Interesting TOPICS in I FAC2014

1. Interesting TOPICS in IFAC2014 xiaodong sun MESA (Mechatronics, Embedded Systems and Automation)Lab School of Engineering, University of California, Merced E: xsun7@ucmerced.edu Phone:209 201 1947 Lab: CAS Eng 820 (T: 228-4398) SEP 8, 2014. Applied Fractional Calculus Workshop Series @ MESA Lab @ UCMerced

2. What attract my attention about ifac2014? topic 1: Relation between fractional order modelsand diffusion in the body topic 2: A fractional order impedance model to capture the structural changes in lungs

3. ★ Relation between fractional order modelsand diffusion in the body • Main idea: Fractal time series analysis and fractional calculushave been used to improve the modeling accuracy ofmany phenomena in natural sciences (West (2013)).This paper use fractional calculus to the modeling of diffusion in the human body. The respiratory diffusion, as well as drug diffusion, arediscussed and presented with their common mathematical framework. This paper suggests that emerging tools from fractional calculus are natural solutionsfor modeling complex phenomena in biological tissue.

4. ★ Relation between fractional order modelsand diffusion in the body • Respiratory diffusion:The complexsystem ofairways and lung texture facilitate air flow into the body to the capillaries. It hasbeen shown that a structural, geometrical and morphologicalmodeling leads to fractional orderimpedance models (Ionescu (2013)). Carbon dioxide (CO2)， Oxygen transport: The systemic capillariesdeliver oxygen to the tissues and remove carbon dioxide . fig a the gas exchange in the blood capillaries of the lungs and systemic circulation.

5. fig b the heat transfer through a sphere is represented (Levitzky (2007)). ★ Relation between fractional order modelsand diffusion in the body Sphere heat transfer (diffusion) modeling for the respiratory system: Cellular level Diffusion is performed with energy loss , producing heat. Here it employ heat unidirectional conduction in a homogeneous material with a spherical geometry. Problem consistsin computing the heating temperature Tin(t) at the innersurface of a sphere of radius r1. Heating temperature T(r，t) is uniform on any spherical slice of radius r ( fig1b). is the flux passing through the sphere. Assuming the heat conduction is isotropic, theheat diffusion is an unidirectional phenomenon governedby the following equations:

6. ★ Relation between fractional order modelsand diffusion in the body Sphere heat transfer (diffusion) modeling for the respiratory system: the thermal impedance of the spherebehaves like a non-integer integrator whose order is equalto 0.5: Conclusion： respiratory diffusion with loss of energy and heat production, can be modeled by fractional order impedance models.

7. A fractional order impedance model tocapture the structural changes in lungs Main idea: Analysis the correlation between the structural changes occurringin the lungs and the corresponding variations in the fractional order value of an impedancemodel. The paper discussed how variations in the wall thickness, cross- sectional area and elasticmoduli in distal airways involved in respiratory process affect changes in the fractional ordervalue. Two lumped models were discussed: i) a theoretical model derived from morphologicalinformation and ii) a lumped parametric model.

8. The term airway remodeling refers to the process of modfication and sustained disruption of structural cellsand tissues leading to a new airway-wall structure withimplicit new functions. Airway remodeling is supposedto be a consequence of long-term airway diseases. The 3D structure of the lung like honeycomb structure of thin-walled septa which form a fractal network (Hogg et al. (2004); Ionescu et al. (2009a)). Changes in mechanical properties of the lung tissue by pathology will influence this process. A fractional order impedance model tocapture the structural changes in lungs

9. Ionescu et al. (2009b) developed an electrical analogy to transmission for the mechanical parameters in the elastic and viscoelastic airways. The model was based on the geometrical parameters: radius and wall thickness (R; h), viscosity and density , the length of an airway tube. A fractional order impedance model tocapture the structural changes in lungs

10. The respiratory tract can be approximated by its electrical analogue, current denotes flow changes and voltage denotes pressure changes. According to morphological structure of the lungs, the quasi-fractal structure of the lungs may be employed, so a simplied ladder network with recurrent impedance elements of the form: A fractional order impedance model tocapture the structural changes in lungs

11. Conclusion:The paper provided a correlation between the struc- tural changes occurring in the lungs and the corresponding variations in the fractional order value of an impedance model. The relationship between fractional order term in the lungs has been related to changes in viscoelasticity. The results indicate that a correlation analysis is possible for various degrees of obstruction and effects may be directly related to the identified fractional order value. Fractional calculus may be a way to detect lung disease. A fractional order impedance model tocapture the structural changes in lungs

12. Thank you!