# US 9,519,823 B2 · Biomarker method

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- Number: US 9,519,823 B2
- Document ID: US9519823B2
- Status: Granted
- Kind: B2
- Application number: 14/046,651
- Filed: 2013-10-04
- Published: 2015-04-09
- Granted: 2016-12-13
- Earliest claimed: 2013-10-04
- Assignees: The University of Manchester
- Applicants: The University of Manchester
- Inventors: Richard John Byers; Christopher Rose
- Web page: https://patentgrep.com/patent/US9519823B2

## CPC

- G06V 20/698: {Matching; Classification}
- G06F 18/21345: {enforcing sparsity or involving a domain transformation}
- G06V 10/7715: {Feature extraction, e.g. by transforming the feature space, e.g. multi-dimensional scaling [MDS]; Mappings, e.g. subspace methods}
- G06V: IMAGE OR VIDEO RECOGNITION OR UNDERSTANDING
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)

## Abstract

In a technique for quantifying the spatial distribution of cells or sub-cellular structures, image data representing a spatial map of biomarkers is processed to obtain a set of coordinates. Each of the coordinates in the set denotes the location of a cell or sub-cellular structure represented by a biomarker or combination of biomarkers. The set of coordinates is processed into a two-dimensional symmetric (2N−1)×(2N−1) or 2N×2N matrix. The resulting matrix may be used for various purposes, such as assigning subjects clinical characteristics, and/or forming and/or testing scientific hypotheses for interventions, for example. Also described herein is an apparatus for performing the described technique.

## Claims

### Claim 1

A method for determining efficacy of a treatment in a subject, the method comprising:
I. quantifying a first spatial distribution of cells or sub-cellular structures in the subject before the treatment, at least in part by:
a. obtaining, using an imaging technique that allows spatial mapping of biomarker positivity, first image data corresponding to an image of a first tissue sample of a patient and comprising a first set of N biomarkers, wherein the first image data represents a spatial map of the first set of N biomarkers;
b. processing, by one or more processors, the first image data to obtain a first set of coordinates, wherein each coordinate of the first set of coordinates denotes the location of a cell or sub-cellular structure represented by a biomarker or combination of biomarkers of the first set of N biomarkers; and
c. processing, by the one or more processors, the first set of coordinates into a two-dimensional symmetric (2N−1)×(2N−1) or 2N×2N matrix (D1), wherein each element (i, j) of the D1 matrix indicates the frequency of a cell or sub-cellular structure represented by a first biomarker, or combination of biomarkers, of the first set of N biomarkers (i) being observed within a first interaction distance, dI 1 of a cell or sub-cellular structure represented by a second biomarker or combination of biomarkers (j) of the first set of N biomarkers, wherein i and j may be the same or different, and wherein the first set of coordinates obtained in step I.b. is a set of (x,y) coordinates;
II. applying the treatment to the subject;
III. quantifying a second spatial distribution of cells or sub-cellular structures in the subject after the treatment, at least in part by:
a. obtaining, using the imaging technique, second image data corresponding to an image of a second tissue sample of the subject taken after the treatment and comprising a second set of N biomarkers, wherein the second image data represents a spatial map of the second set of N biomarkers;
b. processing, by the one or more processors, the second image data to obtain a second set of coordinates, wherein each coordinate of the second set of coordinates denotes the location of a cell or sub-cellular structure represented by a biomarker or combination of biomarkers of the second set of N biomarkers; and
c. processing, by the one or more processors, the second set of coordinates into a two-dimensional symmetric (2N−1)×(2N−1) or 2N×2N matrix (D2), wherein each element (i, j) of the D2 matrix indicates the frequency of a cell or sub-cellular structure represented by a first biomarker, or combination of biomarkers, of the second set of N biomarkers (i) being observed within a second interaction distance, dI 2, of a cell or sub-cellular structure represented by a second biomarker or combination of biomarkers (j) of the second set of N biomarkers, wherein i and j may be the same or different, and wherein the second set of coordinates obtained in step III.b. is a second set of (x,y) coordinates; and
IV. comparing the quantified first spatial distribution determined in step I with the quantified second spatial distribution determined in step III in order to determine efficacy of the treatment in the subject.

### Claim 2 (depends on 1)

The method of claim 1, wherein the frequency is the relative frequency.

### Claim 3 (depends on 1)

The method of claim 1, wherein each of steps I.c. and III.c comprises:
i. assigning a binary vector π=(πs1, . . . , πsN) to each set of coordinates (x,y) to confirm the presence of a biomarker, wherein sk denotes the kth marker; and
ii. assigning a number to each binary vector, wherein the number represents a matrix row or column index number.

### Claim 4 (depends on 3)

The method of claim 3, wherein the number is assigned in step (ii) according to a binary place-value scheme.

### Claim 5 (depends on 1)

The method of claim 1, wherein each of steps I.b. and III.b comprises processing the respective image data to obtain a set of spatial coordinates (x′, y′), wherein each spatial coordinate denotes the location of a group of one or more cells or sub-cellular structures represented by the biomarker or combination of biomarkers.

### Claim 6 (depends on 1)

The method of claim 1, wherein each of steps I.b. and III.b comprises:
a. processing the respective image data to obtain
i. a set of spatial coordinates (x′, y′), wherein each spatial coordinate denotes the location of a group of one or more cells or sub-cellular structures represented by the biomarker or combination of biomarkers, and
ii. a set of region areas, wherein each area represents the two-dimensional surface of each group represented by a biomarker or combination of biomarkers;
b. defining a maximum area for individual cells or sub-cellular structures in the image;
c. discarding groups with region areas larger than the maximum area; and
b. combining the spatial coordinates (x′, y′) that are within a pairing distance, dP, of each other to obtain the set of (x, y) coordinates.

### Claim 7 (depends on 1)

The method of claim 1, wherein each of steps I.c. and III.c. comprises
forming a two-dimensional, symmetric intermediate matrix, wherein each element of the matrix indicates the distance between every combination of coordinates (x,y), and
discarding, for each row or column of the matrix, the entries equal to zero or greater than the interaction distance dI.

### Claim 8 (depends on 1)

The method of claim 1, wherein the method each of steps I and III further comprises:
d. generating a scalar summary statistic from the respective matrix.

### Claim 9 (depends on 8)

The method of claim 8, wherein the scalar summary statistic is selected from:
i. energy, DE=Σi≦j,jDi,j2;
ii. Shannon entropy, H(D)=−Σi≦j,jDi,j logb Di,j, wherein b is preferably equal to 2; and
iii. maximum Dmax=maxi,jDi,j.

### Claim 10 (depends on 8)

The method of claim 8, wherein each of steps I.d. and III.d. further comprises averaging the scalar summary statistic, and relating that average to one or more clinical characteristics.

### Claim 11 (depends on 10)

The method of claim 10, wherein the average is related to the one or more clinical characteristics by applying one or more thresholds to the average value.

### Claim 12 (depends on 11)

The method of claim 11, wherein the threshold is determined via optimisation and statistical survival analysis.

### Claim 13 (depends on 12)

The method of claim 12, wherein the optimisation of the threshold is determined according to formula (1):
γ
T
*
=
arg
⁢
⁢
max
γ
T
⁢
χ
2
⁡
(
s
,
g
γ
T
⁡
(
γ
)
)
wherein for each summary statistic of n subjects the vector γ=(γ1, . . . , γn);
wherein χ2(s,g) is a function returning a test statistic of a survival analysis of subjects with survival times s=(s1, . . . , sn) assigned to groups g=(g1, . . . , gn), wherein gi is a member of a set of two survival groups, and wherein the test statistic is maximised when the groups are maximally distinct in terms of their survival characteristic; and
wherein the function grT returns a vector whose ith element is the group assignment of the ith subject resulting from the application of threshold γT to each element of the vector γ.

### Claim 14 (depends on 10)

The method of claim 10, wherein one of the one or more clinical characteristics is a category that indicates how long the subject may survive after a clinical event associated with a disease.

### Claim 15 (depends on 14)

The method of claim 14, wherein the clinical event is selected from diagnosis, beginning treatment, finishing treatment, relapse after treatment and remission after treatment.

### Claim 16 (depends on 1)

The method of claim 1, further comprising:
V. directing further treatment of the subject based on the determined efficacy of the treatment.

### Claim 17 (depends on 1)

The method of claim 1, further comprising:
V. treating the subject based on the determined efficacy of the treatment.