System and Method For Automatic Detection and Measurement of Malacia In The Airways

• US 20080009683A1
• Filed: 07/02/2007
• Published: 01/10/2008
• Est. Priority Date: 07/07/2006
• Status: Active Grant

• Current Assignee: Siemens Healthcare GMBH (Siemens AG)
• Original Assignee: Siemens Medical Solutions USA Incorporated (Siemens AG)
• Inventors: Bogoni, Luca, Hermosillo Valadez, Gerardo
• Granted Patent: US 8,195,269 B2
• Time in Patent Office: Days
• US Class Current: 600/300
• CPC Class Codes: A61B 5/085 Measuring impedance of respiratory organs or lung elasticity
• CPC Class Codes: A61B 6/5217 extracting a diagnostic or physiological parameter from medical diagnostic data
• CPC Class Codes: G06T 2207/10072 Tomographic images
• CPC Class Codes: G06T 2207/30061 Lung
• CPC Class Codes: G06T 7/0012 Biomedical image inspection
• CPC Class Codes: G06T 7/33 using feature-based methods
• CPC Class Codes: G06T 7/38 Registration of image sequences
• CPC Class Codes: G16H 50/30 for calculating health indices; for individual health risk assessment

Abstract

A method of detecting malacia in airways includes providing a plurality of 3-dimensional (3D) digital lung images acquired over an inhalation/exhalation cycle from a same subject, each said image comprising a set of intensities on a 3-dimensional grid of points, registering a successive pair of images, wherein a registration mapping of the point grid of one image is calculated, locating airways in each of said pair of images, and collecting those points between the airways in each of said pair of images, wherein a volume of said collected points is a measure of an extent of malacia in said airways.

Claims

1. A method of detecting malacia in airways, comprising the steps of:

providing a plurality of 3-dimensional (3D) digital lung images acquired over an inhalation/exhalation cycle from a same subject, each said image comprising a set of intensities on a 3-dimensional grid of points;

registering a successive pair of images, wherein a registration mapping of the point grid of one image is calculated;

locating airways in each of said pair of images; and

collecting those points between the airways in each of said pair of images, wherein a volume of said collected points is a measure of an extent of malacia in said airways.

2. The method of claim 1, wherein said registration mapping is a non-rigid registration mapping φ

that changes spatial coordinates corresponding to said point grid

$\left(\begin{array}{c}x\\ y\\ z\end{array}\right)\to <br><br>\left(\begin{array}{c}X\\ Y\\ Z\end{array}\right)$

from one image to the other defined by

$\{\begin{array}{c}X={\mathrm{\phi <br><br>}}_x<br><br>\left(x,y,z\right)=x+u_x<br><br>\left(x,y,z\right)\\ Y={\mathrm{\phi <br><br>}}_y<br><br>\left(x,y,z\right)=y+u_y<br><br>\left(x,y,z\right)\\ Z={\mathrm{\phi <br><br>}}_z<br><br>\left(x,y,z\right)=z+u_z<br><br>\left(x,y,z\right),\end{array}$

wherein u_x, u_y and u_z are displacements found according to a similarity measure between said pair of images.

3. The method of claim 2, wherein said registration mapping is locally rigid.

4. The method of claim 2, wherein a determinant |Dφ

|(x, y, z) of a Jacobian matrix Dφ

of said registration mapping

$D<br><br><br><br>\mathrm{\phi <br><br>}=\left(\begin{array}{ccc}\frac{\partial <br><br>{\mathrm{\phi <br><br>}}_1}{\partial <br><br>x}& \frac{\partial <br><br>{\mathrm{\phi <br><br>}}_1}{\partial <br><br>y}& \frac{\partial <br><br>{\mathrm{\phi <br><br>}}_1}{\partial <br><br>z}\\ \frac{\partial <br><br>{\mathrm{\phi <br><br>}}_2}{\partial <br><br>x}& \frac{\partial <br><br>{\mathrm{\phi <br><br>}}_2}{\partial <br><br>x}& \frac{\partial <br><br>{\mathrm{\phi <br><br>}}_2}{\partial <br><br>z}\\ \frac{\partial <br><br>{\mathrm{\phi <br><br>}}_3}{\partial <br><br>x}& \frac{\partial <br><br>{\mathrm{\phi <br><br>}}_3}{\partial <br><br>y}& \frac{\partial <br><br>{\mathrm{\phi <br><br>}}_3}{\partial <br><br>z}\end{array}\right),$

is approximately equal to 1.

5. The method of claim 4, further comprising calculating a quality factor Q of said registration mapping, wherein if said quality factor is greater than a predetermined threshold, accepting the registration, otherwise repeating said steps of registering the pair of images and calculating a quality factor until an acceptable registration is calculated.

6. The method of claim 5, wherein said quality factor Q is defined as

$Q=\frac{1}{2}$

∑

i = 1 2 

w i 

( α

i ) , 

wherein ${\mathrm{\alpha <br><br>}}_1=\frac{1}{N}<br><br>\underset{x,y,z}{\sum <br><br>}<br><br>\min <br><br>\left(<br><br>D<br><br><br><br>\mathrm{\phi <br><br>}<br><br><br><br>\left(x,y,z\right),\frac{1}{<br><br>D<br><br><br><br>\mathrm{\phi <br><br>}<br><br><br><br>\left(x,y,z\right)}\right),<br><br>{\mathrm{\alpha <br><br>}}_2=\underset{x,y,z}{\min }<br><br>\left(\min <br><br>\left(<br><br>D<br><br><br><br>\mathrm{\phi <br><br>}<br><br><br><br>\left(x,y,z\right),\frac{1}{<br><br>D<br><br><br><br>\mathrm{\phi <br><br>}<br><br><br><br>\left(x,y,z\right)}\right)\right),$

wherein N is the number points in the grid, and wherein w₁(α

₁) and w₂(α

₂) are sigmoid weighting functions that monotonically increase from 0 to 1 to penalize abnormal local deformations.

7. The method of claim 6, wherein the sigmoid weighting functions are

w₁(α

₁)=exp(−

A(1−

α

₁)^E1),

and

w₂(α

₂)=exp(−

B(1−

α

₂)^E2).

8. The method of claim 7, wherein A=B=10, E₁=4 and E₂=8.

9. The method of claim. 1, further comprising registering each successive pair of images in said time series of images, and for each pair with an acceptable registration mapping, growing a volume between the airways in each of said pair of images, and accumulating said volumes over all pairs of successive images.

17. The computer readable program storage device of claim 15, wherein a determinant |Dφ

|(x, y, z) of a Jacobian matrix Dφ

of said registration mapping,

$D<br><br><br><br>\mathrm{\phi <br><br>}=\left(\begin{array}{ccc}\frac{\partial <br><br>{\mathrm{\phi <br><br>}}_1}{\partial <br><br>x}& \frac{\partial <br><br>{\mathrm{\phi <br><br>}}_1}{\partial <br><br>y}& \frac{\partial <br><br>{\mathrm{\phi <br><br>}}_1}{\partial <br><br>z}\\ \frac{\partial <br><br>{\mathrm{\phi <br><br>}}_2}{\partial <br><br>x}& \frac{\partial <br><br>{\mathrm{\phi <br><br>}}_2}{\partial <br><br>x}& \frac{\partial <br><br>{\mathrm{\phi <br><br>}}_2}{\partial <br><br>z}\\ \frac{\partial <br><br>{\mathrm{\phi <br><br>}}_3}{\partial <br><br>x}& \frac{\partial <br><br>{\mathrm{\phi <br><br>}}_3}{\partial <br><br>y}& \frac{\partial <br><br>{\mathrm{\phi <br><br>}}_3}{\partial <br><br>z}\end{array}\right),$

is approximately equal to 1.

18. The computer readable program storage device of claim 17, the method further comprising calculating a quality factor Q of said registration mapping, wherein if said quality factor is greater than a predetermined threshold, accepting the registration, otherwise repeating said steps of registering the pair of images and calculating a quality factor until an acceptable registration is calculated.

19. The computer readable program storage device of claim 18, wherein said quality factor Q is defined as

$Q=\frac{1}{2}$

∑

i = 1 2 

w i 

( α

i ) , 

wherein ${\mathrm{\alpha <br><br>}}_1=\frac{1}{N}<br><br>\underset{x,y,z}{\sum <br><br>}<br><br>\min <br><br>\left(<br><br>D<br><br><br><br>\mathrm{\phi <br><br>}<br><br><br><br>\left(x,y,z\right),\frac{1}{<br><br>D<br><br><br><br>\mathrm{\phi <br><br>}<br><br><br><br>\left(x,y,z\right)}\right),<br><br>{\mathrm{\alpha <br><br>}}_2=\underset{x,y,z}{\min }<br><br>\left(\min <br><br>\left(<br><br>D<br><br><br><br>\mathrm{\phi <br><br>}<br><br><br><br>\left(x,y,z\right),\frac{1}{<br><br>D<br><br><br><br>\mathrm{\phi <br><br>}<br><br><br><br>\left(x,y,z\right)}\right)\right),$

wherein N is the number points in the grid, and wherein w₁(α

₁) and w₂(α

₂) are sigmoid weighting functions that monotonically increase from 0 to 1 to penalize abnormal local deformations.

20. The computer readable program storage device of claim 19, wherein the sigmoid weighting functions are

w₁(α

₁)→

exp(−

A(1−

α

₁)^E1),

and

w₂(α

₂)=exp(−

B(1−

α

₂)^E2).

21. The computer readable program storage device of claim 20, wherein A=B−

10, E₁=4 and E₂=8.

10. A method of detecting malacia in airways, comprising the steps of:

providing a pair of 3-dimensional (3D) digital lung images, each said image comprising a set of intensities on a 3-dimensional grid of points;

calculating a locally rigid registration mapping φ

that changes spatial coordinates corresponding to said point grid from one image (x,y,z) to the other (X,Y,Z) defined by

$\{\begin{array}{c}X={\mathrm{\phi <br><br>}}_x<br><br>\left(x,y,z\right)=x+u_x<br><br>\left(x,y,z\right)\\ Y={\mathrm{\phi <br><br>}}_y<br><br>\left(x,y,z\right)=y+u_y<br><br>\left(x,y,z\right)\\ Z={\mathrm{\phi <br><br>}}_z<br><br>\left(x,y,z\right)=z+u_z<br><br>\left(x,y,z\right),\end{array}$

wherein u_x, u_y and u_z are displacements found according to a similarity measure between said pair of images; and

calculating a quality factor of said registration mapping, wherein if said quality factor is greater than a predetermined threshold, the registration is accepted, and wherein said malacia is found from said registration.

11. The method of claim 10, further comprising providing a plurality of 3-dimensional (3D) digital lung images acquired over an inhalation/exhalation cycle from a same subject and registering each successive pair of images.

12. The method of claim 11, further comprising segmenting airways in each of said pair of images, and growing a volume between the airways in each of said pair of images, wherein said volume is a measure of an extent of malacia in said airways.

13. The method of claim 10, wherein said quality factor is defined as

$Q=\frac{1}{2}\; <li></li>\underset{i=1}{\overset{2}{\sum <br><br>}}<br><br>w_i<br><br>\left({\mathrm{\alpha <br><br>}}_i\right)$ $\mathrm{wherein}$ ${\mathrm{\alpha <br><br>}}_1=\frac{1}{N}<br><br>\underset{x,y,z}{\sum <br><br>}<br><br>\min <br><br>\left(<br><br>D<br><br><br><br>\mathrm{\phi <br><br>}<br><br><br><br>\left(x,y,z\right),\frac{1}{<br><br>D<br><br><br><br>\mathrm{\phi <br><br>}<br><br><br><br>\left(x,y,z\right)}\right),<br><br>{\mathrm{\alpha <br><br>}}_2=\underset{x,y,z}{\min }<br><br>\left(\min <br><br>\left(<br><br>D<br><br><br><br>\mathrm{\phi <br><br>}<br><br><br><br>\left(x,y,z\right),\frac{1}{<br><br>D<br><br><br><br>\mathrm{\phi <br><br>}<br><br><br><br>\left(x,y,z\right)}\right)\right),$

wherein N is the number points in the grid, wherein |Dφ

| is a determinant of a Jacobian matrix of φ

, and wherein w₁(α

₁) and w₂(α

₂) are sigimoid weighting functions that monotonically increase from 0 to 1.

14. A program storage device readable by a computer, tangibly embodying a program of instructions executable by the computer to perform the method steps for detecting malacia in airways, said method comprising the steps of:

providing a plurality of 3-dimensional (3D) digital lung images acquired over an inhalation/exhalation cycle from a same subject, each said image comprising a set of intensities on a 3-dimensional grid of points,

registering a successive pair of images, wherein a registration mapping of the point grid of one image is calculated;

locating airways in each of said pair of images; and

collecting those points between the airways in each of said pair of images, wherein a volume of said collected points is a measure of an extent of malacia in said airways.

15. The computer readable program storage device of claim 14, wherein said registration mapping is a non-rigid registration mapping φ

that changes spatial coordinates corresponding to said point grid

$\left(\begin{array}{c}x\\ y\\ z\end{array}\right)\to <br><br>\left(\begin{array}{c}X\\ Y\\ Z\end{array}\right)$

from one image to the other defined by

$\{\begin{array}{c}X={\mathrm{\phi <br><br>}}_x<br><br>\left(x,y,z\right)=x+u_x<br><br>\left(x,y,z\right)\\ Y={\mathrm{\phi <br><br>}}_y<br><br>\left(x,y,z\right)=y+u_y<br><br>\left(x,y,z\right)\\ Z={\mathrm{\phi <br><br>}}_z<br><br>\left(x,y,z\right)=z+u_z<br><br>\left(x,y,z\right),\end{array}$

wherein u_x, u_y and u_z are displacements found according to a similarity measure between said pair of images.

16. The computer readable program storage device of claim 15, wherein said registration mapping is locally rigid.

22. The computer readable program storage device of claim 14, the method further comprising registering each successive pair of images in said time series of images, and for each pair with an acceptable registration mapping, growing a volume between the airways in each of said pair of images, and accumulating said volumes over all pairs of successive images.