Fractional derivative reconstruction of forced oscillators

Lin, Guojian; Feeny, Brian F.; Das, Tuhin

doi:10.1007/s11071-008-9359-x

Cited by 9 publications

(5 citation statements)

References 37 publications

(52 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The more "fractured" an object, the larger is the value of the FD. Over the last two decades, FD has increasingly been applied to study a wide range of objects [5][6][7]. In biomedical imaging, FD is used as an indicator for the quantification of complexity of brain morphometry for normal adults and pathological studies.…”

Section: Introductionmentioning

confidence: 99%

Using three-dimensional fractal dimension to analyze the complexity of fetal cortical surface from magnetic resonance images

Shyu

Chen

et al. 2009

Nonlinear Dyn

View full text Add to dashboard Cite

This study aims to investigate the complexity of the developing fetal cortical surface based on the notion of fractal dimension (FD). Forty-four fetal MR images were selected at 22-36 weeks of gestational age (GA) and distributed between two groups: 32 normal fetal brains (excluding twins) and 12 abnormal fetal brains, including twins, mild ventricular dilata-ROC tion, Cornelia de Lange syndrome (small brain), and cortical dysplasia (developmental delay). We adopted the commonly used box-counting (BC) method to estimate the FD of the developing fetal cortical surface. Results from normal fetal brains show that the increase of cortical complexity is highly correlated with fetal developing weeks of GA. In addition, after 28 weeks of GA, the value of FD increases more rapidly because of the faster development of convolved folds. In comparison with results from the normal fetal group, the abnormal fetal brains were examined and the results show that: (1) mild ventricular dilatation has no significant developing difference compared with normal fetal brains; (2) twins had lower FD than that of normal fetal brains, which may be a delay of 2-3 weeks;(3) the case of cortical dysplasia also had low FD, indicating that developing delay may mean less cortical complexity. The results of the normal group are in good agreement with fetal brain development and demonstrate the effectiveness of FD as a promising means for the quantification of complexity of the fetal cortical surface.

show abstract

Section: Introductionmentioning

confidence: 99%

Using three-dimensional fractal dimension to analyze the complexity of fetal cortical surface from magnetic resonance images

Shyu

Chen

et al. 2009

Nonlinear Dyn

View full text Add to dashboard Cite

show abstract

“…, and 0 1 , E E are material constants , ( ) q D f t is the Riemann-Liouville fractional derivative operator; which can be defined as [7]:…”

Section: Dynamic Equationmentioning

confidence: 99%

Dynamic Behaviors of a Fractional Order Viscoelastic Two-Member Truss

Li¹,

Zhang²

2011

AMM

View full text Add to dashboard Cite

The fractional dynamics equation of a viscoelastic two-member truss system, in which fractional derivative model introduced to simulate the materials’ characteristics, is proposed. The simplified single DOF differential equation is developed combined with boundary conditions and symmetry. Dynamic behaviors of the fractional single DOF system with harmonic loads are discussed by numerical calculations. The results show that: the system may lead to chaotic motion via period-doubling bifurcations or intermittent routes; the dynamical character is greatly inflected by the varying of excitation amplitude or damping coefficient or fractional order.

show abstract

“…Thus, (5) can also be applied to the 3D information fractal dimension (FD A EBI ) for estimating the FD of the triangulated fetal cortical surface as…”

Section: Cortical Complexity Analysis Using 3d Information Fractal DImentioning

confidence: 99%

“…A more complex object has a larger FD. FD has been recognized as an extremely compact measure of the complexity of irregular objects, and has been increasingly studied in a wide range of fields and in relation to various applications [4][5][6]. In biomedical imaging, FD has been adopted as an index of brain complexity for normal adults and in pathological studies.…”

Section: Introductionmentioning

confidence: 99%

Analysis of fetal cortical complexity from MR images using 3D entropy based information fractal dimension

Shyu

Chen

et al. 2010

Nonlinear Dyn

View full text Add to dashboard Cite

The fetal cortical complexity is a significant quantification for assessing the development of fetal brain. This study attempts to quantify the development of fetal cortical complexity using the concept of fractal dimension (FD) analysis. Thirty-two fetal MR images were selected from Taipei Veterans General Hospital at 27-37 weeks of gestational age (GA). To investigate the FD of fetal cortical complexity, the entropy based information fractal dimension method (FD EBI ), which is modified from Box-Counting method, was adopted and extended from 2D to 3D. The FD results from overall whole fetal brains show that the increase of cortical complexity is highly correlated with the gestational age of the fetus. Moreover, the FD values of right hemispheric brain are larger than those of left hemispheric brain, show that the development of right hemispheric fetal cortical complexity earlier than the left. These results are in good agreement with normal fetal brain development and suggest that the FD is an effective means for the quantification of fetal cortical complexity.

show abstract

Fractional derivative reconstruction of forced oscillators

Cited by 9 publications

References 37 publications

Using three-dimensional fractal dimension to analyze the complexity of fetal cortical surface from magnetic resonance images

Using three-dimensional fractal dimension to analyze the complexity of fetal cortical surface from magnetic resonance images

Dynamic Behaviors of a Fractional Order Viscoelastic Two-Member Truss

Analysis of fetal cortical complexity from MR images using 3D entropy based information fractal dimension

Contact Info

Product

Resources

About