TRANSPORT IN BONE INTERSTITIAL

Transcription

1 NUMERICAL STUDY OF THE MASS TRANSPORT IN BONE INTERSTITIAL FLOW Emily Tung 1, *, Andrew Hsu 1, Hiroki Yokota 2, Tien-Min G. Chu 3 1 Dept. of Mechanical Engineering, Purdue University 2 Dept. of Biomedical Engineering, Purdue University 3 Dept. of Restorative Dentistry, Indiana University

2 Outline1 Introduction Computational model setup Result and Discussion Conclusion

3 Introduction Bone tissue is composed of compact and spongy bones Bone is 85% composed of solid material. Nutrients ts transport t occurs in the liquid filled space (very limited!! Less than 15% )

4 Introduction Enhance bone remodeling Bone mass loss and Osteoporosis Maintain and increase bone mass Exercise helps keep bone healthy. A loading of low level and high frequency maintains bone mass.

5 Introduction Lacuna-canaliculus network The porous space in bone and is filled with liquid Lacunae: contains osteocyte football shape cavities, long axis: 10μm Canaliculi: communicating between lacunae long gpp pipe, 0.3μm μ in diameter and 30μm μ in length

6 Lacuna-canaliculus network LACUNA (hole) for OSTEOCYTE BODY MATRIX CANALICULUS (tiny channel) for Gap junction contact with next osteocyte OSTEOCYTE PROCESS & FLUID FLOW

7 Introduction Measurement of species transport -- Fluorescent Recovery After Photobleaching (FRAP) 1. Fluorescent dye is injected 2. Photobleaching 3. Recovery 4. Saturated Simulating FRAP process(234)

8 Introduction The FRAP curve (234) It () = A(1 e τt ) Our dye dispersing curve e τ t = 1 I Ti t t i bt i d b fitti Time constant is obtained by curve fitting the dye dispersing curves

9 Introduction 1-D Transport equation (regardless chemical reactions) C v C D C + x = t x x x 0 Cyclic loading enhances mass transport analytical solution by Aris in 1960 Enhanced diffusivity vs. dimensionless frequency (K/D-1)/(delx x/a)^ dimensionless frequency

10 Introduction Navier-Stokes equation Dρ + ρ = Dt v 2 ρ + v v = p+ μ v+ f tt ( v ) 0 conservation of mass conservation of momentum where v v and f are dropped due to fully developed laminar flow and dbalanced dforce. μ and ρ are the fluid s viscosity and density P and v are pressure and flow velocity

11 Computational models The tube model Analysis of the species transport in pulsatile flow A numerical verification The L-C model A more realistic model Similar dimension and geometry The validity of the linear L-C model The flow shear stress on cell process

12 BC of the Tube Model Length: 6mm, radius:0.17mm 017 The bulk fluid: similar to water Same properties of the dye and the bulk fluid Pressure inlet: Magnitude change with a fixed frequency. Frequency change with a fixed magnitude. Pressure outlet: gauge g pressure is zero No slip wall Dye concentration

13 The tube model Species transport behavior when fluctuation is loaded.

14 Results and Discussion The increase in pressure magnitude enhances transport. The increase in loading frequency enhances transport Pressure inlet = Psin( ωt), ω=2π f dye concentration p=2.5 p=1 p=0 1.05E E+00 enhanced by frequencies f=0.5 f=10 f=2 f= location(1e-4m) dye concentration 9.50E E E E location(1e-4m) P=0, 1, and 2.5 when f is fixed at 2Hz f=0, 0.5, 2 and 10 when P is fixed at 1pa

15 Results and Discussion The conversion from the characteristic time constant to effective diffusion coefficient. f The effective diffusivity (K) 2.70E E E E E-07 K/D β Where β is the dimensionless frequency, and K/D is the transport enhancement

16 Results and Discussion The enhancement of species transport against frequency K/D for D= 2.7e-7 K/D 3.50E E E E E E E E beta

17 The L-C model Canaliculus: long pipes Lacuna: sphere Significant change in size between lacunae and canalicui: alternate model, a linear L-Csystem Pressure outlet: gauge pressure is zero No slip wall Dye concentration

18 The L-C model The effect of number of canaliculus on species transport behavior The total contact area: μm 2 Change the number of canaliculus N D(μm) N: The number of canaliculus contacting a single lacuna

19 The L-C model

20 Results and Discussion The diffusion i time constant t resulted by different numbers of canaliculi Canaliculus Number Time constant(s)

21 Results and Discussion The diffusion behavior of 4 canaiculi without pressure fluctuation

22 Results and Discussion Diffusion i under cyclic loading time co onstant (s) frequency effect on transport in a perspective of time constant Loading 5 frequency loading frequency (Hz) Diffusion time constant as a result of increase in fluctuation frequency Time constant (s)

23 Results and Discussion Flow shear stress on the cell process Shear stress on canaliculi walls Shear stress increases linearly as the amplitude of pressure fluctuation increases Shear stress on lacunae walls

24 Conclusions Frequency is more important t than amplitude of a pressure fluctuation. High frequency with low level loading. The numerical result of enhancement to frequency agrees qualitatively Narrow canaliculi lilimit itflow and species transport t Linear L-C model is able to represent the entire system in terms of transport enhancement study Shear stress on cell process is greater on inner than outer walls Shear stress is greater in canaliculi than in lacunae

25 Outline2 The dose design in bone scaffold Model Setup Boundary Conditions Results and Discussion Conclusion

26 The dose design in bone scaffold Dose placement and concentration effect on BMP-2 distribution after diffusion to maximize the effect of BMP-2 Accelerate bone bridging in the segmental defect

27 Model Setup (3-D simulation) Doses divide the scaffold into equal intervals Dose concentration = 100% / number of dose The 1-dose model The shaded area is used in FLUENT with axisymmetrical solution and symmetric boundaries The 2-dose model

28 Boundary Conditions The surrounding tissue of the scaffold is infinite flow flux at boundary is infinite BMP-2 dose concentration ti initial condition Porosity of the scaffold 0.5

29 Results and discussion The snap shots time when the concentration of the 1- dose model has dropped to 60%, 37%, 13%, and 5%. The snap shot of the 1-dose model The snap shot of the 2-dose model

30 Results and discussion The peak retention (%) comparison after diffusion of 0.52, 1.21, 5.79, and weeks The comparison of the fraction of the initial dose concentration Snapshot time t0 t1 t2 t3 t4 case case case case dose model has the most retention The fraction of the initial iti dose concentration ti is similar il to each other at the same diffusion time for case 2-4

31 Conclusion The concentration profile shows the local concentration of the surface area A good start to study if there exists a minimal effective BMP-2 concentration within a minimal surface area BMP-2 distributes evenly in the scaffold by diffusion of weeks

32 Any Question?