# US 7,609,867 B2 · Method for determining a three-dimensional structure from a two-dimensional image, in particular a bone structure

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- Number: US 7,609,867 B2
- Document ID: US7609867B2
- Status: Granted
- Kind: B2
- Application number: 10/583,134
- Filed: 2003-12-17
- Published: 2007-06-21
- Granted: 2009-10-27
- Earliest claimed: 2002-12-17
- Assignees: Pascal Carceller
- Inventors: Laurent Pothuaud
- Web page: https://patentgrep.com/patent/US7609867B2

## CPC

- G06T 7/0012: {Biomedical image inspection}
- G06T: IMAGE DATA PROCESSING OR GENERATION, IN GENERAL

## Abstract

The object of the invention is a process for determining the mechanical resistance of a bone from a digitized two dimensional image, obtained by imaging, characterized in that there is carried out a correlation between the bone mineral density determined from this two dimensional image by any means suitable to this type of image, and a structural parameter obtained from the same two dimensional image.

## Claims

### Claim 1

A process for determining the mechanical resistance of a bone from a digitized two dimensional image, obtained by imaging, characterized in that a correlation is carried out between a bone mineral density determined from the two dimensional image by any means suitable to this type of image and a structural parameter α, the structural parameter α obtained from the same two dimensional image, wherein the structural parameter α is determined by a series of the following steps performed by a computational device configured to process the digitized two dimensional image:
a) choosing a point at random at a first pixel of the two dimensional image, wherein the first pixel has a gray level h(O);
b) choosing a straight line starting from the point and having a direction also determined at random;
c) moving a distance r along this straight line to a new point at a second pixel, h(r) being the gray level of the second pixel at the new point;
d) computing a variance of the gray levels with the formula: V(r)=[h(r)−h(O)]2;
e) tracing a curve associated with V(r) on a log-log scale; and
f) determining the slope of the curve as said parameter α.

### Claim 2 (depends on 1)

The process for determining the mechanical resistance of a bone according to claim 1, wherein steps a) to d) are repeated a number of times sufficiently great to make the mean variance function V(r) converge over an assembly of the repetitions.

### Claim 3 (depends on 1)

The process for determining the mechanical resistance of a bone according to claim 1, wherein the correlation between the bone mineral density obtained from the two dimensional image and said parameter α is evaluated from the two dimensional image according to a mathematical model:
Cu′=b0+b1*exp (b2*DMO)*60
wherein b0, b1, b2 are coefficients obtained by nonlinear regression and Cu′ is a prediction of an ultimate stress Cu of the bone.

### Claim 4 (depends on 1)

The process for determining the mechanical resistance of a bone according to claim 1, further comprising:
determining a correlation between the parameter α and a three dimensional parameter of a trabecular network of the bone.

### Claim 5 (depends on 4)

The process for determining the mechanical resistance of a bone according to claim 4, wherein the three dimensional parameter of the trabecular network of the bone is a connectivity density χv.

### Claim 6 (depends on 2)

The process for determining the mechanical resistance of a bone according to claim 2, wherein the correlation between the bone mineral density obtained from the two dimensional image and said parameter α is evaluated from the two dimensional image according to a mathematical model:
Cu′=b0+b1*exp (b2*DMO)*α
wherein b0, b1, b2 are coefficients obtained by nonlinear regression and Cu′ is a prediction of an ultimate stress Cu of the bone.

### Claim 7 (depends on 2)

The process for determining the mechanical resistance of a bone according to claim 2, further comprising:
determining a correlation between the parameter α and a three dimensional parameter of a trabecular network of the bone.

### Claim 8 (depends on 3)

The process for determining the mechanical resistance of a bone according to claim 3, further comprising:
determining a correlation between the parameter α and a three dimensional parameter of a trabecular network of the bone.