Patent Application
20170090857
The present invention relates to a method of processing signals representative of a biological information in order to allow their efficient medical use by clinicians.
More precisely, it relates to a method of compressing and displaying (i.e. presenting) data contained in signals recorded by sensors, said signals bearing information about biological features.
The signals may be for instance:
Today, more and more biological information can be recorded using sensors, such as:
The signals obtained from such sensors can help in the establishment of a diagnostic, or can be used for therapeutic monitoring.
However, the quantity of recorded signals is so important (for instance the production of protein-DNA data is of the order of one Gigabit per patient) that the data contained in said signals have to be modelled and compressed in order to allow their efficient medical use by clinicians.
It is known to use compression methods based on Fourier technic, or wavelet transforms in order to compress data contained in signals representative of biological information. These method gives good results concerning the compression rate.
However, such compression methods are not efficient for compressing recorded signal that are not periodic in time and/or in space.
Moreover, such compression methods bring no information about the interactions between elements of the living system producing the processed signal.
An object of the present invention is to propose a method for processing biological signals which overcomes at least one of the drawbacks of the aforementioned compression methods.
The present invention overcomes the drawbacks of previously-known methods by providing a method of processing a biological signal including peaks, said biological signal being recorded by at least one sensor, the method comprising:
The biological signal to be processed may be:
Preferred but non-limiting aspects of the device according to the invention are the following:
d
2
x/dt
2
−Q(x)dx/dt+R(x)x=0;
d
2
x/dt
2−μ(1−x2/b2)dx/dt+ω2x=0;
The invention also relates to a system of processing a biological signal of processing a biological signal including peaks, said biological signal being recorded by at least one sensor, the system comprising a processor configured to:
The invention also relates to a program for implementing in a computer a method of processing a biological signal including peaks, said biological signal being recorded by at least one sensor, the method comprising:
Other advantages and features will become better apparent from the following description given as non-limiting example, and from the appended drawings wherein:
The method and system according to the present invention will now be described in reference to the figures. In these different Figures, the equivalent elements bear the same reference numerals.
Referring to
After the reception (step 10) of the Original protein NMR spectroscopy signal recorded by NMR sensors, a peak is extracted (step 20) from the Original protein NMR spectroscopy signal.
The extracted peak is processed in order to model the peak as a solution to a differential equation. More particularly, the method comprises modelling (step 30) the extracted peak as a solution to a van der Pol differential equation.
Indeed, the extracted peak may be modelled mathematically by a second-order differential equation of the van der Pol type of the following type:
d
2
x/dt
2−μ(1−x2/b2)dx/dt+ω2x=0,
where b, ω and μ are three degrees of freedom of the van der Pol equation.
The expression “degree of Freedom” refers to a condition in which more than one possible solution can be reached to the second-order differential equation.
The modelling step consists in finding a van der Pol limit cycle that fits to the extracted peak of the Original protein NMR spectroscopy signal. This is done by achieving an iterative transformation approach that generates new potentials (known as Hamiltonians) from older potentials by incrementally removing degrees of freedom during each iteration.
The processing step allows obtaining a model of the extracted peak. This model is converted into a musical sound defined by:
Advantageously, musical sound obtained by converting the model of the peak is not harmonic, so that said musical sound has a variable pitch and a variable intensity during its beat. Each sound is thus representative of a respective protein, and bears information about said protein.
After having converted a plurality of modelled peaks into respective sounds, it is possible to generate a melody including said musical sounds (step 50) and presenting the result to a user.
The above disclosed method allows processing biological signals and synthesizing sounds in order to facilitate their use in a diagnostic process.
The most immediate application is the sound quality ECG type of physiological signals, EEG and pulse and the spectrograms (mass or NMR) of proteins and/or nucleic acids.
In the preceding description, the method was described in reference of the van der Pol equation. The skilled person will understand that the above method is not limited to the resolution of a Van der Pol equation, and that other type of Liénard systems can be used for the modelling step 30, such as the FitzHugh-Nagumo equation.
The method described above may be applied in a processing system comprising a processing unit for executing the different steps of the method.
The processing unit is for example a computer(s), a processor(s), a microcontroller(s), a microcomputer(s), a programmable automaton(a), a specific application integrated circuit(s), other programmable circuits, or other devices which include a computer such as workstation.
The processing unit is coupled with a memory(ies) which may be integrated to or separated from the processing unit. The memory may be a ROM/RAM memory of the computer, a CD-ROM, a USB stick, a memory of a central server. This memory may allow the storage:
Referring to
When the computer 2 receives a biological signal 1, its processor extracts different peaks from the biological signal 1.
For each peak, the processor determines a peak model corresponding to a solution of a Liénard system, and converts said peak model into a respective musical sound. More particularly, each peak model is converted into a respective electrical audio signal.
A plurality of musical sounds representative of the different peaks are thus obtained. The plurality of musical sounds constitutes a melody 4 that is played on speakers 3 of the computer 2.
The melody 4 thus obtained can be heard by a user 5 in order to assist the user in the diagnosing of a pathology.
With the present annex, the method and system described above may be better understood. Certain notations used earlier may possibly differ in the following.
The goal of spectral density estimation is to estimate the spectral density of a random signal from a sequence of time samples of the signal. Intuitively speaking, the spectral density characterizes the frequency content of the signal.
Spectral density estimation is usually done using Fourier transform or wavelet transform. In the following, a new transform called “Dynalet” based on Liénard differential equations will be disclosed. Dyanlet transform allows modelling the mechanism that is the source of the signal.
In Sections 2, the classical Fourier and wavelet transforms will be described. Then in Section 3, the prototype of the Lienard equations that is the van der Pol equation will be described. In Section 4, the Dynalet transform will be defined, and in Sections 5 to 8, different biological applications using the Dynalet Transform will be discussed.
The Fourier transform comes from the aim by Fourier to represent in a simple way functions used in physics, notably in the heat propagation modelling.
He used a base of functions made of the solutions of the simple not damped pendulum differential equation (cf. a trajectory in
dx/dt=y, dy/dt=−ω
2
x,
whose general solution is:
x(t)=k cos ωt, y(t)=−kω sin ωt.
By using the polar coordinates θ and ρ defined from the variables x and z=y/ω, we get the new differential system:
dθ/dt=ω, dρ/dt=0,
with θ=Arctg(z/x) and ρ2=x2+z2.
The polar system is conservative, its Hamiltonian function being defined by:
H(θ,ρ)=ωρ
The general solution x(t)=k cos ωt, z(t)=k sin ωt has two degrees of freedom, k and ω, respectively the amplitude and the frequency of the signal, and constitutes an orthogonal base, by choosing for ω the multiples (called harmonics) of a fundamental frequency ω0.
Concerning the wavelet transform, Haley used in 1997 a simple wavelet transform for representing signals in astrophysics. He used a base of functions made of the solutions of the damped pendulum differential equation:
dx/dt=y, dy/dt=−(ω2+τ2)x−2τy,
whose general solution is:
x(t)=ke−
By using the polar coordinates θ and ρ defined from the variables x and z=−y/ω−τx/ω, we get the differential system:
dθ/dt=ω, dρ/dt=−τρ.
The polar system is dissipative (or gradient), its potential function being defined by:
P(θ,ρ)=−ωθ+τρ2/2.
The general solution x(t)=k e−
For the Dynalet transform, we propose to use a base of functions made of the solutions of the relaxation pendulum differential equation (van der Pol system), which is a particular example of the most general Liénard differential equation:
dx/dt=y, dy/dt=−R(x)x+Q(x)y,
which is specified in van der Pol case by choosing:
R(x)=ω2, and Q(x)=μ(1−x2/b2).
Its general solution is not algebraic, but can be approximated by a family of polynomials.
The van der Pol system is a potential-Hamiltonian system, defined by the potential PvdP and Hamiltonian HvdP functions, HvdP being for example approximated at order 4, when ω=b=1, by:
H
vdP(x,y)=(x2+y2)/2−μxy/2+μyx3/8−μxy3/8,
which allows to obtain the equation of its limit-cycle:
H
vdP(x,y)≈2.024.
The van der Pol system has three degrees of freedom, b, ω and μ, the last an-harmonic parameter being responsible of the asymptotic stability of pendulum limit-cycle, symmetrical with respect to the origin, but not revolution symmetrical. These parameters receive different interpretations:
The characteristic polynomial of J is equal to:
β2×μβ+ω2=0,
hence:
β=(μ±(μ2−4ω2)1/2)/2 and T≈2π/ω+πμ2/4ω3.
dχ/dt=ζ, dζ/dt=−ω
2χ+μ(1−χ2/μ2)ζ≈−ω2χ+μζ,
with the change of variables:
The Dynalet transform consists in identifying a Liénard system based on the interactions mechanisms between its variables (well expressed by its Jacobian matrix) analogue to those of the experimentally studied system, whose limit cycle is the nearest (in the sense of the Δ set or the mean quadratic distances between sets of van der Pol points and experimental points having the same phase, sampled respectively from the original signal and van der Pol limit cycle) to the signal in the phase plane (xOy), where y=dx/dt.
For example, the Jacobian interaction graph of the van der Pol system contains a couple of positive and negative tangent circuits.
Practically, for performing the Dynalet transform it is necessary to choose:
By repeating this process for the difference between the original signal and the van der Pol limit cycle, it is possible to get successively a polynomial approximation of the fundamental reconstructed signal and its harmonics.
The potential and Hamiltonian parts PvdP and HvdP used for this transform can be calculated using technics known from the skilled person. For example, for μ=1 (resp. μ=2), the corresponding polynomials are respectively P1 and H1 (P2 and H2) defined by:
P
1(x,y)=−3x2/4+y2/4+3x4/32+y4/96−x2y2/16 and H1(x,y)=(x2+y2)/2−3xy/2+3yx3/8−y3x/24−2
(resp. P2(x,y)=−3x2/4+y2/4+3x4/32+y4/96−x2y2/16 and H2(x,y)=(x2±y2)/2−3xy/8+3yx3/8−y3x/24−½).
Using this potential-Hamiltonian decomposition, it is possible to calculate an approximate solution S(ki,μi)(t) of the van der Pol differential system corresponding to the ith harmonics of the Dynalet transform, as a polynomial of order 2+i verifying:
dx/dt=y and dy/dt=−x+μi(1−ki2x2)y
We will search for example for the approximate solution x(t)=S(1,1)(t) as a polynomial of order 3 in the case μ=1:
x(t)=c0+c1t+c2t2+c3t3, y(t)=c1+2c2t+3c3t2
The polynomial coefficients ci's above represent both the potential and Hamiltonian parts of the van der Pol system and they can be obtained by identification with P1 and H1 derivatives:
dx/dt=−∂P
1
/∂x+∂H
1
/∂y, dy/dt=−∂P
1
/∂y−∂H
1
/∂x.
Then, we get:
c
0
2/2+c12/2−3c0c1/2+3c03c1/8−c0c13/24=2,
c
2
c
3−9c32/2−9c0c23+9c0c23/4+27c02c32/8−3c0c2c32/4−c24/24=0
c
2
c
3−27c23/2+9c32−3c2c32/2−c24/24=0,
which implies:
Because of the symmetry of the limit cycle, all the solutions {S(kj,μ/2j)}jεIN are orthogonal and we can decompose any continuous function f on this base, thanks to the Weierstrass theorem.
We propose to apply this new technique to real signals like ECG and pulse rhythm. In these both cases, the rhythmic cardiovascular activity results from the summation of cellular oscillators located in the cardiac sinus node, which are subject to the control of the bulbar cardiovascular moderator and cardio-accelerator centres, which modulate the sinus signal, integrating the influence of the inspiratory bulbar centre, which causes the appearance of harmonics in the cellular rhythm.
The Dynalet transform consists in identifying a Liénard system which expresses interactions between its variables through its Jacobian matrix analogue to those of the experimentally studied system, whose limit cycle is the nearest (in the sense of the distance Δ between sets, or of the mean quadratic distance between points of same phase) to the signal pattern in the phase plane (xOy), where y=dx/dt.
Practically, if the Liénard system is a van der Pol system, it is necessary to execute the following transforms for getting Dynalet approximation from original signal:
Then the whole approximation procedure done for the ECG signal involves the following steps:
Δ(ECG0,VDP0)=Area[(ECG0\VDP0)∪(VDP0\ECG0)],
H
vdP(x,y)=(x2+y2)/2−μxy/2+μyx3/8−μxy3/8=2.024
Let now compare the performance of the Dynalet reconstruction of the ECG signal with a Fourier transform having the same number of parameters, that is 5, i.e., the origin abscissa translation, two values of μ (period) and two abscissa scaling ratios for the fundamental and first harmonic of the Dynalet transform; the period, the origin abscissa translation and three values of sine coefficients for the Fourier transform F(x), whose equation is:
F(x)=0.42142 cos(2πx/176)+0.40773 sin(2πx/176)+0.34225−0.10539 cos(4πx/176).
For defining a quantitative assessment of the error between abscissæ of the K original signal observations Xi's (obtained after extraction of the baseline) and their Fourier or Dynalet approximations we use the notions of Mean Square Error (MSEX) and Signal to Noise Ratio (SNRX) where:
MSE
X=Σi=1,K(Xi−ξi)2/Σi=1,KXi2, SNRX=−10 Log10 MSEX
The calculation made for the QRS signal shows a good Dynalet fit for ordinates values:
In the Fourier reconstitution, QREX Fourier=0.08, SNRX Fourier=22 dB and QREX Dynalet=0.09, SNRX Dynalet=21 dB.
We can notice that this Fourier transform needs six parameters (including the value of the period), while the Dynalet transform requires only five parameters.
Biological rhythms other than the ECG or pulse can be interpreted and compressed using Liénard equations and the Dynalet transform, like the respiratory rhythm or the single cardiac cell activity, which represent a good example of relaxation wave, as well as pulse activity. In summary, the main advantages of the Dynalet transform on the Fourier transform in the case of periodic physiologic signals are:
In addition to the compression of periodic signals, another application of the Dynalet transform is compressing a non-periodic signal.
For example, the Dynalet transform can be used in order to approximate the spectrum of a protein. More generally, it is possible to apply the Dynalet transform to each peak of a protein NMR spectroscopy signal or of a protein mass spectrometry signal.
The identification of proteins by their spectrum allows for example the construction of complex genetic control networks, such as those found in the regulation of immune system, where key proteins are effectors of the genetic expression (activators or inhibitors) and may be subject to pathologic conditions, leading to up- or down-expressions. These regulatory interactions lead to abnormal protein or protein complexes concentrations in excess or in lack, and spectroscopy peaks indicating these pathologic defects can be treated by the Dynalet approach. Of course, other alternative techniques for estimating protein spectra already exist, like kernel functional estimation tools, but there are not related to the mechanism of production of the protein signal.
The Dynalet transform applied to protein data can be considered as a real protein “stethoscope”, which would give sense to numerous metabolic data, which, although very heavy in terms of information (about 5 Go per patient in a modern hospital), are in general not queried and used by clinicians (especially in emergency) and hence remain in the big patient centred data bases, often true cemeteries full of unused data.
In the beginning of the XIXth century, R. Laennec invented the modern stethoscope and described the thoracic sounds in the Traité de l'auscultation médiate (1819), converting into a synthetic functional information for the ear what physicians were previously describing at numerous anatomic and physiologic levels with their eyes, hence creating the modern medical diagnosis based on the auscultation.
We propose to follow the same methodology, by representing the spectral information from NMR and Mass spectroscopy into signals converted in sounds, expecting that this “protein melody”, whose peaks are well enhanced by the human ear at the cochlear level, serve to differentiate pathologies from the normality and remain in the memory of the clinicians (e.g., in the context of a rapid medical decision in an emergency service or of a discussion about a complex case in a cancer staff) as quantitatively correlated and semantically associated to precise metabolic diseases, in order to compensate:
Generalizing compression tools like Fourier or wavelets transforms is possible, if we consider that non symmetrical biological signals are often produced by relaxation mechanisms. In this case, we can propose for the dynamical systems modelling these biological signals Liénard type differential equations, like the van der Pol equation (or equivalent equation, such as the FitzHugh-Nagumo equation) classically used to model relaxation waves and, more generally, non-symmetrical biological relaxation systems often produced by mechanisms based on interactions of regulon type (i.e., possessing at least one couple of positive and negative tangent circuits inside their Jacobian interaction graph).
The corresponding new transform, called Dynalet transform, has been built in the same spirit as the wavelet transform (used for example for representing solutions of turbulent systems like Burger equation), the Hanusse transform, or the methodology proposed for estimating Tailored to the Problem Specificity Mathematical Transforms.
As for the Fourier and wavelet transforms, a fast estimation of the Lienard coefficients (calculable using potential-Hamiltonian decomposition techniques) is needed by the fast Dynalet transform and could be possible following the neural networks methodology.
Then, the Dynalet transform will be for example very useful for compressing in real-time the signals coming from e-health systems necessary to the fusion between actimetric and physiologic data recorded at home, with genetic and protein information coming in general from hospital records, in order to perform adequate personalized surveillance and trigger pertinent alarms without false alerts.
Those skilled in the art will understand that many modifications can be made to the device and method described above without materially departing from new ideas presented here.
It is therefore clear that the examples given above are only particular illustrations and in no way limiting.
As a consequence, all modifications of this type are intended to be incorporated inside the scope of the attached claims.
