BONE MASS ASSESMENT BY MEANS OF HAND PHALANX RADIOABSORPTIOMETRY

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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.

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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).

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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.

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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.
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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

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For last, we need calculate the value to s, ?, tx
y ty using the following expression
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• 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.
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Description of the first three modes of variation
in proximal phalanx.
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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.

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(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.
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(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.
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(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.
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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).
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RADIOGRAPHIC PLATE CONDITIONS.

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

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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 lt 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.

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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.
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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.