Presented at the COMSOL Conference 008 Boston Sheer, F.J. 1, Ghadal, S.N. 1 Mechancal Engneerng Department, Oho State Unversty, Columbus, OH, sheer.4@osu.edu Bomedcal Engneerng Department, Oho State Unversty, Columbus, OH, ghadal.1@osu.edu COMSOL Conference 008
Background and Motvaton Eustachan Tube (ET) connects the Mddle Ear to the Nasopharyn. ET has three prmary functons: Dranage of ME flud Equlbrate ME pressure Protect ME from Pathogens ET dysfuncton has been drectly lnked to Otts Meda. Otts Meda has an annual healthrelated cost of $4 bllon dollars n the US. [1] Reprnted from Bluestone, Charles D, and Klen, Jerome O., Otts Meda n Infants and Chldren Thrd edton, W.B. Saunders Company, 001
Modelng Goals In the clncs, we can perform a dagnostc procedure called a Forced Response Test (FRT) Patent s hooked up to epermental apparatus shown above and asked to swallow Frst Goal: Create a transent COMSOL model that can replcate FRT results to serve as model valdaton Use valdated model to eplore other parameters nvolved n ET functon
Epermental Data Normal ET Functon: R v (mmh O/cc/mn) 40 30 0 10 0 Resstance P/Q Epermental Rv 1 3 4 5 6 Tme (seconds) Patents wth ET dysfuncton: R v (mmh O/cc/mn) 30 Epermental (Inflamed) 5 0 15 10 5 0.5 3.0 3.5 4.0 4.5 5.0 5.5 Tme (seconds)
Structure of the Eustachan Tube Defne Cross Sectons Loft Cross Sectons Full 3D CAD Model y (Superor) Nasopharyn z (Dstal) (Lateral) TVPM Cartlage Lumen Mddle Ear LVPM Glandular Tssue Hamulus
Fnal Analyzed 3D Geometry Green doman s the Cartlage Red doman s the Fatty Tssue Blue doman s the Lumen Openng
Sold Mechancs Propertes Both Cartlage and Glandular Tssue are represented by Mooney Rvln Hyperelastc materal models. E cart 300kPa [,3] E Gland 50kPa [,3] κ E 3(1 υ ) C 1 E 4(1 +υ) 1 C J X W hyp P where u u Y Z W hyp ( I 3) + κ( ) 01 1
Sold Boundary Condtons Boundary Condtons: Attachment of ET to the cranal base of the skull Attachment of soft tssue to the bony portons of the ET at the promal and dstal ends Appled Loads: Tensor Vel Palatn (TVP) muscle force Levator Vel Palatn (LVP) muscle force Flud forces
Sold Boundary Condtons (cont) All TVPM load vectors pont to the poston of the Pterygod Hamulus All LVPM load vectors are normal to the appled surface
Sold Flud Couplng Arbtrary Lagrange Euleran (ALE) equatons 0 j X Z Y X X j z y where & In the Sold Doman, flud force s appled on the nterface boundares In Flud Doman, veloctes from sold deformaton s appled to nterface boundares T n p n T )) ) ( ( ( u u I + + η σ y T y y n p n T )) ) ( ( ( u u I + + η σ z T z z n p n T )) ) ( ( ( u u I + + η σ t u u t v v t w w where u, v, and w are the sold dsplacements and u, v, and w are the flud veloctes
Flud Doman Due to the complety of the geometry, a coarse, tetrahedral mesh s used wth hgh order elements to accommodate the large dsplacements wthout any element collapse. Incompressble Contnuty and Naver Stokes equatons 0 v ρ j j v p v v t v + + μ ρ ρ w v u v where Flud equatons are solved n the movng reference frame!!
Model Results Sold Dsplacement feld and Flud Velocty vectors 510-4 m YZ ε eff ( ε X + εy + ε Z ) + ( ε XY + ε XZ + ε 3 ) Effectve Stran 0.35 Model Troubles: Statc solutons only Model unstable Fcttously vscous flud doman Sold Flud couplng only 0 m 0
Test Model Anatomcally correct lumen openng Lumen openng surrounded by cylnder of cartlage Cylnder s loaded wth a unform, outward radal force to epand lumen openng.
Test Model Results
Test Model Results
Future Work Incorporate a vscoelastc materal model for the Fatty Tssue E 1 E η Smulate the dranage/flow of hghly vscous mucus through the ET U Through the use of Steered Molecular Dynamcs, create a multscale model whch ncludes molecular adhesons Flud-mucosa layer ME or bronch γ μ F a E F m Soft tssue elements Nasal Cavty or Alveol Resstance to Arflow (mmh O/cc/mn) 100 75 50 5 Irreversble Constrcton!! 0 39.5 40.0 40.5 41.0 41.5 4.0 4.5 Tme (seconds)
Acknowledgments Ths work was supported by NIH 5R01DC00730 and NIH 5P50DC007667. References 1. Bondy, J., et al., Drect ependtures related to Otts meda dagnoses: etrapolatons from a pedatrc medcad cohort. Pedatrcs, 000. 105:p. 7. Hung, C.T., et al., A paradgm for functonal tssue engneerng of artcular cartlage va appled physologc deformatonal loadng. Ann Bomed Eng, 004. 3: p. 35 49. 3. Krouskop, T.A., et al., Elastc modul of breast and prostate tssues under compresson. Ultrason Imagng, 1998. 0: p. 60 37.