proceedings - International Tissue Elasticity Conference

102
Session MIP–3: Methods for Imaging Elastic Tissue Properties – III
Thursday, October 30 1:15P – 3:00P
052 ELASTIC MODULUS RECONSTRUCTION USING A NOVEL FAST FINITE ELEMENT MODEL.
Iman Khalaji 1 , Kaamran Rahemifar 2 , Abbas Samani 1 .
1 University of Western Ontario, London, Ontario, CANADA; 2 Ryerson University, Toronto, Ontario,
CANADA.
Background: Ultrasound (US) elastograms are known to have artifacts due to the stress uniformity
assumption used in strain imaging. To eliminate such artifacts, elastic modulus reconstruction
techniques based on inverse problems have been developed. While accurate, such techniques are
computer time demanding. This drawback would deprive US elastography from its attractive real–time
feature. As an attempt to address this drawback, we introduce a novel elastography reconstruction
technique. This technique is based on an accelerated finite element method (FEM) we have recently
developed [1]. While sufficiently accurate, this technique preserves the attractive real–time feature.
Aims: To assess the accuracy and speed of a novel elastography reconstruction technique using a phantom study.
Methods: The proposed technique is based on the iterative reconstruction technique developed by
Samani et al. [2] where the elastic modulus (E) is iteratively updated using Hooke’s law in conjunction
with the stress field calculated from FE analysis. To accelerate this technique, we have made two
modifications: limiting the number of iterations to one and using a novel accelerated FEM. The novel FEM
is based on the Statistical Shape Model (SSM) concept [3] where every shape, X, in a class of objects can
be represented by the summation of the mean shape Xmean and a linear combination of main modes of
variability P, i.e., X = Xmean + Pb. In our technique, the same concept is used in finding tissue
deformation. This means that for the same class of objects, similar boundary conditions and constitutive
model, the displacement field, U, can be obtained by summing the mean displacement field of the object
class, Umean, and a linear combination of the displacements’ principal modes Q, i.e., U = Umean + Qc. In
this equation, c and Q are a weight factor vector and the displacements principal modes, respectively. The
latter fields can be obtained by performing conventional FE analysis on a sufficient number of objects in
the class. For a new object not included in the class, b can be obtained easily. To find U corresponding to
this object, only c needs to be determined. To establish a relationship between the shape space and Finite
Element space, we employed a four–layer feed–forward back–propagation neural network (NN) that
outputs c for any new shape. To demonstrate this reconstruction method, we used a numerical prostate
phantom, which has a stiff inclusion with an inclusion to background modulus ratio of 5.
Results: Analysis of the phantom was conducted using ABAQUS to obtain the simulated strain field. A
class of 1000 prostate shapes was generated numerically by combining trigonometric functions with
random amplitudes with an ellipse. The shapes were first trained and an NN relationship between b and c
was obtained. For the prostate phantom (without the inclusion), b then c were calculated. Using c, U and
then the stresses were calculated and combined with the simulated strains to obtain the modulus image.
This reconstruction took only ~0.07 sec and compared to the strain image, the obtained image has fewer
artifacts and a higher contrast such that the modulus ratio was 3.5 compared to the correct value of 5.
Conclusions: The results demonstrate the feasibility of using the novel accelerated FE technique in
conjunction with Hooke’s law for modulus reconstruction. Although homogeneity assumption of tissue is
not correct, it shows better results compared to strain imaging, and it is almost real–time. Given the
limited shape variability of organs, this approach can be applied successfully in clinical applications.
Acknowledgements: The authors wish to thank NSERC for supporting of this research.
References:
[1] I. Khalaji, K. Rahemifar and A. Samani, “Statistical finite element model,” 30th Figure 1:
(a) (b)
(a) Modulus (E)
(c)
(d)
reconstruction by the
proposed method; (b)
Modulus (E) image; (c) εyy
calculated by ABAQUS;
(d) strain image.
International IEEE EMBS
Conference, pp.5577–5580, 2008.
[2] A. Samani et al “A constrained modulus reconstruction technique for breast cancer assessment,” IEEE–TMI,
20(9): 877–885, 2001.
[3] T. F. Cootes et al, Computer Vision and Image Understanding, 61(1): 38–59, 1995.
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