Computation of dynamical processes in eye during laser cataract extraction
Matematičeskoe modelirovanie, Tome 15 (2003) no. 11, pp. 37-44.

Voir la notice de l'article provenant de la source Math-Net.Ru

Problem of eye biomedium behavior during the eye surgeon operation is solving by numerical method. The behavior of such a solid medium was described by dynamic system of viscoelastic equations (system of differential equations in partial derivatives). For the numerical solving of these equations gridcharacteristic method was used.
@article{MM_2003_15_11_a3,
     author = {N. N. Balanovskii and A. V. Bubnov and A. S. Obukhov and I. B. Petrov},
     title = {Computation of dynamical processes in eye during laser cataract extraction},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {37--44},
     publisher = {mathdoc},
     volume = {15},
     number = {11},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2003_15_11_a3/}
}
TY  - JOUR
AU  - N. N. Balanovskii
AU  - A. V. Bubnov
AU  - A. S. Obukhov
AU  - I. B. Petrov
TI  - Computation of dynamical processes in eye during laser cataract extraction
JO  - Matematičeskoe modelirovanie
PY  - 2003
SP  - 37
EP  - 44
VL  - 15
IS  - 11
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2003_15_11_a3/
LA  - ru
ID  - MM_2003_15_11_a3
ER  - 
%0 Journal Article
%A N. N. Balanovskii
%A A. V. Bubnov
%A A. S. Obukhov
%A I. B. Petrov
%T Computation of dynamical processes in eye during laser cataract extraction
%J Matematičeskoe modelirovanie
%D 2003
%P 37-44
%V 15
%N 11
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2003_15_11_a3/
%G ru
%F MM_2003_15_11_a3
N. N. Balanovskii; A. V. Bubnov; A. S. Obukhov; I. B. Petrov. Computation of dynamical processes in eye during laser cataract extraction. Matematičeskoe modelirovanie, Tome 15 (2003) no. 11, pp. 37-44. http://geodesic.mathdoc.fr/item/MM_2003_15_11_a3/

[1] Burato L., Khirurgiya katarakty. Perekhod ot ekstrakapsulyarnoi ekstraktsii katarakty k fakoemulsifikatsii, Fabiano editorz, Italiya, 1999

[2] Godunov S. K., Elementy mekhaniki sploshnoi sredy, Nauka, M., 1978 | MR

[3] Nikitin L. V., “Model biouprugogo tela”, Izvestiya AN SSSR. Mekhanika tverdogo tela, 1971, no. 3, 154–157 | MR

[4] Stiles R. N., Alexander D. M., “A viscoelastic-mass model for muscule”, Mathematic Bioscience, 14:3–4 (1972), 343–354 | DOI

[5] Regirer S. A., Usik P. I., Chernova I. V., “Matematicheskoe opisanie svoistv myshechnoi tkani”, Mekhanika polimerov, 1975, no. 4, 579–584

[6] Korotin P. N., Ostrik A. V., Petrov I. B., “Chislennoe issledovanie volnovykh protsessov pri ob'emnom teplopogloschenii v mishenyakh konechnoi tolschiny”, DAN, 308:5 (1989), 1065–1070

[7] Magometov K. M., Kholodov A. S., Setochno-kharakteristicheskie chislennye metody, Nauka, M., 1988 | MR

[8] Belotserkovskii O. M., Chislennoe modelirovanie v mekhanike sploshnykh sred, Fizmatlit, M., 1994 | Zbl

[9] Belotserkovskii O. M., Vychislitelnaya mekhanika. Sovremennye problemy i rezultaty, Nauka, M., 1991 | Zbl

[10] Petrov I. B., Kholodov A. S., “Chislennoe reshenie nekotorykh dinamicheskikh zadach mekhaniki deformiruemogo tverdogo tela setochno-kharakteristicheskim metodom”, Zhurnal vychislitelnoi matematiki i matematicheskoi fiziki, 24:5 (1984), 722–739 | MR | Zbl

[11] Ivanov V. D., Kandaurov V. I., Petrov I. B., Kholodov A. S., “Raschet dinamicheskogo deformirovaniya i razrusheniya uprugikh tel setochno-kharakteristicheskimi metodami”, Matem. modelirovanie, 2:11 (1990), 10–29 | MR

[12] Makarov I. M. (red), Informatika i meditsina. Seriya “Kibernetika: neogranichennye vozmozhnosti i vozmozhnye ogranicheniya”, Nauka, M., 1997

[13] Zhukov D. S., Petrov I. B., Tormasov A. G., “Chislennoe i eksperimentalnoe izuchenie tverdykh tel v zhidkosti”, Izvestiya AN SSSR. Mekhanika tverdogo tela, 1991, no. 3, 183–190

[14] Petrov I. B., Polezhaev A. A., Shestakov A. S., “Volnovye protsessy v aktivnykh sredakh”, Matem. modelirovanie, 12:1 (2000), 38–44 | MR | Zbl

[15] Bubnov A. V., Korotin P. I., Kholodova O. A., “Matematicheskoe modelirovanie ultrazvukovykh kolebanii fakoemulsifikatora v srede khrustalika”, Sbornik RAN “Informatika i meditsina”, Nauka, M., 1997, 144–155

[16] Kholodov A. S., “Nekotorye dinamicheskie modeli vneshnego dykhaniya i krovoobrascheniya s uchetom iz svyazannosti i perenosa veschestv”, Sbornik RAN “Kompyuternye modeli i progress meditsiny”, Nauka, M., 2001, 127–164

[17] Agapov P. I., Petrov I. B., Obukhov A. S., Chelnokov F. B., “Chislennoe reshenie dinamicheskikh zadach biomekhaniki setochno-kharakteristicheskim metodom”, Sbornik RAN “Kompyuternye modeli i progress meditsiny”, Nauka, M., 2001, 275–300

[18] Lobanov A. I., Pashkov R. A., Petrov I. B., Polezhaev A. A., “Matematicheskaya model formirovaniya prostranstvennykh struktur khemotaksilnymi bakteriyami Escherichia coli”, Sbornik RAN “Kompyuternye modeli i progress meditsiny”, Nauka, M., 2001, 264–275

[19] Bubnov A. V., Balanovskii N. N., Petrov I. B., “Modelirovanie udarno-volnovykh protsessov, voznikayuschikh pri vozdeistvii na glaz izlucheniya YAG-lazera”, Sbornik “Novye lazernye tekhnologii v oftalmologii”, GU MNTK “Mikrokhirurgiya glaza” im. S. Fedorova, Kaluga, 2002, 11–12

[20] Shmidt R., Tevs G. (red), Fiziologiya cheloveka, T. 1–3, Mir, M., 1996

[21] Petrovskii B. V. (red), Kratkaya meditsinskaya entsiklopediya, T. 1, Sovetskaya entsiklopediya, M., 1989

[22] Korotin P. N., Petrov I. B., Kholodov A. S., “Chislennoe reshenie nekotorykh zadach o vozdeistvii teplovykh nagruzok na metally”, Izvestiya AN SSSR. Mekhanika tverdogo tela, 1989, no. 5, 63–69

[23] Korotin P. N., Petrov I. B., Kholodov A. S., “Chislennoe modelirovanie povedeniya uprugikh i uprugoplasticheskikh tel pod vozdeistviem moschnykh energeticheskikh potokov”, Matem. modelirovanie, 1:7 (1989), 1–12 | Zbl

[24] Petrov I. B., Tormasov A. G., Kholodov A. S., “Ob ispolzovanii setochno-kharakteristicheskikh skhem dlya chislennogo resheniya trekhmernykh zadach dinamiki deformiruemogo tverdogo tela”, Zhurnal vychislitelnoi matematiki i matematicheskoi fiziki, 30:8 (1990), 1237–1244 | MR

[25] Ivanenko S. A., Charakhchyan A. A., “Krivolineinye setki iz vypuklykh chetyrekhugolnikov”, Zhurnal vychislitelnoi matematiki i matematicheskoi fiziki, 28:4 (1988), 503–514 | MR