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WO2018222871A1 - Methods for creating and delivering neuromodulatory stimulation - Google Patents

Methods for creating and delivering neuromodulatory stimulation Download PDF

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WO2018222871A1
WO2018222871A1 PCT/US2018/035393 US2018035393W WO2018222871A1 WO 2018222871 A1 WO2018222871 A1 WO 2018222871A1 US 2018035393 W US2018035393 W US 2018035393W WO 2018222871 A1 WO2018222871 A1 WO 2018222871A1
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nerve stimulation
patient
stimulation signal
sequence
symbols
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Erika PETERSEN
Karl Petersen
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BioVentures LLC
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    • AHUMAN NECESSITIES
    • A61MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61BDIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B5/00Measuring for diagnostic purposes; Identification of persons
    • A61B5/48Other medical applications
    • A61B5/4836Diagnosis combined with treatment in closed-loop systems or methods
    • AHUMAN NECESSITIES
    • A61MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61BDIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B5/00Measuring for diagnostic purposes; Identification of persons
    • A61B5/02Detecting, measuring or recording for evaluating the cardiovascular system, e.g. pulse, heart rate, blood pressure or blood flow
    • A61B5/0205Simultaneously evaluating both cardiovascular conditions and different types of body conditions, e.g. heart and respiratory condition
    • A61B5/02055Simultaneously evaluating both cardiovascular condition and temperature
    • AHUMAN NECESSITIES
    • A61MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61NELECTROTHERAPY; MAGNETOTHERAPY; RADIATION THERAPY; ULTRASOUND THERAPY
    • A61N1/00Electrotherapy; Circuits therefor
    • A61N1/18Applying electric currents by contact electrodes
    • A61N1/32Applying electric currents by contact electrodes alternating or intermittent currents
    • A61N1/36Applying electric currents by contact electrodes alternating or intermittent currents for stimulation
    • A61N1/3605Implantable neurostimulators for stimulating central or peripheral nerve system
    • A61N1/36128Control systems
    • A61N1/36146Control systems specified by the stimulation parameters
    • A61N1/36167Timing, e.g. stimulation onset
    • A61N1/36178Burst or pulse train parameters
    • AHUMAN NECESSITIES
    • A61MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61BDIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B5/00Measuring for diagnostic purposes; Identification of persons
    • A61B5/02Detecting, measuring or recording for evaluating the cardiovascular system, e.g. pulse, heart rate, blood pressure or blood flow
    • A61B5/021Measuring pressure in heart or blood vessels
    • AHUMAN NECESSITIES
    • A61MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61BDIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B5/00Measuring for diagnostic purposes; Identification of persons
    • A61B5/02Detecting, measuring or recording for evaluating the cardiovascular system, e.g. pulse, heart rate, blood pressure or blood flow
    • A61B5/024Measuring pulse rate or heart rate
    • AHUMAN NECESSITIES
    • A61MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61BDIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B5/00Measuring for diagnostic purposes; Identification of persons
    • A61B5/103Measuring devices for testing the shape, pattern, colour, size or movement of the body or parts thereof, for diagnostic purposes
    • A61B5/11Measuring movement of the entire body or parts thereof, e.g. head or hand tremor or mobility of a limb
    • A61B5/1101Detecting tremor
    • AHUMAN NECESSITIES
    • A61MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61BDIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B5/00Measuring for diagnostic purposes; Identification of persons
    • A61B5/103Measuring devices for testing the shape, pattern, colour, size or movement of the body or parts thereof, for diagnostic purposes
    • A61B5/11Measuring movement of the entire body or parts thereof, e.g. head or hand tremor or mobility of a limb
    • A61B5/112Gait analysis
    • AHUMAN NECESSITIES
    • A61MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61BDIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B5/00Measuring for diagnostic purposes; Identification of persons
    • A61B5/24Detecting, measuring or recording bioelectric or biomagnetic signals of the body or parts thereof
    • A61B5/316Modalities, i.e. specific diagnostic methods
    • A61B5/369Electroencephalography [EEG]
    • AHUMAN NECESSITIES
    • A61MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61BDIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B5/00Measuring for diagnostic purposes; Identification of persons
    • A61B5/40Detecting, measuring or recording for evaluating the nervous system
    • A61B5/4005Detecting, measuring or recording for evaluating the nervous system for evaluating the sensory system
    • A61B5/4023Evaluating sense of balance

Definitions

  • the stimulation to a patient may be changed using an iterative method that takes neurophysiological recordings and patient activity or other biometric data into account.
  • the iterative method may be used to modify the stimulation delivered to the patient.
  • the method may use conventional neurostimulators that provide fixed rate trains of either monophasic or biphasic electrical pulses of a fixed amplitude to stimulate neural tissue using constant pulse-to-pulse or burst-to-burst intervals.

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  • General Health & Medical Sciences (AREA)
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  • Medical Informatics (AREA)
  • Heart & Thoracic Surgery (AREA)
  • Pathology (AREA)
  • Physiology (AREA)
  • Physics & Mathematics (AREA)
  • Nuclear Medicine, Radiotherapy & Molecular Imaging (AREA)
  • Radiology & Medical Imaging (AREA)
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  • Electrotherapy Devices (AREA)

Abstract

Methods for providing variation in nerve stimulation and methods for delivering patient-specific nerve stimulation to a patient are disclosed. The method of creating variation in nerve stimulation may include generating a sequence of a plurality of symbols; and generating a nerve stimulation signal represented by the sequence of symbols. In an aspect, the generated nerve stimulation signal is uniformly recurrent and non-periodic.

Description

METHODS FOR CREATING AND DELIVERING NEUROMODULATORY
STIMULATION
CROSS REFERENCE TO RELATED APPLICATION
[0001 ] This application claims benefit to U.S. Provisional Patent Application No. 62/513,787, filed on June 1 , 2017, which is herein incorporated by reference in its entirety.
FIELD OF THE INVENTION
[0002] The disclosure is directed to methods for creating variation in a nerve stimulation signal. In particular, this disclosure is directed to delivering patient-specific nerve stimulation to a patient using variation in a nerve stimulation signal.
BACKGROUND OF THE INVENTION
[0003] Neuromodulation involves influencing the signals in the nervous system through the application of an external stimulus, for example, with the delivery of an electrical pulse through a stimulator device. A pulse generator delivers a signal of a certain pattern through an electrode that is implanted at a neural target. Variations include the use of a wireless generator to deliver the impulse through an RF coupling antenna or the use of direct magnetic or direct current stimulation through an external device.
[0004] In existing neurostimulation paradigms, the pattern of pulses delivered is repetitive and does not always harmonize with neurophysiology. Numerous neurophysiological outputs have been recorded, including local field potentials (LFPs), basal ganglia neuronal firing activity (through microelectrode recordings), and cortical brain activity (through electrocorticography and EEG). Analysis of these waves shows that there is both natural variation and some predictability. Using the output of the nervous system from nerve, brain, or spinal cord recordings may shape the type of stimulation delivered. [0005] Input signals for neural stimulation may be white or other noise or perhaps periodic signals. However, periodic signals may be ineffective, boring, or possibly even detrimental to an organism, and pure noise can be ineffective.
Furthermore, FDA-approved waveforms currently available in stimulation devices are rudimentary and lack sophistication, while investigational waves are simplistic or random.
[0006] A need exists in the art for methods for altering all the variables of the stimulation delivered to the target: amplitude, pulse number and width, and frequency in a predictable yet non-repeating manner that can be influenced by numerous inputs in order to optimize stimulation efficacy.
DESCRIPTION OF THE FIGURES
[0007] The following figures illustrate various aspects of the disclosure.
[0008] FIG. 1 is a flow diagram of an iterative method for modifying nerve stimulation delivered to a patient in one aspect.
[0009] FIG. 2 is a flow diagram of a mathematically based method for modifying nerve stimulation delivered to a patient in one aspect.
[0010] FIG. 3A illustrates sample input signals.
[001 1 ] FIG. 3B illustrates examples of generated nerve stimulation signals.
[0012] While multiple embodiments are disclosed, still other embodiments of the present disclosure will become apparent to those skilled in the art from the following detailed description, which shows and describes illustrative embodiments of the disclosure. As will be realized, the disclosure is capable of modifications in various aspects, all without departing from the spirit and scope of the present disclosure.
Accordingly, the drawings and detailed description are to be regarded as illustrative in nature and not restrictive.
DETAILED DESCRIPTION
[0013] This disclosure describes signals and a method for creating new waveforms that may be delivered using a neurostimulation device and further details a process for selecting optimal stimulation patterns that are customized to the individual patient. The method provides a highly individualizable means of delivering stimulation that can be tailored to a patient's own clinical condition using both external and internal inputs. Variation in stimulation will likely harmonize with the patient's intrinsic
neurophysiological patterns to deliver better tolerated and more effect stimulation.
[0014] Applications for the method of neurostimulation include deep brain stimulation (DBS), motorcortex stimulation (MCS), responsive neurostimulation (RNS), vagal nerve stimulation (VNS), spinal cord stimulation (SCS), dorsal root ganglion stimulation (DRG), peripheral nerve stimulation (PNS), peripheral nerve field stimulation (PNfS), transcranial direct current stimulation, and transcranial magnetic stimulation. In various aspects, the method may be used for the stimulation of any nerve or neural tissue in the body. In other aspects, the method may be used for the stimulation of other areas of the body, including but not limited to neuromuscular stimulation, muscle stimulation, cardiovascular pacing, gastrointestinal stimulation, and autonomic nervous stimulation. The method may also be used to modify the delivery of therapeutic ultrasonic waves, or may be delivered wirelessly or in conjunction with TMS or TDCS, ultrasound, or functional electrical stimulation.
[0015] In neurostimulation, an electrical signal pulse is shaped by the following parameters: pulse width, frequency, and amplitude. Delivery of the pulse into the neural tissue can be affected by which electrode contacts are activated and their polarity. The majority of today's devices deliver a continuous pulse using a simple rule, referred to as "conventional stimulation" or "tonic stimulation." Generally this ranges from frequencies between 20 and 1200 Hz and pulse widths between 30 and 300 microseconds. Amplitude is adjusted to achieve a beneficial effect while producing limited to no side effects, as revealed through examining the patient receiving
stimulation. High frequency neurostimulation, delivered at 30 microseconds pulse width and frequency of 10,000 Hz operates through the same delivery mechanism. "Burst" stimulation alternates higher and lower frequency stimulation waves in a predictable pattern.
[0016] Responsive neurostimulation involves observing the neural patterns through a sensor electrode and then deploying a neurostimulation signal in response to the observed pattern. Another mechanism senses motion and other physically observable body signs in order to adjust stimulation. Finally, detection of
neurotransmitter levels or other substances can be used to modify stimulator outputs.
[0017] The method for delivering stimulation may include signals that, while not periodic, still have long- range order. In various aspects, the order may be
manifested by recurrence properties, in which every segment of the signal is
guaranteed to occur within a fixed time interval (of length determined by the segment); or by hierarchical or self-similarity properties, in which recoding of the signal at larger scales reproduce the signal; or by low or zero entropy, which means that what occurs next in the signal is determined or influenced by what came before. Signals with any of these properties may be thought of as 1 -dimensional quasicrystals.
I. METHOD FOR DELIVERING THE OPTIMAL PATIENT-SPECIFIC STIMULATION
[0018] In an aspect, the stimulation to a patient may be changed using an iterative method that takes neurophysiological recordings and patient activity or other biometric data into account. The iterative method may be used to modify the stimulation delivered to the patient. The method may use conventional neurostimulators that provide fixed rate trains of either monophasic or biphasic electrical pulses of a fixed amplitude to stimulate neural tissue using constant pulse-to-pulse or burst-to-burst intervals.
[0019] FIG. 1 illustrates the iterative method in one aspect. In this method, an initial waveform may be delivered to the patient, feedback or responses from the patient may be gathered, and then the algorithm may be applied to the patient. Then, changes in some or all of the variables may be made and a modified waveform may be delivered to the patient. Feedback and responses may be again gathered in response to the modified waveform and then the algorithm may then be applied again. This cyclical method of modifying the waveform may be repeated as many times as needed. Non- limiting examples of variables that may be affected by algorithm outputs include voltage, current amplitude, pulse width, rate (pulses per second), duration, burst frequency, and number of pulses per burst. The frequency may range from about 20 Hz to about 10,000 HZ. In some aspects the frequency may be about 20 Hz to about 100 Hz, about 50 Hz to about 150 Hz, 100 Hz to about 500 Hz, 300 Hz to about 1000 Hz, 500 Hz to about 1500 Hz, 1000 Hz, to about 5000 Hz, 3000 Hz to about 8000 Hz, or about 5000 Hz to about 10,000 Hz. The pulse width may range from about 30 s to about 50 s, about 40 s to about 70 s, about 50 s to about 100 s, about 75 s to about 150 s, or about 150 s to about 300 s. In an aspect, any parameter of the algorithm may be changed based on the output from the algorithm. Non-limiting examples of the feedback or responses gathered after the delivery of the initial or modified waveform include subjective perception of symptoms, objective assessment of symptoms by a clinician, or biometrics. The biometrics may include, but is not limited to cardiovascular changes, blood pressure, heart rate, mobility, balance, gait, tremor, temperature, neurotransmitter levels, body chemistry changes, and neurophysiologic signals (i.e., EEG, LFPs,
CMAPs, etc.). In another aspect, the method may include the ability to change the stimulation with an external programmer.
[0020] FIG. 2 illustrates a method for modifying the stimulation delivered to a patient using a mathematical application. For example, neural signals from the patient may first be sent to a signal analyzer. The properties of the waves received by the signal analyzer may be examined by software, for example Matlab's Signal Processing modules. In an aspect, after the doctor or technicians have examined the signal and studied its properties, they may select input signals from a previously generated set to modify and combine in a mixer. In another aspect, the selection of input signals may be automated. In yet another aspect, the selection of input signals may also incorporate other inputs including physiological measurements from other sensors. The signals produced by the mixer may then be analyzed by the software and modifications to the signals may be made, if desired. In an aspect, a plan may be produced for applying the signals. Non-limiting examples of plans may include a single signal, several signals in a sequence, rotating several signals according to a scheme which could be periodic, almost periodic, or random. The patient's neural signals may be monitored throughout the entire process.
[0021 ] In an aspect, the software or signal processing module may provide, autocorrelation, power spectrum, mean frequency, RMS amplitude, periodicities, and/or hierarchical structure. In another aspect, the input signals may be, but are not limited to being constant, periodic, substitution, Toeplitz, or random. In an aspect, the mixer may adjust or combine input sequences, pulse width, amplitude, frequencies, and/or smoothness.
II. APPLICATION OF MATHEMATICAL MODELING TO INCREASE VARIATION IN STIMULATION DELIVERED
[0022] Variation in delivered stimulation was previously done by brute force testing of combinations using computational modeling. The method of increasing variation in a delivered stimulation may include using possible inputs for neural stimulation being represented by symbol strings on a finite alphabet that have some long-range order or hierarchical structure while not being periodic. In the opposite direction, measured neurological outputs may be measured for their recurrence properties or any possible hierarchical structure, as well as entropy, power spectrum, etc.
[0023] In an aspect, the stimulation signals signals may be based on sequences of symbols from a finite alphabet of symbols. Non-limiting examples of sequences of symbols include 0 and 1 , A, C ,G, T, or other symbols. In an aspect, each symbol may specify the amplitude of a square wave maintained for a unit time duration. Alternatively, each symbol may be read as an instruction to use as an input from a signal generator labeled by that symbol. These signal generators may have random or periodic properties, so the combined system would provide for mixing periodic, recurrent non-periodic, and random aspects. For example, a very long signal generated using symbols may repeat periodically. Without being limited to a particular theory, the body's memory is likely limited and therefore may not remember a repeated, long signal.
Therefore, it may be easier to generate a long signal and repeat it periodically or with some variations rather than generating one enormously long signal. In other aspects, the method may include looking for recurrent and hierarchical structure.
[0024] FIG. 3A provides sample input signals, which may be represented by a symbol, for generating new stimulation waves using a mathematically-derived
sequence. Non-limiting examples of input signals include square waves, pulsed signals, variable amplitude signals, and variable frequency of pulses. FIG. 3B illustrates examples of generated nerve stimulation signals. Non-limiting examples include variable frequencies within pulses, pulses applied almost periodically, varied pulse durations, or pulses applied at random.
[0025] The sequences generated may be uniformly recurrent and not periodic. The sequences may be generated using a Fibonacci sequence, "Multinacci" sequences, a Rudin-Shapiro sequence, a Chacon substitution, a Prouhet-Thue-Morse sequence, a Toeplitz sequence or a period-doubling sequence, substitutive sequences, positive entropy Toeplitz sequences, or any other mathematical sequence capable of generating a uniformly recurrent, non-periodic sequence.
EXAMPLES
Example 1: Non-repeating predictable math for generating stimulation settings
[0026] 'A' may denote an alphabet of symbols. For example, A = {0, 1 }, or {0, 1 , , d— 1 }, or {a, b, c, ...}. A* denotes the set of finite-length blocks (also called words or strings) on the alphabet A. Thus if A consists of the two symbols 0 and 1 , then A* consists of the empty block e together with the blocks 0, 1 , 00, 01 , 10, 1 1 , 000, .... A sequence refers to an infinite sequence x = x1x2 ... on the alphabet A, i.e. each j is a symbol from A. Indexing may also start at 0 or any other integer.)
[0027] A sequence x as above is called uniformly recurrent if each block B = x/cx/c+1. . . x/c+i_1that appears in x appears in x with bounded gap which means that there is a positive integer K (which may depend on B) such that every block C that appears in x of length K contains an appearance of B. More formally, given a block B = xkxk+1. . . Xk+i-i that appears in x (having a length I), there is a positive integer M such that if C = XiXi+ 1. . . x;+M-i f°r some i, then there is a j between 0 and i + M— I such that xj x j+ x . . . Xj+ l_x = B. Every periodic sequence is uniformly recurrent. In an aspect, uniformly recurrent sequences may be constructed which are not periodic.
[0028] The topological entropy htop of a sequence x is the exponential growth rate of the number of sub-blocks of x. More precisely, for each n let Nn denote the number of blocks of length n (strings of length n consisiting of consecutive symbols in x) seen in x. Then
(1 ) fttop(*) = limn→oe l2^ [0029] A substitution is a function or map Θ ·. A→ A* , i.e., a procedure or rule for replacing each symbol of the alphabet by a block of symbols from that alphabet. When a substitution is iterated by applying it simultaneously to every symbol in the block so far arrived at, longer and longer blocks may be built up (except in trivial cases), and in the limit, infinite sequences are reached. If the substitution assigns to some symbol in A a block that starts with that symbol, say 0(a) = acd for example, then starting with a and iterating eventually provides an infinite sequence which is fixed by Θ . Fixed points of substitutions, and related sequences, including the sequences in their orbit closures under the shift transformation and their images under factor maps (sliding block codes), are the main presenters of hierarchical structure.
[0030] A dynamical system consists of a set X and a map T · X→ X (or a family of maps). A point x in X represents the state of the system at time 0, and then Tx gives the state of the system at time 1 , T2x = T Tx) gives the state at time 2, etc. A partition of X is a family of pairwise disjoint (i.e. non-overlapping) sets P = {PQ, . . . , Pd--1} whose union is all of X. The orbit of x consists of all the points x, Tx, T2x, . .. The coding of the orbit of x by the alphabet A = {0, 1, . .. , d - 1} is the sequence u = ΐί0ΐίχ . .. defined by ui = k if Tlx is in Pk. Dynamical systems with good properties can give rise to interesting sequences when orbits are coded according to partitions in this way.
Example 2: The Fibonacci sequence
[0031 ] This is the fixed point φ of the substitution 0→ 01, 1→ 0, starting with the symbol 0. The first few steps in the process of building up this sequence are as follows:
0
01
(2) 01 0
01 0 01
01 0 01 01 0
[0032] The resulting sequence is uniformly recurrent and not periodic. It has a hierarchical or self-similar structure: for example, if each block 01 in the infinite sequence is replaced by 0 and the 0s that are not part of a block 01 are replaced by 1 , the sequence reappears. Similarly with longer blocks cn = θη0 or dn = θη1 that are images of 0 and 1 under a fixed number n of applications of the substitution: for each n, the sequence 0 resolves into a concatenation of these blocks cn and dn .
[0033] The sequence φ is also the coding of the orbit of 0 under the map of the unit interval X = [0,1] = {t = 0 < t≤ 1} that takes t to t + a mod 1 , where a is the solution of a + a2 = 1 (the reciprocal of the golden mean) and "mod 1 " means fractional part. This means that the sequence 0 is Sturmian and thus has minimal complexity among all nonperiodic sequences: for every n, the number of different blocks of length n that exist in the sequence φ is n + 1.
[0034] Because φ is the coding of the orbit of 0 under translation mod 1 by the reciprocal of the golden mean, its dynamical system has purely discrete spectrum: the eigenvalues are the integer multiples of a (more precisely exp(2nika), k any integer), and the corresponding eigenfunctions span the entire Hilbert space of observable square-integrable functions.
Example 3: "Multinacci" sequences
[0035] These are fixed points of substitutions such as
(3) 0→ 01, 1→ 02, 2→ 0
[0036] The "Perron-Frobenious eigenvalue" λ is the root of x3 = x2 + x + 1. The corresponding dynamical system is isomorphic (by a coding with a partition) to translation by (1/Λ, l/λ2) on the 2-torus (doughnut) Μ.22, and therefore has a purely discrete spectrum. The first few steps in generating the sequence are as follows:
0
01
(4) 01 02
01 02 01 0
01 02 01 0 01 02 01
[0037] This sequence and associated dynamical system generalize to the substitution
(5) 0→ 01, 1→ 02, .. . , n - 1→ 0n, n→ 1. Example 4: The Rudin-Shapiro sequence
[0038] This is the fixed point u starting with 0 of the substitution
(6) 0→ 01, 1→ 02, 2→ 31, 3→ 32.
[0039] The first few steps in generating the sequence are as follows:
0
01
(7) 01 02
01 02 0131
01 02 0131 0101 3202
[0040] This sequence also has low complexity: for every n there are 8n— 8 blocks of length n in the sequence. Replacing a and b by 1 , and c and d by— 1 (a letter- to-letter factor map or sliding block code), produces the sequence r = Γ0Γχ . .. on the alphabet {1 ,— 1 } defined recursively by
[0041 ] r0 = 1, r2n = rn, r2n+1 = (-l)nrn, n > 0.
[0042] The sequences u and r define equivalent (topological^ conjugate, isomorphic) dynamical systems. The eigenvalues are the dyadic rationals k/2n, but there are observables with spectral measure equivalent to Lebesgue measure (the ordinary measure defined by length on the real line). The correlation measure is
Lebesgue.
Example 5: The Chacon substitution
[0043] This is the fixed point of the primitive substitution (eventually the image of each symbol under iterations of the substitution contains all symbols)
(9) 0→ 0012, 1→ 12, 2→ 012,
[0044] which is equivalent (producing a topological^ conjugate system, under the factor map which changes each 2 to a 0) to the fixed point v of the non-primitive substitution
(10) 0→0010, 1→1.
[0045] The sequence v also has very low complexity, containing only 2n— 1 blocks of each length n. The associated dynamical system is weakly mixing: there are no square integrable eigenfunctions except the constant functions. Thus, although the sequence is uniformly recurrent and has hierarchical structure, it is very nonperiodic, possessing a kind of disorder: there are no resonances. The spectral measure is singular with respect to Lebesgue measure: it assigns measure 0 to some set that has full Lebesgue measure 1 .
Example 6: The Prouhet-Thue-Morse sequence
[0046] This sequence p is the fixed point of the substitution
[0047] (1 1 ) 0→01, 1→ 10.
[0048] The first few steps in its construction are as follows:
0
01
(12) 01 10
01 10 10 01
01 10 10 01 10 01 01 10
[0049] The associated dynamical system has all dyadic rationals as eigenvalues, but it does not have purely discrete spectrum: the eigenfunctions do not span the entire space of observable square integrable functions.
Example 7: A simple Toeplitz sequence, also called the period-doubling sequence
[0050] This sequence is the fixed point of the substitution
[0051 ] (13) 0→ 11, 1→ 10, equivalent^ 0→ 01, 1→ 00.
[0052] The first few steps in its construction (in the second form) are as follows:
0
01
(14) 01 00
01 00 01 01
01 00 01 01 01 00 01 00
[0053] The sequence may also be constructed as follows. First write 0 at all even places 0, 2, 4, ... , leaving blanks at the odd places. Then fill in "half of the blanks by alternating 1 and "blank", starting at the first blank (in place 1 ). Then fill in "half of the remaining blanks by writing 0 at every other one, starting with the first blank. Continue, alternating filling in with 0 and 1 at alternating stages, and always leaving infinitely many blanks. Eventually the first blank appears very far to the right, so there is an arbitrarily long initial block of the desired sequence.
[0054] The associated dynamical system has purely discrete spectrum, with eigenvalues the dyadic rationals (2fc'th roots of unity for any k). In fact the system is isomorphic to the 2-odometer, also known as the von Neumann-Kakutani adding machine, which consists in adding 1 in base 2 notation.
Example 8: Substitutive sequences
[0055] A substitutive sequence is the image under a factor map (a sliding block code, e.g. a letter-to-letter recoding) of a sequence from a dynamical system associated to the fixed point of a substitution. In such sequences the hierarchical structure may be less apparent than in a fixed point of a substitution, but nevertheless it is present and can be detected alogorithmically.
Example 9: Positive entropy Toeplitz sequences
[0056] The construction of Toeplitz sequences using periodic structures and "blanks" or "holes" which eventually get filled in generalizes. All the examples discussed so far have zero entropy: thus the signals are somewhat predictable, although, being nonperiodic, in general a segment of finite length, however long, does not contain enough information to determine what the succeeding symbol will be; we would have to see the entire infinite past to be sure (with probability 1 ) of what will come next. It is possible to construct alogorithmically Toeplitz sequences which do have positive entropy— and retain uniform recurrence due to their structure of nested periodicities— but the constructions are more complicated than above. Here is a particular example.
[0057] Select sequences of integers q'm < qm, let sx = qlt s0 = l, sm+1 = qm+1sm for m≥ 1, and similarly for s'm. To be specific, using q'm = 2m(m+1)/2 and qm = q'm + 1, such that [0058] (15)
s'
lim— > 0,
m→∞ Sm
[0059] a necessary condition for the example to succeed.
[0060] For each m = 1 , 2, ... select a block of length tm = s'm^ such that (*) every finite block on the alphabet {0, 1 } appears as the initial block of some Bm. The lengths of the Bm are growing so fast that Bm can contain all 0, 1 blocks of length m— 1 as sub-blocks. These sub-blocks can be arranged in order within Bm to be sure that the condition (*) gets satisfied.
[0061 ] The nonnegative integers can be thought of as arrayed on a line, with a blank associated to each one. Divide this line into segments of length sx = qx = q + 1 = 3, called s-Hntervals. Fill in the first s^places in each s-Hnterval with the preselected block S-i , which has length s'Q = 1. This leaves s = 2 blanks per Si- period.
[0062] Now group q2 = 23 + 1 = 9 consecutive Si -intervals into an S2-interval. In each s2-interval there are 18 blanks in 9 "clusters" (si -intervals). Fill the first part of each of these clusters with the preselected block B2. This leaves q'2 · s = s'2 blanks per s2-period.
[0063] Continue this way: g3 consecutive s2-intervals group together to form an s3-interval with s'2c73 blanks. Fill in the first t3 = s'2 = 16 of these with S3, leaving s'2q'3 = s'3 blanks per s3-period.
[0064] The result is an "irregular" Toeplitz sequence with positive (topological) entropy. The associated system has uncountably many ergodic shift invariant Borel probability measure, many of which have positive measure-theoretic entropy. The sequence is uniformly recurrent and contains hierarchically arranged periodic
structures, although it is not itself periodic.
[0065] It should be understood from the foregoing that, while particular embodiments have been illustrated and described, various modifications can be made thereto without departing from the spirit and scope of the invention as will be apparent to those skilled in the art. Such changes and modifications are within the scope and teachings of this invention as defined in the claims appended hereto.

Claims

CLAIMS We claim the following:
1 . A method for creating variation in a nerve stimulation signal, comprising:
generating a sequence of a plurality of symbols; and
generating a nerve stimulation signal represented by the sequence of symbols,
wherein the generated nerve stimulation signal is uniformly recurrent and non-periodic.
2. The method of claim 1 , wherein the sequence of symbols comprises symbols from a finite alphabet of symbols.
3. The method of claim 2, wherein the symbols are selected from 0, 1 , A, C, G, T, and combinations thereof.
4. The method of claim 1 , wherein each symbol specifies waveform and amplitude, or any waveform that is maintained for a unit time duration, or other time duration, or varies continuously.
5. The method of claim 1 , wherein each symbol comprises an instruction to use an input signal from a signal generator labeled by that symbol.
6. The method of claim 5, wherein the signal generators comprise random, periodic, or nonperiodic properties.
7. The method of claim 5, wherein the input signal is selected from shape of waves, pulsed signals, variable amplitude signals, variable frequency of pulses, and combinations thereof.
8. The method of claim 1 further comprising repeating periodically or nonperiodically the generated sequence of symbols to generate the nerve stimulation signal.
9. A method for delivering patient-specific nerve stimulation to a patient in need
thereof, comprising:
generating a nerve stimulation signal;
adjusting at least one property of the nerve stimulation signal;
delivering the nerve stimulation signal to the patient; and
monitoring the patient,
wherein the generated nerve stimulation signal is uniformly recurrent and non-periodic.
10. The method of claim 9 further comprising adjusting the properties of the nerve
stimulation signal during or after delivery to the patient.
1 1 . The method of claim 9 further comprising analyzing the properties of the nerve
stimulation signal and the patient's response.
12. The method of claim 9 further comprising combining more than one input signals to generate the nerve stimulation signal.
13. The method of claim 12, wherein the combination of input signals is analyzed and modifications to the properties of the combined input signals are made if necessary.
14. The method of claim 9, wherein the adjusting, delivering, and monitoring steps are repeated iteratively.
15. The method of claim 9, wherein the properties of the nerve stimulation signal are selected from the group consisting of voltage, current amplitude, pulse width, rate, duration, burst frequency, waveform, and pulses/burst.
16. The method of claim 9, wherein monitoring the patient comprises subjective assessment of the patient, objective assessment of the patient, or combinations thereof.
17. The method of claim 16, wherein the objective assessment of the patent is selected from the group consisting of blood pressure, heart rate, temperature,
neurotransmitter levels, body chemistry changes, neurophysiologic signals, and combinations thereof.
17
RECTIFIED (RULE 91) - ISA/US
PCT/US2018/035393 2017-06-01 2018-05-31 Methods for creating and delivering neuromodulatory stimulation Ceased WO2018222871A1 (en)

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US20100114189A1 (en) * 2008-10-31 2010-05-06 Medtronic, Inc. Therapy module crosstalk mitigation
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