# Numerical Computation for MRE (Magnetic Resonance Elasticity) by Applying Numerical Differentiation Method

### Kazuaki Nakane

#### Abstract

Palpation is a standard medical method to detect of abnormalities of the human body, because a pathological state of soft tissues is often correlated with changes in stiffness. However, a pathological lesion may be undetectable by palpation if it is located deep in the body or if it is too small. Recently, new technics are developing to identify stiffness (Young’s modulus). The observed data contain noise, it prevent to substitute the data for the mathematical model equation of the human body. Because the model equation includes the second differential terms. “Numerical differentiation” is a numerical method to determine the derivatives of an unknown function from the given noisy values of the unknown function at the scattered points. In this talk, we will apply this method to the noisy data, and introduce numerical results.

#### References

- G. Nakamura, S. Wang and Y. Wang, Numerical differentiation for the second order derivatives of functions with two variables, preprint.
- Y. B. Wang, Y. C. Hon and J. Cheng, Reconstruction of High Order Derivatives from Input Data, Submitted to Journal of Inverse and Ill-posed Problems(2004).
- Y. B. Wang and T. Wei, Numerical Differentiation for two-dimensional scattered data, Submitted to Journal of Mathematical Analysis and Applications(2004).

#### Paper Citation

#### in Harvard Style

Nakane K. (2008). **Numerical Computation for MRE (Magnetic Resonance Elasticity) by Applying Numerical Differentiation Method** . In *Proceedings of the 2nd International Workshop on e-Health Services and Technologies - Volume 1: EHST, (ICSOFT 2008)* ISBN 978-989-8111-56-2, pages 73-77. DOI: 10.5220/0001896600730077

#### in Bibtex Style

@conference{ehst08,

author={Kazuaki Nakane},

title={Numerical Computation for MRE (Magnetic Resonance Elasticity) by Applying Numerical Differentiation Method},

booktitle={Proceedings of the 2nd International Workshop on e-Health Services and Technologies - Volume 1: EHST, (ICSOFT 2008)},

year={2008},

pages={73-77},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0001896600730077},

isbn={978-989-8111-56-2},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 2nd International Workshop on e-Health Services and Technologies - Volume 1: EHST, (ICSOFT 2008)

TI - Numerical Computation for MRE (Magnetic Resonance Elasticity) by Applying Numerical Differentiation Method

SN - 978-989-8111-56-2

AU - Nakane K.

PY - 2008

SP - 73

EP - 77

DO - 10.5220/0001896600730077