WO2008107604A2

WO2008107604A2 - Method for standardizing a set of measurements

Info

Publication number: WO2008107604A2
Application number: PCT/FR2008/050094
Authority: WO
Inventors: Jean Feuillard; Abdelghafour Marfak; David Rizzo; Jean-Luc Faucher; Chantal Jayat-Vignolle
Original assignee: Centre Hospitalier Universitaire De Limoges
Priority date: 2007-01-24
Filing date: 2008-01-22
Publication date: 2008-09-12
Also published as: FR2911683B1; WO2008107604A3; FR2911683A1

Abstract

The invention concerns a method for standardizing a set of measurements, comprising the following steps: a. performing a first set of measurements for a first given sample using first measuring means comprising at least a first photomultiplier; and b. providing a referent for the first set of measurements, said referent comprising a set of values corresponding to a second set of measurements performed for a second given sample using second measuring means comprising at least a second photomultiplier. According to the invention, it also comprises the following steps: c. calculating the values of the parameters of a rule for the deviation between the set of measurements and the set of values of the referent from subsets of the first set of measurements and from corresponding subsets of the referent; and d. recalculating the values of the first set of measurements as a function of the parameters of the deviation rule.

Description

A method of normalizing a set of measurements.

The present invention relates to the field of standardization of a set of measurements. It is advantageously used in the field of imaging, in particular in biology.

More specifically, the invention relates to a method for normalizing a set of measurements, comprising the steps of: a) producing a first set of measurements for a first sample given by first measuring means comprising at least a first photomultiplier, and b) providing a reference to the first set of measurements, said referent comprising a set of values corresponding to a second set of measurements made for a second sample given by second measuring means comprising at least one second photomultiplier.

The problem that the invention aims to solve is related to the use of photomultipliers.

This problem is illustrated in particular in the field of flow cytometry which, for the sake of clarity, will be the only technique described here. Flow cytometers are apparatus for analyzing or sorting biological cells comprising at least one photomultiplier.

Their operating principle is based on the constant speed of a cell suspended in a liquid vein (flow) in front of a fixed laser source. The light diffracted by the cell during its brief passage in front of the laser depends in particular on its physical characteristics such as its size, granulosity, etc. If the cell has previously been labeled with one or more fluorochromes associated with different biological parameters, the light emitted by each of the fluorescent molecules also participates in its characterization.

The collection of light at different wavelengths using filters (in particular bandpass), and the measurement of the luminous intensity emitted, using photomultipliers associated with appropriate electronic and computer means, allow a so-called "multicolor" analysis of cells (currently 4 to 6 colors currently).

Flow cytometry is a high performance, fast, highly sensitive, quantitative, easy to implement, and allows the characterization and / or rapid sorting of pure and specific cell subpopulations (up to 30,000 events per second) . It applies to all areas of biology (plant biology, microbiology, cell biology, oncology ...). And it is well developed in hospitals and often necessary for the care of patients with for example cancers, including hematological cancers, and diseases with immunological consequences (HIV infection, allergy ...). A flow cytometer easily analyzes 1000 to 2000 cells per second, ie in 3 minutes (average time of an acquisition) close to 2.10 ⁵ events (analysis object, cell or other object marked by one or more fluorochrome) and 1, 5.10 ⁶ measurements (for an analysis of 6 parameters simultaneously). The rapidity of this technique compared to other biological techniques like molecular biology makes it a tool of choice in the aid to the decision-making strategies and in patient follow-up.

The main current limitation is the lack of standardization procedure, standardization, cytometers between them, which "attaches" a result of analysis to its machine (photomultiplier), which poses problems both in the characterization of abundant cell populations only for the quantification of rare events. This problem mainly limits the applications of flow cytometry to qualitative analysis, since the lack of standardization of analysis results (histograms) between machines makes it impossible to directly implement a machine analysis protocol. to the other, linking the result for a patient to a particular machine, with its particular settings.

The object of the present invention is to overcome these drawbacks by proposing a method which, moreover, complies with the preamble cited above, is essentially characterized in that it furthermore comprises the steps of: c) calculating the parameters of a law of difference between the set of measurements and the set of values of the referent from subsets of the first set of measurements and corresponding subsets of the referent, and d) recalculating the values of the first set of measurements according to the parameters of the law the gap.

Preferably, the calculation of the deviation law parameters comprises at least one of the preliminary steps of:

- make a position correction, and - Perform a slope correction, between a first graph corresponding to a portion of the first set of measurements and a first graph corresponding to a corresponding part of the referent, the difference law to compensate for compression / expansion between said graphs.

Advantageously, the position correction step comprises the steps of: selecting at least a first characteristic point relating to the first graph, and at least a second corresponding characteristic point relating to the graph of the referent,

calculate the offset between the coordinates of the characteristic points, and

- update the values of the first set of measurements according to the calculated offset.

In one embodiment, the slope correction step comprises the steps of:

calculating the differences between the slopes of two straight lines respectively formed by two characteristic points relating to the first graph and their corresponding corresponding points relating to the graph of the referent, and

- update the values of the first set of measurements according to the differences of calculated slopes.

In one embodiment, the compression / expansion compensation step comprises the steps of: calculating the compression / expansion coefficient between a plurality of characteristic points relating to the first set of measurements and their respective corresponding points relating to the reference, and

- update the values of the first set of measurements according to the calculated coefficient.

In one embodiment, a feature point and its correspondent are the respective centroids of the first graph and the referent graph.

According to the invention, the difference law is of the type

Log (Itest) = γLog (Iref) ^Λ δ where: δ and Y are constants determined in step c,

It is the measurement of the intensity of the electrical signal at the output of the first photomultiplier used for step a, and Iref is the measurement of the intensity of the electrical signal at the output of the second photomultiplier used for step b.

Advantageously, the first and second samples are the same.

Preferably, at least the first set of measurements is performed on a first flow cytometry machine.

The invention according to another of its objects relates to a computer program comprising program code instructions for executing the steps of the method according to The invention when said program is run on a computer.

Thanks to the invention, the monitoring of the measurements of the same sample over time, the comparison of the samples measured with each other, the comparison of the measurements obtained for a machine or an analysis center, with those obtained on other samples by other analysis centers or on other machines, or with those published in the literature, becomes possible.

Thanks to the invention, the counting of abnormal events

(rare) is achieved by successively conditioning the histograms of interest on windows defined graphically and identifying the target events. This count is particularly important for the monitoring of a tumor mass and the adaptation of therapeutic prescriptions to the patient considered.

Thanks to the invention, it is possible to obtain a posterior correction of histograms obtained by any flow cytometer, with respect to a reference histogram, arbitrarily defined reference. Thus multiparametric histograms resulting from the reading of corrected test data and reference source data can be superimposed when the source data obtained for the test machine and the source machine come from the same sample.

The applications of the invention concern in particular flow cytometry, and more generally all the data and histograms obtained by multiparametric representation of simultaneous measurements of intensities of amplified electrical signals. That is, the invention relates to all areas of biology and imaging using devices for simultaneous measurement of amplified electrical signals, obtained either directly or by converting an electrical signal of a detectable and measurable physical signal (photon, electron, positron ...).

These applications include the comparison of measurements between different samples and the comparison of successive measurements over time of the same sample, in particular on different analysis machines.

Other characteristics and advantages of the present invention will emerge more clearly on reading the following description given by way of illustrative and nonlimiting example and with reference to the appended figures in which:

FIG. 1A represents a first set of measurements for a given sample on first measuring means comprising at least a first photomultiplier,

FIG. 1B a second set of measurements for the same sample given for FIG. 1A on second measuring means comprising at least one second photomultiplier; FIG. 2A represents the arbitrary selection of characteristic points in FIG.

FIG. 2B represents the arbitrary selection of characteristic points in FIG. 1B.

Conventionally, the technology of flow cytometers, which are dedicated to fluorescence measurements, is based on on the conversion and amplification of a light signal into an electrical signal, using photomultipliers.

The amplified electrical signals are digitized and sampled on channels each of which represents a voltage range applied to the photomultiplier.

According to the chosen mode of representation, linear or logarithmic, each channel therefore comprises either a value corresponding to the value of a measurement of the intensity at the output of the photomultiplier, in response to the light signals emitted by the marker (s) ) passing in front of the laser source, the logarithm of this value.

The simultaneous physical measurements of each event, in other words the channel numbers, are archived in electronic form in a data file.

An event is understood to mean a particular object to be studied (particle, microbe, bacterium, cell, ball, etc.). Each event includes one or more light markers (fluorochrome). Each light marker is configured to emit at a specific wavelength.

For the analysis of the data, the cells are represented as events or points on graphs (bi or tri parametric histograms), the coordinates being chosen so that all the measurements (the channel numbers) relating to each other are graphically displayed. to the events studied.

Figures 1A and 1B illustrate two such graphs. These two figures represent two light emission measurement histograms respectively at 520 nm and at 575 nm, corresponding to the fluorescence emission measurement of fluorescein and phycoerythrin of the same sample on two different machines, after adjustment. of the photomultipliers using fluorescence calibration beads. For example, FIG. 1A illustrates a first set of measurements, and FIG. 1B the corresponding reference.

According to the so-called calibration methods of the prior art, it is assumed that there is a strict linearity, a direct proportionality, between the intensity of the light received, the intensity of the electrical signal amplified by the photomultiplier, its digitization and its one-channel sampling whose value defines the measurement. We classically define

I = FkV ^Λ a (1), with I the intensity of the signal measured by the cytometer, F the light emitted,

V is the amplification voltage applied to the photomultiplier, and k and has constants specific to the photomultiplier.

That is according to (1), that:

Log (I) = Log (F) + KO (2),

With KO a constant for a given voltage applied to the photomultiplier. In other words: x = Log (F) + KO (2 ') with x the channel comprising the logarithm of the value of a measurement of the intensity at the output of the photomultiplier, in response to the light signals emitted by the (s) luminous marker (s) passing in front of the laser source, as defined above. Surprisingly, this pre-supposition is in fact inaccurate and the measurements of the amplified electrical signals, in other words the channel numbers allocated to electrical signals, are not strictly linear with respect to the received physical signal. Thus, the current methods of calibration do not make it possible to standardize / normalize flow cytometry histograms obtained from different machines.

According to the invention, it appears in fact that the measurements of the intensities of the amplified, digitized and sampled electrical signals are not strictly linear with respect to the received physical signal, each cytometer having its own nonlinear amplification constants of the signal.

Consequently, although similar, the histograms represented in FIGS. 1A and 1B are different, and clearly illustrate that, despite the calibration of the respective photomultipliers using identical fluorescence calibration beads, it is not possible to obtain superimposable graphics.

The assumption of linearity between the emitted light signal and the measurement of the amplified electric signal is therefore inaccurate. This assumption of linearity is an approximation that does not take into account differences in design and aging between machines, in particular.

According to the invention, the comparative analysis of the measurement data obtained for several flow cytometers, from the same sample, leads to replacing the preceding equation (1) by a relationship between the light signal and the signal measurement. amplified electric type:

Log (I) = p.Log (F) ^Λ a + K (3), where p and a are characteristic constants of the machines (photomultipliers) and K is a constant for a given photomultiplier voltage.

In other words: x = p.Log (F) ^Λ a + K (3 ') with x the channel comprising the logarithm of the measured value at the photomultiplier output.

Thus, for two datasets from two different machines, it can be shown that:

Log (Itest) = g. Log (Iref) ^Λ d (4),

Where It is the measurement of the intensity of the amplified electrical signal on a test machine,

Iref is the measurement of the intensity of the amplified electrical signal on the reference machine, g and d are constants to be determined. As before we can define: xtest = g.xref ^Λ d (4 ')

let xref = γ.test ^A δ withδ = l / det ^ (l / g) ^Λ (l / d)

Where xtest is the channel comprising the logarithm of the measurement of the intensity of the amplified electrical signal on a test machine, and xref is the channel comprising the logarithm of the measurement of the intensity of the amplified electrical signal on the reference machine.

Equations (3) and (4) (or equivalently equations (3 ') and (4')) represent a deviation law according to the invention, and the respective constants the respective parameters of said laws. From this difference law, one can calculate its parameters between the set of measurements (in other words of channels) and the set of values of the referent from subsets of the first set of measurements (or channels) and corresponding subsets of the referent, and one can recalculate the values of the first set of measurements (or channels) according to these parameters of the law the deviation.

For this purpose, it is desirable in a first step to arbitrarily define, by an operator for example, at least three subsets T1, T2 and T3 (FIG. 2A) of the first set of measurements (or channels) and their corresponding R1. , R2 and R3 in the reference (Figure 2B).

In one embodiment, the subsets are such that the skeleton joining the three center points of these three regions best traverses the histogram studied, for the reference and for the test.

The GR and GT barycenters are then computed from the reference and test graphs, each center of gravity serving as a characteristic point.

In another embodiment, the GR and GT barycenters are calculated with the set of measurements referent and test respectively, or from the calculation of local centers of gravity. By local centroid, we mean the calculation of the center of gravity of a subset T1, T2, T3 or another subset.

In another embodiment, one of the subsets T1, T2 and T3 or one of their points can serve as a characteristic point. In this example, we define the coordinates of the points as follows:

R1 (r1x, r1), R2 (r2x, r2y), R3 (r3x, r3y), T1 (t1x, tly), T2 (t2x, t2y), T3 (t3x, t3y),

GR (grx, gry) and GT (gtx, gty).

In this case, rlx, r2x, r3x, tlx, t2x, t3x, grx, gtx are the channels corresponding to the logarithm of the fluorescence measurement of a first fluorochrome FL1 (x-axis) and rly, r2y, r3y, tly , t2y, t3y, gry, gty the channels corresponding to the logarithm of the fluorescence measurement of a second fluorochrome FL2 (y-axis) points R1, R2, R3, T1, T2, T3, GR and GT respectively.

In a second step, it is desirable to perform a position correction between the first graph corresponding to a part of the first set of measurements (test) and a first graph corresponding to a corresponding part of the referent. This position correction corresponds to the superposition of two corresponding arbitrary characteristic points between the reference graph and the first set of measurements.

The values of the first set of measurements are then recalculated according to this position correction.

In the example given:

T'Kt'lx, t'iy), T'2 (t'2x, t'2y), and T'3 (t'3x, t'3y), the coordinates of the respective points T1, T2 and T3 after this position correction step by superposition of the GR and GT centers of gravity.

This superposition can be done in two ways. In a first embodiment, and preferably, it is posited that grx = Cor_x * gtx, and gry = Cor_y * gty, in which Cor_x and Cor_y are multiplicative factors of position correction. from where Cor_x = grx / gtx, and Cor_y = gry / gty, and t 'Ix = Cor_x * tlx, t' Iy = Cor_y * tly, t'2x = Cor_x * t2x, t'2y = Cor_y * t2y, t '3x = Cor_x * t3x, and t' 3y = Cor_y * t3y

As an alternative, in a second embodiment, it is posited that grx = Cor_x + gtx, and gry = Cor_y + gty, in which Cor_x and Cor_y are additive position correction factors. hence Cor_x = grx - gtx, and Cor_y = gry - gty, and t 'Ix = Cor_x + tlx, t' Iy = Cor_y + tly, t'2x = Cor_x + t2x, t'2y = Cor_y + t2y, t '3x = Cor_x + t3x, and t' 3y = Cor_y + t3y

A third embodiment comprises the combination of the two embodiments described above. In this case, we put that grx = Corm_x * gtx + Cora_x, and gry = Corm_y * gty + Cora_y.

Corm_x and Cora_x (respectively Corm_y and Cora_y) are computed by taking a second point of reference of the graph, for example Rl and Tl. Thus, we have a system of two equations with two unknowns: grx = Corm x * gtx + Cora x, rlx = Corm_x * tlx + Cora_x and gry = Corm_y * gty + Cora_y, rly = Corm y * tly + Cora_x

From a graphical point of view, the position correction step by superposition makes it possible to compensate for any shift by translation between the graph of the first set of measurements (test) and the referent.

In a third step, it is desirable to perform a correction (compensation) of slope (or inclination) between a first graph corresponding to a part of the first set of measurements (test) and a first graph corresponding to a corresponding part. of the refers. This so-called "slope correction" step consists of superimposing the axes defined by two points of the histogram skeleton of the first set of measurements with respect to their corresponding reference histogram.

The values of the first set of measurements are then recalculated according to this slope compensation.

In the example given:

T "1 (t" 1x, t "ly), T" 2 (t "2x, t" 2y), T "3 (t" 3x, t''3y) the coordinates of the respective points T1, T2 and T3 after this step of correction of slope, and correction of position, such that, for i = 1 to 3 in the present example: T '' (f 'ix, t''iy), with f'ix = t'ix - CompX * t'iy, and t "iy = t'iy - CompY * t'ix, in which CompX and CompY are constants determined by differences of the slopes along the x-axis and the y-axis respectively between the lines most parallel to the possible axes.

That is to say, with reference to FIGS. 2A and 2B, CompX is determined by the difference in slope between the line defined by the points R2 and R3 on the one hand, and the line defined by the points T2 and T3 d. 'somewhere else.

Similarly, CompY is determined by the difference in slope between the line defined by the points R1 and R2 on the one hand, and the line defined by the points T1 and T2 on the other hand.

Indeed, in flow cytometry, the emission spectrum of fluorochromes is always spread over a wide spectrum.

Thus, in one embodiment in which two fluorochromes FL1 and FL2 with a relatively close emission spectrum are used (emission peak at 520 nm and at 575 nm, respectively), the light received by the photomultipliers of the same machine comes from both FL1 and FL2 fluorochromes at a time, despite the use of bandpass filters in front of photomultipliers.

We can define :

FL1 and FL2 two fluorochromes used for a given test,

PMTl and PMT2 two photomultipliers, on the same machine, dedicated to fluorochromes FLl and FL2 thanks to bandpass filters,

Fl_mis and F2_emis the light emitted by fluorochromes FL1 and FL2 excited by the laser of the machine, The total light received by the PMTl,

Fl2 receives the light received by the PMT1 from fluorochromes FL1 and FL2 respectively,

Ftot_2 received the total light received by the PMT2, Fl 2 received and F2_2 received the light received by the PMT2 of fluorochromes FL1 and FL2 respectively, and garlic, a21, al2, a22 constants between 0 and 1.

We then have:

Ftot lreçue = Fl_lreçue + F2_lreçue, Ftot_2revenue = Fl_2reçue + F2_2eceived.

Thus, by expressing Fl_lreçue and Fl_2reçue according to Ftot lreçue and Ftot_2reçue:

Fl_lreçue = garlic * Fl_emis,

F2_leceived = a21 * F2_MIS,

Fl_2 received = al2 * Fl_ed, F2_2 received = a22 * F2_emitted.

However, preferably, the fluorochromes and bandpass filters are chosen and specific so that one has: garlic »a21 with a21 ~ 0, and a22» al2 with al2 ~ 0.

So we have :

Fl_emis = Fl_lreçue / garlic,

F2_emis = F2_2 received / a22,

Ftot_lreçue = Fl_lreçue + a21 * F2_émis, Ftot_2revenue = al2 * Fl_émis + F2_2eceived,

Ftot lreçue = Fl lreçue + a21 / a22 * F2 2reviewed, Ftot_2 received = al2 / all * Fl_leceived + F2_2 received,

Ftot lreçue = Fl_lreçue

+ a21 / a22 * (Ftot_2referred - al2 / all * Fl_leceived),

Ftot_2 received = al2 / all * (Ftot_leceived - a21 / a22 * F2_2 received) + F2_2 received

Ftot_leceived = (1 - al2 / all) * Fl_received + a21 / a22 * Ftot_2 received,

Ftot_2revenue = al2 / all * Ftot_leceived

+ (1- a21 / a22) * F2_2 received.

Preferably, the bandpass filters are selected and selective so that al2 / all -0 and a21 / a22 ~ 0, whence

Fl_received ≈ Ftot_leceived - a21 / a22 * Ftot_2 received, and F2_2 received ≈ Ftot_2 received - al2 / all * Ftot_leceived

Thus, a21 / a22 and al2 / all correspond to CompX and CompY respectively.

The choice of CompX and CompY as constants determined by differences of the slopes along the abscissa and the ordinate respectively between the lines most parallel to the possible axes, comes from the fact that for these points, it is reasonable to imagine that Fl lreçue and F2 2revenue is close to 0, and therefore that

Ftot_l ≈ a21 / a22 * Ftot_2 received, Ftot_2 ≈ al2 / all * Ftot_leceived

Other methods of calculation can be envisaged, for example by defining a characteristic point such as a center of rotation (barycentre or other) of the graph representative of the first set of measurements around which the representative graph of the referent would have rotated by a certain angle, the angle being able to be determined by the method of the slopes here exposed.

From a graphical point of view, this slope correction step makes it possible to compensate for any angular or even rotational offset between the graph of the first set of measurements (test) and the referent.

Finally, according to the invention, the method comprises a step for compensating compression / expansion between said graphics. This step consists in solving the difference law (3), in other words calculating the (constant) parameters from the characteristic points of the histogram skeletons of the first set of test measurements and the reference histogram. The values of the first set of measurements are then recalculated according to this compression / expansion compensation.

Let in the given example: T '' '1 (f' 'Ix, t' '' Iy),

T '"2 (t'" 2x, t '"2y), and

T '' '3 (f' '3x, t' '' 3y) the coordinates of the respective points T1, T2 and T3 after this step of compression / expansion compensation, position correction and slope correction.

By generalizing for i = 1 to n (number of points of the test graph): T '''((f''ix,t''' iy), with rix = a _x * t '' ix ^bx and ri y = a _γ * t '' iy ^bY

We therefore have rlx = a _x * t '' lx ^bx and r3x = a _x * t''3x ^bx , that is:

Log (rlx) = Log (a _x ) + bX * Log (t "Ix), and Log (r3x) = Log (a _x ) + bX * Log (t" 3x),

from which by subtraction of these two equations: bX = (Log (r3x) - Log (rlx)) / (Log (t "3) - Log (t" l))

Since Log (a _x ) = Log (r3x) - bX * Log (t / '3x), we deduce the value of the parameter a _x .

The same calculations are performed along the y-axis of the ordinates to determine the values of the parameters _γ and _γ .

In the present invention, there is described a step sequence sequence of performing position correction, slope correction, and compensating for compression / expansion between a first graph corresponding to a portion of the first set of measurements and a second graph corresponding to a corresponding part of the referent. According to the invention the order of the above steps may be different, the invention covering any combination of these three steps.

Claims

A method of normalizing a set of measurements, comprising the steps of: a. performing a first set of measurements for a first sample given by first measuring means comprising at least a first photomultiplier, and b. providing a reference to the first set of measurements, said reference comprising a set of values corresponding to a second set of measurements made for a second sample given by second measuring means comprising at least one second photomultiplier, characterized in that it comprises in in addition to the steps of: c. calculating the parameter values of a difference law between the set of measurements and the set of values of the referent from subsets of the first set of measurements and corresponding subsets of the referent, and d. recalculate the values of the first set of measurements according to the parameters of the law the difference, the law of difference making it possible to compensate a compression / expansion between a first graph corresponding to a part of the first set of measurements and a second graph corresponding to a corresponding part of the referent.

The method of claim 1, further comprising at least one of the preliminary steps of performing: position correction, and slope correction between said graphs.

3. Method according to claim 2, wherein the position correction step comprises the steps of: selecting at least a first characteristic point relating to the first graph, and at least a second corresponding characteristic point relating to the graph of the referent, calculating the offset between the coordinates of the characteristic points, and update the values of the first set of measurements according to the calculated offset.

The method according to any of claims 2 or 3, wherein the step of correcting a slope comprises the steps of: calculating the difference in slope between two straight lines respectively formed by two characteristic points relating to the first graph and their points respective correspondents relative to the graph of the referent, and update the values of the first set of measurements according to this difference in slope.

5. Method according to any one of claims 3 or 4, wherein a characteristic point and its corresponding are the respective centroids of the first graph and the graph refer.

6. Method according to any one of claims 3 to 5, wherein the deviation law is of the type

Log (Itest) = γLog (Iref) ^Λ δ where: δ and Y are the parameters determined in step c, It is the measurement of the intensity of the electrical signal at the output of the first photomultiplier used for step a, and

Iref is the measurement of the intensity of the electrical signal at the output of the second photomultiplier used for step b.

The method of any one of the preceding claims, wherein the first sample and the second sample are the same.

The method of any of the preceding claims, wherein the first photomultiplier and the second photomultiplier are the same.

The method of any of the preceding claims, wherein at least the first set of measurements is performed on a first flow cytometry machine.

A computer program comprising program code instructions for performing the steps of the method of any one of the preceding claims when said program is run on a computer.