DE102009005207A1 - Method for the determination of lipoprotein components in a lipoprotein mixture to be analyzed - Google Patents

Abstract

A method for the determination of lipoprotein components in a lipoprotein mixture to be analyzed comprises the steps: A method for the determination of lipoprotein components in a lipoprotein mixture to be analyzed, comprising the steps of: A) recording N> 1 measurement spectra of the lipoprotein mixture to be analyzed at N different measurement conditions, each of B) providing a mixed matrix W with N times L randomly chosen, nonnegative mixing parameters, a source spectrum matrix H with L source spectra each with M randomly chosen, nonnegative source spectral points and a measurement spectra matrix X, which is formed by the N measurement spectra, C) modifying the respective M source spectral points of the L source spectra by approximating the matrix product of the mixed matrix W and the source spectrum matrix H to the measurement spectra matrix X by means of a nonnegative matrix factorization under the boundary condition that the L source spectra D) assigning the L source spectra obtained from step C by the modification to known spectra of lipoprotein components.

Description

in the Following is a method for the determination of lipoprotein components a lipoprotein mixture and a data processing system thereto specified.

The Identification, description and quantitative recording of in of a blood plasma or serum sample containing lipoprotein subclasses or lipoprotein components is in the medical risk prevention of Cardiovascular diseases of considerable value. dimensional Nuclear magnetic resonance spectra ("nuclear magnetic resonance", NMR) of blood plasma or serum samples and in particular the signals however, lipoproteins often show considerable overlap the underlying component spectra of the individual spin groups or species (lipoprotein subclasses, lipoprotein components) and thus complicate identification, description and quantitative Capture of this species. But also the composition of single lipoprotein subclasses is one for atherosclerosis risk assessment Important Information. Known methods for the determination of lipoproteins However, they are unable to produce anomalous subclasses with high accuracy and taking into account patient-specific deviations and to identify and quantify variations.

The publication DE 10 2004 026 903 describes a method for the determination of lipoprotein subclasses by NMR spectroscopy.

At least It is an object of one embodiment to provide a method for the determination of lipoprotein components in an analyte Specify lipoprotein mixture. At least one more task is it, a data processing system to carry out at least indicate some steps in the procedure.

These Tasks are achieved by a method and apparatus according to the independent claims solved. Other embodiments and further embodiments go From the dependent claims, the figures and the description below.

• A) Aufnahme von N > 1 Messspektren des zu analysierenden Lipoproteingemischs bei N verschiedenen Messbedingungen, wobei jedes der N Messspektren jeweils M Messpunkte aufweist,
• B) Bereitstellen einer Mischmatrix W mit N mal L zufällig gewählten, nicht-negativen Mischparametern, einer Quellspektrenmatrix H mit L Quellspektren mit jeweils M zufällig gewählten, nicht-negativen Quellspektrumspunkten und einer Messspektrenmatrix X, die gebildet wird durch die N Messspektren,
• C) Modifizieren der jeweils M Quellspektrumspunkte der L Quellspektren durch Annäherung des Matrixprodukts der Mischmatrix W und der Quellspektrenmatrix H an die Messspektrenmatrix X mittels einer nicht-negativen Matrixfaktorisierung unter der Randbedingung, dass die L Quellspektren sparsam kodiert sind,
• D) Zuordnen der aus dem Schritt C durch die Modifizierung erhaltenen L Quellspektren zu bekannten Spektren von Lipoproteinkomponenten.

In accordance with at least one embodiment, a method for the determination of lipoprotein components in a lipoprotein mixture to be analyzed comprises in particular the following steps:
Method for the determination of lipoprotein components in a lipoprotein mixture to be analyzed, comprising the steps:

• A) recording N> 1 measurement spectra of the lipoprotein mixture to be analyzed at N different measurement conditions, each of the N measurement spectra having M measurement points in each case,
• B) providing a mixed matrix W with N times L randomly chosen, non-negative mixing parameters, a source spectrum matrix H with L source spectra each having M randomly selected, non-negative source spectral points and a measurement spectra matrix X, which is formed by the N measurement spectra,
• C) modifying the respective M source spectral points of the L source spectra by approximating the matrix product of the mixed matrix W and the source spectrum matrix H to the measurement spectra matrix X by means of a non-negative matrix factorization under the boundary condition that the L source spectra are economically coded,
• D) assigning the L source spectra obtained from step C by the modification to known spectra of lipoprotein components.

Especially the method step C can be carried out under the assumption be that the measured spectra of the lipoprotein mixture to be analyzed to a superimposition of real, characteristic spectra approximated the lipoprotein components of the lipoprotein mixture can be.

there It may be possible that the L source spectra are due to the Methods described here are determinable without concrete Assumptions about the nature or composition of the to be determined Lipoprotein components are required. In particular, that can mean that in step B before performing the step C only the number L of the source spectra to be analyzed for the procedure must be chosen. This can make it possible be that investigations, especially automated routine examinations, of lipoprotein mixtures and the lipoprotein components contained therein are feasible through which the lipoprotein components in terms of their concentration, composition and / or identification analyzable and determinable without any prior knowledge of the lipoprotein components are required. That can continue in particular also have the consequence that an analysis in terms of the concentration, composition and / or identification of lipoprotein components possible in abnormal, rare and / or diseased stages is.

Just the possibility of the composition of the lipoprotein components in lipoprotein mixtures, especially in anomalous stages, can identify and quantify in a patient-specific way by the method described here in contrast to already known Be given procedure. In this case, each of the lipoprotein components of the lipoprotein mixture have a characteristic spectrum, the identification of the respective lipoprotein component possible can make. By assigning the available through the steps A to C. Source spectra in further step D to known, characteristic spectra Of lipoprotein components, this identification may be possible be.

The Lipoprotein components to be determined from the lipoprotein mixture can for example be selected from the following Chylomicrons-A, Chylomicrons-B, Chylomicrons-C, Chylomicrons Remnants, VLDL-A, VLDL-B, VLDL-C, IDL, small dense LDL, LDL-A, LDL-B, LDL-C, HDL-2, HDL-3 and Lp (a).

Farther Alternatively, by the method described herein or additionally also non-lipoprotein components in the lipoprotein mixture be determined, which contribute to the measurement spectra to be analyzed. Such non-lipoprotein components may be, for example Be like components in body fluid samples such as lactates, alcohols, amino acids, peptides, nucleic acids, Fatty acids, carbohydrates, pharmaceuticals and / or proteins.

The characteristic spectra of these lipoprotein components or non-lipoprotein components For example, characteristic reference parameters such as peak positions, line shapes and / or line widths, from which the lipoprotein components are identifiable. With Help known, characteristic spectra of the lipoprotein components then the source spectra can be assigned. By This assignment can then be a determination of the lipoprotein mixture contained lipoprotein components in terms of their identification, Composition and / or quantification may be possible. there it does not have to be mandatory that the source spectra agree with the known, characteristic spectra. For example, just deviations with respect Peak positions, line shapes and / or line widths in the determined Source spectra compared to the known, characteristic Spectra Information about patient-specific variations or abnormal, rare and / or abnormal stages of lipoprotein components give.

deviations regarding peak positions, line shapes and / or line widths in the source spectra can be determined just by that for the method no pre-assumptions about the source spectra regarding the characteristic reference parameters are required. Consequently The procedure can offer the possibility, in addition to the determination the lipoprotein components in terms of their concentration, composition and identification also patient-specific additional information concerning medically abnormal and / or diseased stages without further analysis. This can be a significantly increased compared to conventional methods Information yield possible at the same time less time be.

each The N measurement spectra may be a superposition of the characteristic Spectra of the lipoprotein components contained in the lipoprotein mixture exhibit. Furthermore, the measurement spectra can also be characteristic Have spectra of non-lipoprotein components, which, as already mentioned above, also identifiable and quantifiable could be. The relative contribution of a characteristic spectrum a lipoprotein component or a non-lipoprotein component to a measurement spectrum can, for example, of the concentration the relevant lipoprotein component or non-lipoprotein component in the lipoprotein mixture, its composition, other components in the lipoprotein mixture and / or external influences depend on the characteristic spectrum. An outer one Influence can be for example a magnetic field and / or a Be temperature. In particular, an outer Influence by the detailed measurement conditions be given.

The N measurement spectra may in particular be magnetic resonance spectra be, for example, by means of a nuclear magnetic resonance spectroscopy technique ("Nuclear magnetic resonance", NMR) are recorded can. In particular, it may be diffusion-weighted Act NMR spectroscopy.

An example of a measurement method for diffusion-weighted NMR spectroscopy is from the document DE 10 2004 026 903 known. In this case, to record each of the N measurement spectra, a one-dimensional spin-echo experiment is performed in which a static, constant magnetic field is superimposed, which is superimposed by an adjustable magnetic field gradient. The lipoprotein mixture to be analyzed can in this magnetic field in the form of a liquid, in particular in the form of a solution or a Emulsion can be arranged. In particular, the lipoprotein mixture may comprise or be a body fluid such as a blood sample, serum or urine sample or a solution thereof.

By those in the lipoprotein components and non-lipoprotein components of the lipoprotein mixture contained atomic nuclei, so about hydrogen, Carbon and / or nitrogen nuclei, the lipoprotein mixture have a magnetic moment or a total magnetization, for example, by the thermal (Boltzmann-) distribution of given individual spin orientations in the static magnetic field is. In the equilibrium case, the total magnetization is formed along the static, constant magnetic field as longitudinal Magnetization off. By those known to those skilled so-called chemical shift, that is the influence of one Nucleons surrounding electrons to the magnetic field at the location of an atomic nucleus, can the individual atoms of the lipoprotein components and Non-lipoprotein components have different precession frequencies (Larmorfrequenzen) in the static, constant magnetic field. In the equilibrium case, the total magnetization has no transverse Component perpendicular to the static, constant magnetic field.

By a suitable sequence of one or more so-called π / 2 pulses and / or so-called π-pulses can the total magnetization be influenced and in particular relative to the provided static, constant magnetic field from its equilibrium position to be turned around. The π / 2 pulses and π pulses can doing so by one in addition to the static magnetic field generated pulse of an oscillating magnetic field can be effected. The strength of the oscillating magnetic field and the pulse duration can be chosen such that the total magnetization rotated by 90 ° or 180 ° relative to the static magnetic field becomes. Depending on the choice and number of π / 2 and / or π pulses it can be a one-dimensional or multi-dimensional Act NMR method.

A from the equilibrium position by a π / 2 pulse rotated by 90 ° Total magnetization now has a static, constant Magnetic field transverse component in the static magnetic field precess. The precessing transverse total magnetization component can generate an oscillating magnetic field, for example can be measured and recorded by means of pick-up coils. The Precession frequency is for each atom in the Lipoprotein mixture of the respective local magnetic field strength as well as the individual chemical shift. Due to the latter, nuclear spins precess with different chemical shift with different Larmor frequencies. Dephase through spin-spin interactions in the spin system the individual nuclear spins over time. This breaks up or relaxes the transverse component of the total magnetization with time.

Farther While the various lipoprotein components and non-lipoprotein components can be used while precess them, diffuse through the lipoprotein mixture. The diffusion rate of a lipoprotein component or non-lipoprotein component can be, for example, of their respective size depend, so that about small lipoprotein components faster can diffuse through the lipoprotein mixture as lipoprotein components, which are larger in comparison to these. If that static, constant magnetic field superimposed purely by way of example a magnetic field gradient is, the various lipoprotein components can become depending on their diffusion rate in the time average in different middle magnetic fields are located, so that the nuclear spins of the individual Atoms of different lipoprotein components, each with different Precess frequencies can precess and thus different depending on the time Accumulate precession phases. Through this Dephasing of the individual nuclear spins of the individual lipoprotein components, by the above-mentioned dephasing due to the chemical shift as well as by other relaxation processes such as collisions of the the components contained in the lipoprotein mixture with each other can Total magnetization decrease, so that after a π / 2 pulse the measurable, oscillating magnetic field signal generated by the precessing Total magnetization is evoked, in its intensity decreases with time. Such a signal is also known to those skilled in the art so-called "free induction decay" (FID) known. The thereby measurable frequencies, for example, relative to a frequency standard and with the unit "ppm", approximately in the sense of Hz / MHz.

By Irradiation of a π-pulse can be the dephasing process at least partially for at least some of them Nuclear spins of the atoms of lipoprotein components reverse be made, so that after the π-pulses another oscillating magnetic field signal, by the then resulting Total magnetization is caused, measurable and absorbable can be.

Such a signal which can be measured according to a π / 2 and / or a π-pulse can then have an oscillation with a variable amplitude over the period of time. For example, by means of an analog / digital converter ("Analog-to-digital converter", ADC), this signal can be converted in the period in a digital, ie discrete time and amplitude values comprehensive oscillation signal and recorded digitally.

For example, by means of Fourier transformation or by means of another suitable transformation method, such an oscillation signal can be transformed in the time domain into a spectrum with M ₀ measuring points in the frequency domain. The spectrum with M ₀ measuring points may include a frequency range F ₀ . The number and resolution of the M ₀ measurement points may depend, for example, on the resolution of the ADC and the selected transformation method. A spectrum thus obtained may have a superposition of magnetic resonance curves corresponding to the NMR signals of the individual atoms of the lipoprotein components and non-lipoprotein components. Especially with such recorded NMR spectra, the signal-to-noise ratio (SNR) can be so large that no further measures to suppress noise must be required.

From the spectrum with M ₀ measuring points in the frequency range F ₀ , a partial spectrum in a frequency subrange F ₁ ≤ F ₀ with M ≤ M ₀ measuring points can be selected for a measuring spectrum and provided as a measuring spectrum. In this case, in the case of N measured spectra with M ₀ measuring points in each case, the same frequency subrange F ₁ ≦ F ₀ with M ≦ M ₀ measuring points can be selected for each of the N measuring spectra.

As a result, it may be possible, for example, for a frequency range to be selected from the N measured spectra, which is particularly suitable for analyzing the lipoprotein components contained in the lipoprotein mixture. The frequency range can be particularly suitable if only lipoprotein components contribute to the measurement spectra in this frequency range or if the contribution of non-lipoprotein components in this frequency range is negligibly small. Furthermore, the frequency range may be particularly suitable if a known number of lipoprotein components contribute to the measurement spectra in this frequency range. Particularly suitable for identifying lipoprotein components in a lipoprotein mixture may be, for example, a frequency or abscissa range of 1.5 to 0.5 ppm in an NMR ¹ H spectrum in which the methyl and methylene peaks of the lipoprotein components present in the blood are present ,

The N measurement spectra can be performed at N different measurement conditions be recorded by N variations of at least one or several measurement parameters can be set. By the variation of the one or more measurement parameters may be be possible that the respective contribution of the above NMR signals of the atoms of the individual lipoprotein components to the N measurement spectra can be different in size, so that the N measurement spectra N different superimpositions of the spectra correspond to the lipoprotein components contained in the lipoprotein mixture. The measurement parameter can be, for example, the magnetic field strength and / or a magnetic field gradient of the constant, static magnetic field. A magnetic field gradient can be a linear gradient and / or a higher-order gradient, such as a quadratic one Gradients, or be such. Furthermore, the Gradient longitudinal to the static, constant magnetic field, so along the direction of the static, constant magnetic field, or be transversal to this.

Farther the measuring parameter to be varied can be the magnetic field strength and / or a magnetic field gradient of the oscillating magnetic field, its oscillation frequency and / or its pulse duration. Furthermore, can the measurement parameter is a temperature that is during the N measurements are varied at the N different measurement conditions. In addition, the measurement parameter can be the concentration a component of the lipoprotein mixture, such as a solvent such as water. By varying amounts of solvent additions can the lipoprotein mixture and thus the contained therein Lipoprotein components and / or non-lipoprotein components differ be heavily diluted.

Especially it is preferable to set the N different measurement conditions a static, constant magnetic field gradient of the static, constant Magnetic field can be varied. This can be a reproducible Setting the N measurement conditions are enabled.

As a model for the N measurement spectra, in the simplest case a linear superposition of the underlying characteristic spectra of the lipoprotein components and non-lipoprotein components contained in the lipoprotein mixture to be analyzed can be assumed in each case. By means of the method described herein, it may be possible to determine source spectra and mixing parameters from the measurement spectra, each with the exception of a proportionality factor, the source spectra of the previously unknown characteristic spectra of the lipoprotein components and the non-lipoprotein components in the lipoprotein mixture and the mixing parameters to the pre unknown underlying overlay processes can be approached. Since the characteristic spectra and the underlying superposition processes are unknown, the method may include features of blind source separation (BSS) and further features of information-theoretical methods that allow the analysis of the recorded measurement spectra with regard to the source spectra to be determined , BSS methods usually use a statistical method called "independent component analysis" (ICA), which is based on information theory principles. In order to provide a clear solution except for permutations and scaling, BSS methods generally require that additional assumptions and / or knowledge about the characteristics of the characteristic spectra and / or the mixing processes be used as a basis for the method. It is often assumed that the associated source spectra should be statistically independent.

at The method described here must be the underlying characteristic spectra not statistically independent be. Rather, it is based on the boundary condition that the underlying characteristic spectra and thus the to be determined source spectra are economically coded. Thus, in The method described here, the economical coding of the source spectra and thus also the economical coding of the overlay matrix be exploited to solve the BSS problem of decomposing the measurement spectra into their underlying source spectra without further prior knowledge or without additional, usually elaborate experiments such as multidimensional NMR spectroscopy.

wobei ||h||_i mit i = 1, 2 die L_i-Norm des Vektors h ist. Die L₁-Norm des Vektors h ist dabei die Summe der Beträge der M Vektorkomponenten des Vektors h, also

wobei h_i die Vektorkomponenten von h sind, während die L₂-Norm des Vektors h die Wurzel aus der Summe der Quadrate der M Vektorkomponenten h_i des Vektors h ist, also

Aus Gleichung (1) ergibt sich, dass σ(h) ≤ 1, wobei die Sparsamkeit des The economy or economical coding σ (h) of a vector h with M vector components can be given by the following equation:

where || h || _i with i = 1, 2 is the L _i -norm of the vector h. The L ₁ -norm of the vector h is the sum of the amounts of the M vector components of the vector h, ie

where h _{i are} the vector components of h, while the L ₂ -norm of the vector h is the root of the sum of the squares of the M vector components h _{i of} the vector h, ie

From equation (1) it follows that σ (h) ≤ 1, where the economy of the

vector h is greater, the closer σ (h) is at the value 1. In particular, σ (h) = 1 when the vector h has only one vector component which is not equal to 0. Farther can be the boundary condition of the economical coding in the here described Process additionally mean that the components of a sparingly encoded vector h greater than or equal to 0, that is, the vector is positive semi-definite is. In addition, economical coding can mean that a majority of the components of the vector h are equal to 0 or only small noise amplitudes. For the The procedure described below can be an economical coding The source spectra also mean that the amplitude values of the source spectra in wide spectral ranges are equal to 0 or only small ones Have noise amplitudes.

To Recording of the N measurement spectra with each M measurement points can be done in step B of the method described here, a matrix X is provided each having a measurement spectrum in a row. The may mean that the vector components of the first row vector of the matrix X by the M measurement points of a first of the N measurement spectra are formed, the vector components of the second row vector of Matrix X through the M measurement points of a second of the N measurement spectra etc., so that the matrix X is an (N × M) matrix of N rows and M columns. In this case, the assignment of the N rows of the matrix X be arbitrary to the N measurement spectra and does not have the order in which the N measurement spectra were recorded.

In the following, the method steps B and C are described only as starting from the previously described matrix X with the N measurement spectra as row vectors of X. Alternatively, however, the matrix X can also be provided such that in each case one of the N measurement spectra forms a column vector of the matrix X. det, so that in comparison with the above-mentioned matrix X, in which the N measurement spectra form the row vectors of the matrix X, a matrix transposed thereto is provided. In the following description, in this case, according to the known rules of matrix calculation for transposed matrices and matrix equations, rows and columns in the described matrices as well as the order of matrices as factors in matrix products are to be exchanged.

in the Method step B can be the source spectrum matrix H with L rows be provided with each row of the source spectrum matrix H represent one of the L source spectra with M points each can. The mixed matrix W can be L column vectors, each with N mixing parameters as vector components, wherein the mixing parameter in the I-th column with 1 ≤ 1 ≤ L and in the nth row with 1 ≤ n ≤ N, the contribution of the l-th source spectrum can represent the nth measurement spectrum.

Especially In step B, the number of L source spectra with L <N or L = N can be selected become. This may mean that in the case of L = N in the process step C as many source spectra are determinable as measuring spectra in Step A will be recorded. In the case of L <N, compared to those in step C to be determined source spectra recorded in step A more spectra. In particular, it may be necessary for method step C. be that at least as many measurement spectra are recorded in step A. How to determine source spectra in step C.

In step B, each M random, non-negative source spectrum points of each of the L source spectra can be chosen so that each of the provided L source spectra, ie each of the L row vectors of the matrix H, a parsimony of greater than or equal to 0.7, preferably greater or equal to 0.8 and more preferably greater than or equal to 0.9. The economies of the L source spectra may be the same or different. In particular, the respective M source spectral points of the L source spectra can be selected in such a random and non-negative manner that the same applies to the economy according to equation (1) of the L source spectra σ (h 1 ) ≤ σ (h 2 ) ≤ ... ≤ σ (h L (2) that is, the economy of the first row vector h _{1 is} less than or equal to the economy of the second row vector h ₂ , the economy of the second row vector h _{2 is} less than or equal to the economy of the third row vector h ₃ , etc. The choice of a high economy of the source spectra of Matrix H, which is a thrift as mentioned above, can be an integral part of the process described here. Precisely because of this, the specification of further boundary conditions for method step C may no longer be necessary so that a high flexibility and performance of the method described here can result.

Farther In step B, the N vector components of L can also be used Column vectors of the mixed matrix W such random and non-negative be chosen that each of the L column vectors a thrift greater than or equal to 0.7, preferably greater or equal to 0.8 and more preferably greater or equal to 0.90. It can also the austerity each of the L column vectors of W is the same or different.

there contain the provided matrices W and H except for the assumed ones Frugality does not have any information about the actual, underlying characteristic spectra or the the measurement spectra actual, underlying mixing parameters or mixing mechanisms.

By the choice of equal savings for the L source spectra of H and / or the L column vectors of W may be the one needed Effort, for example, in terms of computing power and / or computing time, of step C for first approximation steps of the matrix product WH to the measurement spectra matrix X in comparison to chosen different economies are kept small. In contrast, the choice of different economies the flexibility of the approximation process in the Step C compared to the same thrift increase.

The method is further based on the consideration that the characteristic spectra of the lipoprotein components or of the lipoprotein components and non-lipoprotein components can be expressed in the form of an unknown and at least prior to the determination method not yet known matrix S, wherein each of the assumed L characteristic spectra of the Lipoprotein components or lipoprotein components and non-lipoprotein components a row vector of the matrix S, respectively M vector components, ie with M spectrum points forms. The superimpositions of the L characteristic spectra caused by the N measurement conditions can be represented by another unknown matrix A, wherein each of the 1 column vectors of the matrix A with 1 ≦ 1 ≦ L each have N components and respectively the contribution of the lth characteristic spectrum of the Indicates matrix S to the N measurement spectra. The matrix X can thus be used as the matrix product of the unknown matrices A and S X = AS (3) be expressed. The method described here may be suitable for approximating the matrix product WH to the measurement spectra matrix X by non-negative matrix factorization, ie WH → X, (4) wherein the source spectrum matrix H provided in step B can be approximated to the unknown matrix S up to an arbitrary scaling matrix and furthermore the provided matrix W can be approximated to the unknown matrix A up to an arbitrary permutation and scaling matrix, so that the matrices W and In essence, this may mean, except for permutations and / or scaling, each equal to the unknown matrices A and S. As a result, it may be possible to determine not only the L source spectra by the method but also additionally to determine the N × L mixing parameters of the matrix W. As a result, the relative contributions of the individual source spectra to the measurement spectra can be determinable, which makes it possible to draw conclusions about the mixing mechanisms underlying the measurement spectra with respect to the underlying characteristic spectra.

The approximation of the matrix product WH in method step C to the measurement spectra matrix X may mean that a measure of the difference between WH and X is minimized. Such a measure can be given by a cost function K, which can be, for example, the L ₂ -norm of the difference between X and WH, ie K = || X - WH || 2 , (5)

wobei x_n,m das Matrixelement in der n-ten Zeile und der m-ten Spalte von X ist und wh_n,m das Element in der n-ten Zeile und in der m-ten Spalte der durch das Matrixprodukt aus W und H gegebenen Matrix WH ist.Alternatively, the cost function may also be a relative entropy-based norm, such as the Kullback-Leibler divergence:

where x _{n, m is} the matrix element in the n-th row and the m-th column of X and wh _{n, m is} the element in the n-th row and in the m-th column of the matrix product of W and H given matrix WH is.

In this case, the approximation of the matrix product WH to the measurement spectra matrix X for the assignment of the matrix H obtained from step C with the L source spectra to known spectra of the lipoprotein components in step D may be sufficient if the cost function K reaches a sufficiently small value, that is to say: K ≤ ε, (7) where ε is a barrier which may be less than or equal to 10 ^-4 , preferably less than or equal to 10 ^-5 and particularly preferably less than or equal to 10 ^-6 . The barrier ε can mean a termination criterion for the approximation method in method step C, in which the measure for the difference between WH and X in the above sense is minimized. In other words, for K ≦ ε, the matrix product of W and H may be converged sufficiently close to X that identification and / or quantification of the lipoprotein components or lipoprotein components and non-lipoprotein components from the L source spectra in step D may be possible can.

In addition to the pure identification of lipoprotein components by assignment to known spectra, the concentrations of the lipoprotein components contained in the lipoprotein mixture can be determinable from the source spectra determinable by step C, for example via amplitudes of resonance lines contained in the approximated source spectra. For this purpose, it may be necessary for the lipoprotein mixture to contain a reference component whose concentration in the lipoprotein mixture is known and which can be identified in step D from one of the determined source spectra. The reference comp It may be added before the process step A the lipoprotein mixture or be a lipoprotein or non-lipoprotein component of the Lipoproteingemischs.

According to one Another embodiment is a data processing system described at least part of the steps described herein can perform. For example, the Fourier transform of the method step A and / or the method steps B and C. doing so in a suitable data processing system, such as a digital Data processing system such as a personal computer (PC) performed become. Likewise, the assignment of those obtained from step C. L source spectra performed in the data processing system become. Alternatively, for one or several process steps one or more specifically suitable Data processing systems are provided, wherein the plurality Data processing systems may be suitable to one another Exchange data.

Further advantages and advantageous embodiments and developments of the method will become apparent from the following in connection with the 1A to 6E described embodiments.

It demonstrate:

1 various one-dimensional NMR ¹ H spectra of a blood plasma sample with and without magnetic field gradient,

2 a schematic representation of a method according to an embodiment,

3A and 3B schematic representations of methods according to further embodiments,

4A to 4C a simulation of artificial NMR data sets, which are analyzed by a method according to an embodiment.

1 purely by way of example shows several one-dimensional NMR spectra of ¹ H nuclei in a blood plasma sample provided as a lipoprotein mixture to be analyzed under different measurement conditions. The different measurement conditions correspond to different magnetic field gradients, in which the blood plasma sample was arranged in addition to a static, constant magnetic field. The horizontal x-axis shows the chemical shift in ppm and the vertical y-axis the intensity of the NMR signals in arbitrary units.

That with 101 designated one-dimensional NMR spectrum was recorded without magnetic field gradients. The measuring spectrum 101 represents a superimposition of the NMR signals of the lipoprotein components and non-lipoprotein components contained in the blood plasma sample. The typical linewidths of the magnetic resonance signals (peaks) are about 0.05 to 0.08 ppm. With 102 and 103 designated measuring spectra were with by 102 to 103 recorded increasing magnetic field gradients. It can be seen that with increasing magnetic field gradients the peaks are attenuated to different degrees, which corresponds to the different diffusion properties of the associated lipoprotein components and non-lipoprotein components in the blood plasma sample and, associated therewith, the different respective averaging of the magnetic field gradient.

2 shows a schematic representation of a method for the determination of lipoprotein components in a lipoprotein mixture to be analyzed according to an embodiment. The lipoprotein mixture is purely exemplary, as mentioned above, a blood plasma sample. It is in a with 10 labeled method step A a plurality of N> 1 measurement spectra recorded. For this purpose, FID spectra are recorded according to the NMR technique described in the general part, digitized by means of an analog-to-digital converter (ADC) and by means of a discrete Fourier transform in measurement spectra in the frequency domain, as exemplified in 1 shown, transformed. Each of the N measurement spectra has M measurement points resulting from the resolution of the ADC converter and from the boundary conditions of the Fourier transformation. A typical number M of measurement points may be 32768 at a resolution of 0.37 Hz / measurement point. The number N of the measurement spectra recorded in this way corresponds at least to the number of lipoprotein components to be determined and / or non-lipoprotein components in the lipoprotein mixture.

In another, in 2 With 20 designated method step B, a measurement spectra matrix X with N × M matrix elements is provided in which each of the N row vectors of the measurement spectra matrix X by in each case one of the N measurement spectra is formed with in each case M measurement points. Furthermore, in method step B, a source spectrum matrix H with L source spectra is provided as row vectors, the L source spectra each having M random, non-negative source spectral points. Furthermore, a mixed matrix W with N × L random, non-negative mixing parameters is provided. The number L of the source spectra corresponds to the number of lipoprotein components to be determined and non-lipoprotein components in the lipoprotein mixture, where L is less than or equal to N.

In another, in the 2 With 30 method step C, the L source spectra are determined by approximating the matrix product of W and H to the measurement spectra matrix X by means of a non-negative matrix factorization method (NMF method). In this case, the L column vectors of the mixed matrix W can be interpreted as basis vectors of a basic system and the L row vectors of H correspondingly the development coefficients in the base assumed by W. The NMF method is an optimization method which is solved under the additional boundary condition that the L source spectra, that is to say the L row vectors of the matrix H, are economically coded. The economy results from equation (1).

These Boundary condition may be necessary for the optimization procedure is clearly solvable. Therefore, in the process step B provided the L source spectra, each with 0.9 economy. Around a great flexibility of the NMF method in the To achieve process step C, the respective economies The L source spectra may also be different.

In another, in the 2 With 40 designated method step D are assigned the known in step C L source spectra spectra of lipoprotein components. In addition, known spectra of non-lipoprotein components in method step D can also be used. Deviations in terms of peak positions, line shapes and / or line widths in the determined source spectra can be taken into account in the assignment in comparison to the known spectra in order to identify abnormal and / or pathological patient-specific stages. Furthermore, information about the relative amounts of the lipoprotein components and / or non-lipoprotein components contained in the lipoprotein mixture can also be obtained from the source spectra determined in the method described above and the mixing matrix determined therefrom.

The Fourier transformation of method step A and the method steps B and C are in the illustrated embodiment in a suitable digital data processing system performed. As well becomes the assignment of the L source spectra obtained from step C. performed in the data processing system. alternative can also for one or more process steps one or several specifically suitable data processing systems provided where the multiple data processing systems are suitable, exchange data with each other.

In the 3A and 3B Methods according to further embodiments are shown. The correspond with the 10 . 20 and 40 designated method steps A, B and D the method steps described in the previous embodiment.

The method according to the embodiment in 3A has the with 30 designated method step C, with the 31 to 35 designated method steps C1 to C5. It is in with 31 method step C1 replaces the source spectrum matrix H with a matrix resulting from the following assignment statement: H ← H-μ S W T (WH-X), (8) where W ^{T is} the transposed matrix of W. The parameter μ _S is a measure of the step size in this calculation step and has a value less than or equal to 10 ^-2 and greater than or equal to 10 ^-5 . The choice of the size of the parameter μ _S can be understood as attenuation factor in method step C, which ensures that the matrix product WH does not begin to oscillate due to the approximation method of the matrix product WH performed in step C, but converges asymptotically to X. Here, μ _S may be chosen smaller in the specified range, the closer to X WH. The above-mentioned assignment statement can also ensure that H and W remain positively semidefinite in the further process.

In the further, with 32 designated method step C2, the economy according to equation (1) is determined each of the row vector obtained from step C1. The row vectors are then rewritten after their jewei permutated in the matrix H so that the L source spectra are sorted according to their economy after the permutation. In the exemplary embodiment shown, the L row vectors or source spectra are arranged in ascending order according to their economy, so that after the permutation the first row vector has the lowest and the Lth row vector has the greatest economy.

In the further, with 33 designated method step C3, the mixed matrix W is replaced by a matrix, which results from the following assignment statement: W ← W ⊗ (XH T ) ⌀ (WHH T ), (9) where H ^{T is} the transposed matrix of H and ⊗ is an element-wise multiplication and ⌀ is an element-wise division.

In the following, with 34 designated method step C4, a cost function K is calculated, which indicates the degree of the degree of approximation of the matrix product WH to the measurement spectra matrix X. The cost function K in the exemplary embodiment shown here is the L ₂ -norm of the difference between WH and X, that is K = || WH - X || ₂ .

In the further, with 35 designated method step C5, the cost function K calculated in step C4 is compared with a preselected barrier ε, where ε is less than or equal to 10 ^-4 and greater than or equal to 10 ^-6 . If K> ε, the process steps C1 to C4 are repeated one more time. For K ≤ ε, on the other hand, it is assumed that the matrix product WH has converged to the measurement spectra matrix X, ie is approached sufficiently accurately to the measurement spectra matrix X, so that in method step D the assignment of the L source spectra now to be taken from the source spectrum matrix H is possible. The method steps C4 and C5 can also be carried out before the step C1.

When in conjunction with 3B shown methods are in with 10 designated method step A at the N measurement conditions N spectra recorded with each M ₀ measurement points. These can be about the in 1 cover the frequency range F ₀ from 10.00 to -1.00 ppm. This in 3B shown method has in comparison to the previous method according to 3A the additional with 11 designated method step, in which from each of the N spectra a measurement spectrum with M ≤ M ₀ measurement points in a frequency subrange F ₁ ≤ F _{0 are} selected. In the exemplary embodiment shown, the M measurement points for the N measurement spectra are selected from each of the measured N spectra with M ₀ , which are in the frequency subrange F ₁ of 1.4 ppm to 0.8 ppm and thus the methyl and methylene peaks of the present in the blood Correspond to lipoprotein components. By selecting a suitable frequency subrange from the measured spectra, the computational effort required for method step C can be reduced. In addition, the in 3B shown method for one or more other frequency sub-ranges of the measured N spectra with M ₀ measuring points are repeated.

To demonstrate the performance of the method described herein, reference is made to FIGS 4A to 4C a simulation of artificial NMR data sets shown by means of a method according to the embodiment in 3A were analyzed.

For this purpose, a lipoprotein mixture with 15 lipoprotein components was assumed. Accordingly, a matrix of 15 line vectors was provided for which 15 simulated, randomly chosen NMR-like measurement spectra were generated as data sets that simulate real lipoprotein component spectra in NMR ¹ H spectra of lipoprotein components in blood plasma. The 15 data sets corresponding to the unknown characteristic spectra on which the measurement spectra are based. The data sets were calculated from the weighted sum of two absorptive Lorentz curves S (ω) = r 1 Re {L 1 (ω)} + r 2 Re {L 2 (ω)} (10) where ω is the frequency on the abscissa, Re {...} is the real part, r ₁ and r _{2 are} weighting factors that are random numbers in the range [0,5; 1]. The Lorentz functions L ₁ and L ₂ are given by L k (ω) = [λ (K) + i (ω - Ω (K) )] -1 , (11) with k = 1, 2 and i = (-1) ^1/2 . In this case, Ω ^{(k) is} the peak position of the absorption line L _k (ω) on the frequency axis and λ ^{(k) of} the parameters is their half-width in frequency units.

The 15 NMR-like spectra S (ω) calculated in this way form the 15 row vectors of a matrix S in the form of discrete value pairs. The 15 NMR-like spectra S (ω) are in 4A shown.

Furthermore, a mixed matrix A with the matrix elements a _{nk was} provided with

T → ⁽ⁿ⁾ = (t ₀ , ..., t ₁₄ ) ^{T is} a vector with the vector components t _n = 0 + n × 0.05, n = 0,..., 14, and b → ^{( k)} = (b ₀ , ..., b ₁₄ ) a vector with the random vector components b _k , k = 0, ..., 14, from the interval [0; 1].

The simulated measurement spectra matrix X was obtained according to X = AS, with all matrix elements that were smaller than a predetermined threshold being set equal to zero. This is necessary to suppress ubiquitous noise on the measured data and to ensure economical coding. The 15 line vectors of X thus obtained, which represent the 15 simulated measurement spectra, are in 4B shown.

According to the with 20 and 30 designated method steps B and C of in 3A As shown, the matrices W and H provided in step B were approximated to the simulated measurement spectra matrix X, providing the source spectrum matrix H with 15 line vectors. In this case, the inverse or pseudo-inverse mixed matrix W was calculated using a projective version of the k-means clustering method known to the person skilled in the art. Figuratively speaking, the data points are projected onto the unit matrix. The 15 source spectra obtained from step C are in 4C shown. These can be the in 4A underlying spectra are assigned by comparing peak positions and relative amplitudes. If one of the measurement spectra contains a reference peak with a known concentration of the associated lipoprotein component, it can be achieved by normalization of the row vectors of the source spectrum matrix that the entries of the mixed matrix W can be interpreted as concentrations.

The Embodiments and embodiments to the methods described herein are not limited to the determination of lipoprotein components described herein in a lipoprotein mixture, but can also affect others chemical substances used in the medical, biological, and chemical applied to pharmaceutical analysis and industry and applied. In particular, this may be for analysis apply where sparingly encoded spectra in one or more Multicomponent spectra overlaid are measurable, as the Here described method only the economical coding of Source spectra used as boundary condition and otherwise no further Preliminary information about the source spectra to be determined are to be used. Therefore, the method described here, for example also for analyzes in general magnetic resonance and / or optical spectroscopy and mass spectrometry applicable be. The advantage here too can be a considerable information yield at the same time be a little time spent in the analysis without that in advance, for example, peak positions, line widths and / or line shapes must be known. The term "spectrum" is to be interpreted broadly and not only to the advance from spectroscopic Applications and methods limited to known forms. Rather, it may be possible that with the one described here Process an unknown overlay of information in terms of their underlying information, ie in terms of the source information, let analyze, if only the overlays of information as well as the source information in a matrix notation can be displayed and the source information is coded sparingly.

The The invention is not by the description based on the embodiments limited to these. Rather, the invention comprises each new feature as well as any combination of features, which in particular any combination of features in the claims includes, even if this feature or this combination itself not explicitly in the patent claims or embodiments is specified.

QUOTES INCLUDE IN THE DESCRIPTION

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Cited patent literature

• - DE 102004026903 [0003, 0016]

Claims (21)

Method for the determination of lipoprotein components in a lipoprotein mixture to be analyzed, comprising the steps: A) Inclusion of N> 1 Measuring spectra of the lipoprotein mixture to be analyzed at N different Measurement conditions, each of the N measurement spectra each M measurement points having, B) Provide a mixed matrix W with N times L randomly selected, non-negative mixing parameters, a source spectral matrix H with L source spectra, each with M random selected, non-negative source spectral points and a Measurement spectra matrix X, which is formed by the N measurement spectra, C) Modify the respective M source spectrum points of the L source spectra by approximation of the matrix product of the mixed matrix W and the source spectrum matrix H to the measurement spectra matrix X by means of a non-negative matrix factorization under the constraint that the L source spectra are economically coded, D) Assign the the step C obtained by the modification L source spectra to known spectra of lipoprotein components. The method of claim 1, wherein - each the lipoprotein components have a characteristic spectrum. The method of claim 2, wherein - the N measurement spectra respectively superimpositions of the characteristic Have spectra of the lipoprotein components of the lipoprotein mixture. Method according to one of the preceding claims, in which - the N measurement spectra Magnetic resonance spectra are. Method according to one of the preceding claims, in which - The lipoprotein mixture a body fluid is. Method according to one of the preceding claims, in which - the N different measurement conditions N variations of at least one measurement parameter can be set and - The at least one measurement parameter from a group is selected, which is formed by: a magnetic field strength and / or a magnetic field gradient of a constant magnetic field, a magnetic field strength and / or a magnetic field gradient of a oscillating magnetic field, an oscillation frequency of an oscillating Magnetic field, a duration of an oscillating magnetic field pulse, a temperature, a concentration of a component of the lipoprotein mixture. Method according to the previous claim, in which - exclusively a magnetic field gradient of a constant magnetic field for adjustment the N different measuring conditions is varied. Method according to one of the preceding claims, in which - N spectra in the N measurement conditions are recorded with M ₀ measuring points in a frequency range F ₀ in method step A, and - a sub-spectrum is selected from each of the N spectra with M ≤ M ₀ measuring points in each case the same frequency subrange F ₁ ≦ F ₀ and - the method steps B) to C) are performed with the sub spectra as the N measurement spectra. Method according to one of the preceding claims, in which - In step B, the number L of the source spectra with L <N or L = N is selected. Method according to one of the preceding claims, in which In step B, the L source spectra of the matrix H each with a thrift of greater or equal to 0.9. Method according to one of the preceding claims, in which The economy of the L source spectra of Matrix H are the same. Method according to one of the preceding claims, in which method step C comprises the following steps: C1) replacing the matrix H by a matrix resulting from the calculation step H-μ _S W ^T (WH-X), where W ^{T is} the transposed matrix of W and for μ _S a value less than or equal to 10 ^-2 and greater than or equal to 10 ^-5 , C2) determining the economy of each of the L source spectra of the matrix H obtained from step C1 and ordering the L source spectra within the matrix H according to their economy, C3) replacing the matrix W with a matrix, is given by the calculation step W (XH ^T ) ⌀ (WHH ^T ), where H ^{T is} the transposed matrix of H and ⊗ is an element-wise multiplication and ⌀ is an element-by-element division, C4) a cost function K is calculated as a measure of a degree of approximation of the matrix product from W and H to the measurement spectra matrix X, C5) repeating steps C1 to C4 to K ≦ ε, where ε is less than or equal to 10 ^-4 and greater than or equal to 10 ^-6 . Method according to the previous claim, in which - in the Step C2 ascending the L source spectra within the matrix H. be organized according to their thriftiness, so that the first of the L Source spectra in the matrix H after ordering the smallest thrift and the L-th of the L source spectra the greatest thrift having. Method according to claim 12 or 13, wherein - the cost function K is an L ₂ -norm or a Kullback-Leibler-divergence of a difference between the measurement spectra matrix X and the matrix product of W and H. Method according to one of the preceding claims, in which In addition, in step C, the N × L Mixing parameters of the matrix W are determined. Method according to one of the preceding claims, in which - In step D additionally the concentrations and / or the composition of those contained in the lipoprotein mixture Lipoprotein components are determined. Method according to one of the preceding claims, in which - In addition, medically in step D. abnormal and / or diseased stages of lipoprotein components can be determined are. Method according to one of the preceding claims, in which In addition to the lipoprotein components in the lipoprotein mixture contained non-lipoprotein components become. Method according to the previous claim, in which - the Non-lipoprotein components are selected from a Group formed by lactates, alcohols, amino acids, Peptides, nucleic acids, fatty acids, carbohydrates, Pharmaceuticals and proteins. Method according to one of the preceding claims, in which - The lipoprotein components selected are from a group formed by chylomicrons A, chylomicrons B, Chylomicron C, Chylomicron Remnants, VLDL-A, VLDL-B, VLDL-C, IDL, small dense LDL, LDL-A, LDL-B, LDL-C, HDL-2, HDL-3 and Lp (a). Data processing system for implementation at least the method steps B and C according to one of previous claims.