are the output of the agonist to Population 3, red lines are the output of the antagonist to Population 3. A stimulus was applied to Population 4 of both groups, which varied from 0 to 1. The frequency increases as the stimulus increases. While one of the two groups is active, the contralateral group is inhibited. The two populations were plotted on top of each other.

[0104] To intervene externally in the behavior of activity and rest, the afferent signals of a group must be taken into account. It would be particularly important to recognize when a movement, e.g., in a gait pattern, has ended by sending an afferent signal to the respective CPG upon contact with the ground [Prochazka, A., Gosgnach, S., Capaday, C., & Geyer, H. (2017). Neuromuscular models for locomotion. In Bioinspired Legged Locomotion (pp. 401-453). Butterworth-

[0105] REVISED SHEET (RULE 91) ISA / EP Heinemann.; Morand, EM, Zitzewitz, J., Miehlbradt, J., Wurth, S., Formento, E., DiGiovanna, J., ... & Micera, S. (2018). Closed-loop control of trunk posture improves locomotion through the regulation of leg proprioceptive feedback after spinal cord injury. Scientific reports, 8(1), 76.]. This would have to cause additional inhibition of the CPG and terminate the activity prematurely.

[0106] In the fourth embodiment, the model (see Fig. 10) was extended so that each population receives a corresponding glial system (yellow crescent). Due to the modeled self-excitation of population 1, the model can previously excite itself (without a glial system) to a certain maximum without the intervention of an external stimulus. The connectivity between the populations is dynamic due to the glial system. The pattern generator is self-excited; a stimulus to population 5 allows it to be controlled. The corresponding program code for a corresponding simulation is, for example:

[0107] % struct net net=createModel ( ) ;

[0108] % necessary time constants for models 1 and 2. ptau=[20, 10, 3, 30, 30] ; % for model S2 alpha =[0.001 0.001 0.001 0.001 0.0001] ; beta =[0.03 0.03 0.02 0.03 0.03] ;

[0109] % own weight matrix wMat= [ 0.9 0 0 0 0; % pl

[0110] 1 0 2.5 -1.7 -0.8; % P2 0 1.8 0 -1.2 -0.; % P3 0 1 1 0 0 % P4 0 0 0 0 0] ; % P5 y= [ 0.7 , 0.7, 0.3, 0.01, 0.3] ;

[0111] [net, P] =addPO (net , ptau, 'wMatrix', wMat, 'Alpha ' , alpha, 'Beta', beta, ' inityl ' , y) ;

[0112] % create stimulate dt=0.05; % stepwidth of the integrator tspan=3000; % total time span

[0113] S4=ones ( 1 , 50 / dt ) * 3 ; % rectangle net = addStimulus (net, P.node{l}, S4, 10) ;

[0114] % start simulation

[0115] R = runModel(net, dt, tspan, 'solver', 'S2', ' si gm ', @sigm2Ca); Fig. 11 shows that the system is still controllable. To do this, we will again apply a stimulus to Population 5 and vary its amplitude. Fig. 11 shows the output signal of Population 3 in more detail – the stimulus to Population 5 was varied from 0.01 to 0.9.

[0116] As expected, the pattern generator behaves similarly to before. However, the sigmoidal transfer function is no longer visible in the waterfall diagram. A linear control range is given for a stimulus from 0.1 to approximately 0.6.

[0117] This disclosure contains portions of the dissertation "Modeling the lumbar spinal cord to explain functional deviations in the movement pattern in paraplegic patients" by Manfred Anzinger-Weitmann, Vienna University of Technology, which will be published on the date of filing this application. The portions necessary for understanding and comprehending the invention have been reproduced here. Should additional portions be useful for this application, they are to be considered part of this disclosure by reference and incorporated as needed.

Claims

Claims:

1. A method for simulating physiological neuronal signals originating from the lumbar spinal cord, in particular transmitted to motor neurons, wherein a simulation model comprises a plurality of populations of neurons connected to one another in an excitatory or inhibitory manner, characterized in that, during the simulation, a stimulus signal is redirected via a first population of interneurons, the first population having no input value dependent on other populations.

2. Method according to claim i, characterized in that the first population has an inhibitory effect on a second population of neurons, the second population belonging to a central pattern generator to which at least a third population of neurons in the simulation model belongs.

3. Method according to claim 2, characterized in that the second population has an excitatory effect on the third population and the third population, conversely, has an inhibitory effect on the second population with a delay.

4. Method according to claim 3, characterized in that the delay is defined by a time constant (T), wherein the time constant (T) is between 0.1 and 30 milliseconds, in particular between 0.1 and 20 milliseconds.

5. Method according to one of claims 2 to 4, characterized in that the populations belonging to the central pattern generator are selected so that they are predominantly excitatory.

6. Method according to one of claims 2 to 5, characterized in that at least a fourth population of neurons in the simulation model belongs to the central pattern generator, wherein preferably the fourth population has a mutually exciting effect on the second population and the fourth population has an exciting effect on the third population and conversely is inhibited by the third population with a delay.

7. The method according to claim 6, characterized in that the central pattern generator includes at least a fifth population of neurons in the simulation model, the fifth population being a self-exciting population, the fifth population preferably having an excitatory effect on the second population.

8. The method according to claim 6 or 7, characterized in that a simulated physiological neuronal signal is formed by an output value of the central pattern generator, wherein this output value is preferably compared with a measured physiological neuronal signal in order to adapt the simulation model.

9. The method according to claim 8, characterized in that the central pattern generator includes at least a sixth population of neurons in the simulation model, the sixth population being excited by the fourth population and an output value of the sixth population being used as the output value of the central pattern generator.

10. The method according to claim 9, characterized in that the central pattern generator includes at least a seventh population of neurons simulation model, wherein the seventh population has an inhibitory effect on the sixth population.

11. Method according to one of claims 2 to 10, characterized in that the interaction between the populations is influenced by moderation parameters, wherein each population is assigned a moderation parameter, wherein the moderation parameters in turn follow a temporal development which is dependent on the excitation of the respective population.

12. A method for determining an electrical signal for treating a neurological dysfunction of a patient, wherein a method for simulating physiological neuronal signals according to one of claims 1 to 11 is used, wherein, based on measured physiological neuronal signals of the patient, a simulation model is adapted to replicate these physiological neuronal signals, wherein an external electrical signal is simulated using the adapted simulation model and the parameters of the electrical signal are adapted such that the replicated physiological neuronal signals are approximated to a signal curve without dysfunction.

13. The method according to claim 12, characterized in that the method is used to determine an electrical signal for treating a neurological dysfunction of a patient in the area of ​​the musculoskeletal system, in particular in the area of ​​the lumbar spinal cord. 14- A data processing system comprising means for carrying out the method according to any one of claims 1 to 13.

15. A computer program product comprising instructions which, when executed by a computer, cause the computer to carry out the method according to any one of claims 1 to 13.

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