An inverse method to determine the mechanical properties of the iris in vivo

BioMedical Engineering OnLine

Kunya Zhang¹  Xiuqing Qian¹  Xi Mei¹  Zhicheng Liu¹ 

[1] School of Biomedical Engineering, Capital Medical University, Beijing 100069, China

关键词: Multi-island genetic algorithm;    Finite element method;    In vivo experiment;    Iris;   

Others  :  793251
DOI  :  10.1186/1475-925X-13-66

 received in 2013-12-30, accepted in 2014-05-23,  发布年份 2014

【 摘 要 】

Background

Understanding the mechanical properties of the iris can help to have an insight into the eye diseases with abnormalities of the iris morphology. Material parameters of the iris were simply calculated relying on the ex vivo experiment. However, the mechanical response of the iris in vivo is different from that ex vivo, therefore, a method was put forward to determine the material parameters of the iris using the optimization method in combination with the finite element method based on the in vivo experiment.

Material and methods

Ocular hypertension was induced by rapid perfusion to the anterior chamber, during perfusion intraocular pressures in the anterior and posterior chamber were record by sensors, images of the anterior segment were captured by the ultrasonic system. The displacement of the characteristic points on the surface of the iris was calculated. A finite element model of the anterior chamber was developed using the ultrasonic image before perfusion, the multi-island genetic algorithm was employed to determine the material parameters of the iris by minimizing the difference between the finite element simulation and the experimental measurements.

Results

Material parameters of the iris in vivo were identified as the iris was taken as a nearly incompressible second-order Ogden solid. Values of the parameters μ₁, α₁, μ₂ and α₂ were 0.0861 ± 0.0080 MPa, 54.2546 ± 12.7180, 0.0754 ± 0.0200 MPa, and 48.0716 ± 15.7796 respectively. The stability of the inverse finite element method was verified, the sensitivity of the model parameters was investigated.

Conclusion

Material properties of the iris in vivo could be determined using the multi-island genetic algorithm coupled with the finite element method based on the experiment.

【 授权许可】

   
2014 Zhang et al.; licensee BioMed Central Ltd.

【 图 表 】

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【 参考文献 】

• [1]Curran EJ: A new operation for glaucoma involving a new principle in the aetiology and treatment of chronic primary glaucoma. Arch Ophthalmol 1920, 49:131-155.
• [2]Niyadurupola N, Broadway DC: Pigment dispersion syndrome and pigmentary glaucoma - a major review. Clin Exp Ophthalmol 2008, 36:868-882.
• [3]Heys J, Barocas VH: Mechanical characterization of the bovine iris. J. Biomech 1999, 32:999-1003.
• [4]Whitcomb JE, Barnett V, Olsen TW, Barocas VH: Ex vivo porcine iris stiffening due to drug stimulation. Exp Eye Res 2009, 89:456-461.
• [5]Lei Y, Zhang K, Chen C, Song H, Li T, Lin D, Liu Z: Experimental research on the mechanical properties of porcine iris. Clin Biomech 2008, 23:S83-S87.
• [6]Whitcomb JE, Amini R, Simha NK, Barocas VH: Anterior–posterior asymmetry in iris mechanics measured by ation. Exp Eye Res 2011, 93:475-481.
• [7]Yoo L, Reed J, Shin A, Kung J, Gimzewski JK, Poukens V, Goldberg RA, Mancini R, Taban M, Moy R: Characterization of ocular tissues using microindentation and hertzian viscoelastic models. Invest Ophthalmol Vis Sci 2011, 52:3475-3482.
• [8]Tabandeh H, Thompson GM, Kon C, Bolton T: Phenylephrine and pilocarpine in the treatment of post-operative irido-corneal adhesion. Eye 1995, 9:452-455.
• [9]Yamaji K, Yoshitomi T, Usui S, Ohnishi Y: Mechanical properties of the rabbit iris smooth muscles. Vis Res 2003, 43:479-487.
• [10]Jin Y, Xue-Feng B, Xiu-Qing Q, Qian W, Wang Jian-Xia L, Jin-Qiu QH-Y, Zhi-Cheng L: Measuring iris elastic modulus based on holistic iris deformation experiment. J Med Biomech 2010, 25:182-185.
• [11]Jouzdani S: Biomechanical characterization and computational modeling of the anterior eye. Dissertation of the University of Minnesota 2003, 85-117.
• [12]Manickam K, Machireddy RR, Seshadri S: Characterization of biomechanical properties of agar based tissue mimicking phantoms for ultrasound stiffness imaging techniques. J Mech Behav Biomed 2014, 35:132-143.
• [13]Elsheikh A, Kassem W, Jones SW: Strain-rate sensitivity of porcine and ovine corneas. Acta Bioeng Biomech 2011, 13:25-36.
• [14]Karimi A, Navidbakhsh M, Alizadeh M, Shojaei A: A comparative study on the mechanical properties of the umbilical vein and umbilical artery under uniaxial loading. Artery Res 2014, 8:51-56.
• [15]Untaroiun CD, Lu YC: Material characterization of liver parenchyma using specimen-specific finite element models. J Mech Behav Biomed 2013, 26:11-22.
• [16]Rashid B, Destrade M, Gilchrist MD: Mechanical characterization of brain tissue in compression at dynamic strain rates. J Mech Behav Biomed 2012, 10:23-38.
• [17]Jingwen H, Klinich KD, Miller CS, Nazmi G, Pearlman MD, Schneider LW, Rupp JD: Quantifying dynamic mechanical properties of human placenta tissue using optimization techniques with specimen-specific finite-element models. J. Biomech 2009, 42:2528-2534.
• [18]Sparrey CJ, Keaveny TM: Compression behavior of porcine spinal cord white matter. J. Biomech 2011, 44:1078-1082.
• [19]Martínez-Martínez F, Rupérez MJ, Martín-Guerrero JD, Monserrata C, Lago MA, Pareja E, Bruggerc S, López-Andújar R: Estimation of the elastic parameters of human liver biomechanical models by means of medical images and evolutionary computation. Comput Meth Prog Bio 2013, 111:537-549.
• [20]Flynn C, Taberner AJ, Nielsen PMF, Fels S: Simulating the three-dimensional deformation of in vivo facial skin. J Mech Behav Biomed 2013, 28:484-494.
• [21]Koo TK, Cohen JH, Zheng Y: A mechano-acoustic indentor system for in vivo measurement of nonlinear elastic properties of soft tissue. J Manip Physiol Ther 2011, 34:584-593.
• [22]Bosboom EMH, Hesselink MKC, Oomens CWJ, Bouten CVC, Drost MR, Baaijens FPT: Passive transverse mechanical properties of skeletal muscle under in vivo compression. J. Biomech 2001, 34:1365-1368.
• [23]Brinkhues S, Klawonn A, Rheinbach O, Schröder J: Augmented Lagrange methods for quasi- incompressible materials- Applications to soft biological tissue. Int J Numer Meth Biomed Engng 2013, 29:332-350.
• [24]Horgan CO, Murphy JG: Simple shearing of soft biological tissues. Proc R Soc A 2011, 467:760-777.
• [25]Harb N, Labed N, Domaszewski M, Peyraut F: A new parameter identification method of soft biological tissue combining genetic algorithm with analytical optimization. Comput Method Appl M 2011, 200:208-215.
• [26]Aptel F, Denis P: Optical Coherence Tomography quantitative analysis of iris volume changes after pharmacologic mydriasis. Ophthalmol 2010, 117:3-10.
• [27]Moran CM, Pye SD, Ellis W, Janeczko A, Morris KD, McNeilly AS, Fraser HM: A comparison of the imaging performance of high resolution ultrasound scanners for preclinical imaging. Ultrasound Med Biol 2011, 37:493-501.
• [28]Sampaolesi R, Sampaolesi JR, Zárate J: The Glaucomas. Berlin Heidelberg: Springer-Verlag; 2014:294-295.
• [29]Silver DM, Quigley HA: Aqueous flow through the iris-lens channel: estimates of differential pressure between the anterior and posterior chambers. J Glaucoma 2004, 13:100-107.
• [30]Amini R, Barocas VH: Anterior chamber angle opening during corneoscleral indentation: the mechanism of whole Eye globe deformation and the importance of the limbus. Invest Ophthalmol Vis Sci 2009, 50:5288-5294.
• [31]Crowder TR, Ervin VJ: Numerical simulations of fluid pressure in the human eye. Appl Math Comput 2013, 219:11119-11133.
• [32]Ogden RW: Large deformation isotropic elasticity on the correlation of theory and experiment for incompressible rubberlike solids. Proc R Soc Lond A 1972, 326:565-584.
• [33]Ogden RW, Nearly isochoric elastic deformations: Application to rubberlike solids. J Mech Phys Solids 1978, 26:37-57.
• [34]Hjortdal JO: Regional elastic performance of the human cornea. J Biomech 1996, 29:931-942.
• [35]Tahija S, Hong Y, Vijayasekaran S, Constable IJ: Synthetic polymers as materials for artificial vitreous body: review and recent advances. J Biomater Appl 1994, 9:121-137.
• [36]Bettelheim FA, Wang TJY: Dynamic viscoelastic properties of bovine vitreous. Exp Eye Res 1976, 23:435-441.
• [37]Zimmerman RL, Instituto De Fisica e Quimica De So Carlos: In vivo measurements of the viscoelasticity of the human vitreous humor. Biophys J 1980, 29:539-544.
• [38]Albrecht M, Eisner G: The hyalo-capsular zonula. Graefe's Arch Clin Exp Ophthalmol 1982, 218:88-92.
• [39]Liu Z, Wang B, Xiuying X, Wang C: A study for accommodating the human crystalline lens by finite element simulation. Comput Med Imag Grap 2006, 30:371-376.
• [40]Kling S, Remon L, Pe´rez-Escudero A, Merayo-Lloves J, Marcos S: Corneal biomechanical changes after collagen cross-linking from porcine eye inflation experiments. Invest Ophthalmol Vis Sci 2010, 51:3961-3968.
• [41]He L, Wendt M, Glasser A: Manipulation of intraocular pressure for studying the effects on accommodation. Exp Eye Res 2012, 102:76-84.
• [42]Hefazi H, Mizine I, Schmitz A, Klomparens S, Wiley S: Multidisciplinary synthesis optimization process in multihull ship design. Naval Eng J 2010, 3:29-47.