1. BONE MASS ASSESMENT BY MEANS OF HAND PHALANX RADIOABSORPTIOMETRY
J. M. SOTOCA1, M. A. BELMONTE2, J. M. IÑESTA3.
1 Unidad de Biofísica. Dpto de Fisiologia. U. de Valencia.
2 Unidad de Reumatología. Hospital General de Castellón.
3 Dpto de lenguajes y sistemas informáticos. U. de Alicante.

2. OBJECTIVES:
Obtain a robust system to automatically segment phalanxes whose average grey level variability in the segmented area is lower than 2%.
Establish the necessary theoretic conditions for the measurement methods by radiographic absorptiometry to be feasible.
Validate the data obtained compared to those obtained through using the DEXA system(Accudexa).

3. INTRODUCTION:
The osteoporosis implicate a low bone mass and the deterioration of the bone micro-architecture that produces an increasing of fracture risk.
There are a different techniques of bone mass determination: SPA, DPA, DEXA, RA (Compumed).
The biggest inconvenience of these techniques is the high cost of the equipment and the few of then that can be found only the principal cities.
This facts limit the predictive medical over risk population sectors.

4. ACTIVE SHAPES MODEL Examples set to train the model.
Establish homogeneous nodes between the differents shapes.
The set of examples forms a point distribution model (PDM) that reflects the variations of the shape contained in the training set.
This process involves an alignment phase among the different shapes: scale with a factor s, rotation with an angle and translation with a (tx, ty) vector minimising the expression:
where pref( x1,y1) y p(x2,y2) contain the co-ordinates of the nodes of the reference object and that we want to align.

5. W is the matrix of statistical weight of the distances and is obtained through the expression:
where Rkl is the distance between the points k and l, and VRkl is the variance of the distance over the shapes set.
M is the transformation matrix for aligning the vector p respect to pref

6. For last, we need calculate the value to s, , tx y ty using the following expression:

7. The modes of variation can be found using a principal component analysis over the covariance matrix. Using this, we can establish the eigenvalues i obtained for the main modes of variation.
The forms can be reconstructed from the main components of a PDM
where pm is the vector by the main form of the PDM, Pk is the matrix whose columns are the first k eigenvectors of the covariance matrix, and b is a vector of standard deviations for those k eigenvectors.

8. Description of the first three modes of variation in proximal phalanx.

9. PHALANX SEGMENTATION. We work over a smoothing the gradient image.
We have used a rectangle template to determinate which is the finger orientation ref.
We have introduced a rotation transformation to be applied on the resultant curve at each interación using the shape central moments.
At each iteration, the curve searches around perpendicular segments of each pount of the model, the candidate points in which the grey level gradiente Ix,y is maximum.
The curve will extend or contract itself through the variability of the model, preserving the shape during the process.

10. (a)
(b)
(c)
Segmentation in proximal phalanx: (a) The active contours begin with the mean shape oriented with the same angle found for the finger. (b) and (c) status of the model after 5 iterations and at the end of the process.

11. (a)
(c)
(b)
Segmentation in medial phalanx: (a) The active contours begin with the mean shape oriented with the same angle found for the finger. (b) and (c) status of the model after 5 iterations and at the end of the process.

12. (a)
(b)
(c)
Segmentation in metacarpus bone: (a) The active contours begin with the mean shape oriented with the same angle found for the finger. (b) and (c) status of the model after 5 iterations and at the end of the process.

14. MEASUREMENT OF THE BONE DENSITY.
We use aluminium as reference material with density and shape known.
If two regions with diferent density have the same grey level, and therefore they have the same optical opacity I / Io, we can relate the characteristics of the material (in this case bone) to other material whose characteristics are known that are also included in the image. Through the attenuation law to the intensity radiation, we can say that:
where xbone, xal are the mass per area unit (gr/cm2) of the bone and aluminium respectively, and ()bone, ()al are the coefficients of mass absorption (cm2/gr).

15. RADIOGRAPHIC PLATE CONDITIONS.
BEAM HARDNESS.
(Kilovoltage) => 46 KV => 35.5 KeV
PHOTONS NUMBER TO FALL IN THE RADIOGRAPHIC PLATE.
(miliamperage x time) => 50 mA x 0.05 sg => 2.5 mAs
PLATE EMULSION.
Mark.
Storage time and light exposition.
BEAM GEOMETRY.

16. VARIABILITY OF THE MEASUREMENTS.
For assessing the reliability of the measurement obtained and compare it to other standardised method, it is necessary a repetivity criterion. It is expressed through the variation coefficient (VC) and is defined as follows:
If we aim that these measurement have medical prognosis value, the variation coefficient should have less VC < 2%.
To assess the degree of variability of the measurements, two processes have to be clearly distinguished:
The variability introduced by the algorithms in the border location. A VC = 1.12% was found for medial phalanx on differents captures).
The variability produced by the beam shot conditions, inherent to the radiographic plate.

17. Diagram of the linear correlation between the measurement obtained both with a comercial device (accudexa) and those obtained through our method over medial phalanx of the heart finger.

18. CONCLUSIONS AND FUTURE LINES.
We have developed an automatic segmentation method of hand bones in radiographic images using point distribution models PDM.
The use of active curves and their variation modes of the shape to segment can solve problem to the proximity of other objects and with precision sufficient.
There is a good correlation linear between a comercial device (accudexa) and those obtained though our method.
Establish a simple protocol that guarantee the shot homogeneity.
Other development line is to check if the results can be improved eliminating the hand muscle tissue attenuation in the segmented region, and study whether one or two shots are needed to do this.