Volume of retinal lesion

Greetings everyone,

I am trying to measure the volume of a retinal lesions in an image obtained using OCT. Each section parameters (X and Z parameters) and the distance between each scans are available. I studied a few paper and it seems that Cavalieri principle is the main method that have been used to measure the volume using the area (by ImageJ). I just wanted to be sure that the proposed method is the accurate method so I can measure the volume of lesions.

My scans of retinal lesion are atttached.

Proposed method to measure the retinal lesions:

It would be great if you could give me your opinion or any suggestions.

Thank you

Answer 1

[John D'Errico]

It seems clear. You have multiple slices. Compute the area of each slice. At that point, you could just sum the area of each slice, multiplied by the thickness of a slice. That would be the rectangle rule, an entirely valid estimator.

The paper suggests using trapezoidal rule, a little better estimator of the volume.

And the implementation is trivial. Compute the area of each slice, as a vector of areas, one element for each slice. Then call trapz, giving it the slice thickness as the X argument.

help trapz

 TRAPZ  Trapezoidal numerical integration.
    Z = TRAPZ(Y) computes an approximation of the integral of Y via
    the trapezoidal method (with unit spacing).  To compute the integral
    for spacing different from one, multiply Z by the spacing increment.
 
    For vectors, TRAPZ(Y) is the integral of Y. For matrices, TRAPZ(Y)
    is a row vector with the integral over each column. For N-D
    arrays, TRAPZ(Y) works across the first non-singleton dimension.
 
    Z = TRAPZ(X,Y) computes the integral of Y with respect to X using the
    trapezoidal method. X can be a scalar or a vector with the same length
    as the first non-singleton dimension in Y. TRAPZ operates along this
    dimension. If X is scalar, then TRAPZ(X,Y) is equivalent to X*TRAPZ(Y).
 
    Z = TRAPZ(X,Y,DIM) or TRAPZ(Y,DIM) integrates across dimension DIM
    of Y. The length of X must be the same as size(Y,DIM)).
 
    Example:
        Y = [0 1 2; 3 4 5]
        trapz(Y,1)
        trapz(Y,2)
 
    Class support for inputs X, Y:
       float: double, single
 
    See also SUM, CUMSUM, CUMTRAPZ, INTEGRAL.

    Documentation for trapz
       doc trapz

    Other uses of trapz

       codistributed/trapz    gpuArray/trapz