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Mathematical models of retinitis pigmentosa: the oxygen toxicity hypothesis. (English) Zbl 1381.92050
Summary: The group of genetically mediated diseases, known collectively as retinitis pigmentosa (RP), cause retinal degeneration and, hence, loss of vision. The most common inherited retinal degeneration, RP is currently untreatable. The retina detects light using cells known as photoreceptors, of which there are two types: rods and cones. In RP, genetic mutations cause patches of photoreceptors to degenerate and typically directly affect either rods or cones, but not both. During disease progression, degenerate patches spread and the unaffected photoreceptor type also begins to degenerate. The cause underlying these phenomena is currently unknown. The oxygen toxicity hypothesis proposes that secondary photoreceptor loss is due to hyperoxia (toxically high oxygen levels), which results from the decrease in oxygen uptake following the initial loss of photoreceptors. In this paper, we construct mathematical models, formulated as 1D systems of partial differential equations, to investigate this hypothesis. Using a combination of numerical simulations, asymptotic analysis and travelling wave analysis, we find that degeneration may spread due to hyperoxia, and generate spatio-temporal patterns of degeneration similar to those seen in vivo. We determine the conditions under which a degenerate patch will spread and show that the wave speed of degeneration is a monotone decreasing function of the local photoreceptor density. Lastly, the effects of treatment with antioxidants and trophic factors, and of capillary loss, upon the dynamics of photoreceptor loss and recovery are considered.

MSC:
92C50 Medical applications (general)
35Q92 PDEs in connection with biology, chemistry and other natural sciences
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[1] Bender, C. M.; Orszag, S. A., Advanced mathematical methods for scientists and engineers I: asymptotic methods and perturbation theory, (1999), Springer · Zbl 0938.34001
[2] Burns, J.; Clarke, G.; Lumsden, C. J., Photoreceptor death: spatiotemporal patterns arising from one-hit death kinetics and a diffusible cell death factor, Bull. Math. Biol., 64, 1117-1145, (2002) · Zbl 1334.92110
[3] Camacho, E. T.; Colón Vélez, M. A.; Hernández, D. J.; Bernier, U. R.; van Laarhoven, J.; Wirkus, S., A mathematical model for photoreceptor interactions, J. Theor. Biol., 267, 4, 638-646, (2010) · Zbl 1414.92080
[4] Camacho, E. T.; Léveillard, T.; Sahel, J. A.; Wirkus, S., Mathematical model of the role of rdcvf in the coexistence of rods and cones in a healthy eye, Bull. Math. Biol., 78, 7, 1394-1409, (2016) · Zbl 1361.92024
[5] Camacho, E. T.; Melara, L. A.; Villalobos, M. C.; Wirkus, S., Optimal control in the treatment of retinitis pigmentosa, Bull. Math. Biol., 76, 2, 292-313, (2014) · Zbl 1297.92040
[6] Camacho, E. T.; Punzo, C.; Wirkus, S. A., Quantifying the metabolic contribution to photoreceptor death in retinitis pigmentosa via a mathematical model, J. Theor. Biol., 408, 75-87, (2016) · Zbl 1352.92078
[7] Camacho, E. T.; Radulescu, A.; Wirkus, S., Bifurcation analysis of a photoreceptor interaction model for retinitis pigmentosa, Commun. Nonlinear Sci. Numer. Simulat., 38, 267-276, (2016)
[8] Camacho, E. T.; Wirkus, S., Tracing the progression of retinitis pigmentosa via photoreceptor interactions, J. Theor. Biol., 317, 0, 105-118, (2013) · Zbl 1368.92080
[9] Chrysostomou, V.; Stone, J.; Stowe, S.; Barnett, N. L.; Valter, K., The status of cones in the rhodopsin mutant P23H-3 retina: light-regulated damage and repair in parallel with rods, Invest. Ophthalmol. Vis. Sci., 49, 3, 1116-1125, (2008)
[10] Cideciyan, A. V.; Hood, D. C.; Huang, Y.; Banin, E.; Li, Z.-Y.; Stone, E. M.; Milam, A. H.; Jacobson, S. G., Disease sequence from mutant rhodopsin allele to rod and cone photoreceptor degeneration in man, Proc. Natl. Acad. Sci., 95, 12, 7103-7108, (1998)
[11] Cingolani, C.; Rogers, B.; Lu, L.; Kachi, S.; Shen, J.; Campochiaro, P. A., Retinal degeneration from oxidative damage, Free Radic. Biol. Med., 40, 4, 660-669, (2006)
[12] Clarke, G.; Collins, R. A.; Leavitt, B. R.; Andrews, D. F.; Hayden, M. R.; Lumsden, C. J.; McInnes, R. R., A one-hit model of cell death in inherited neuronal degenerations, Nature, 406, 195-199, (2000)
[13] Clarke, G.; Lumsden, C. J., Heterogeneous cellular environments modulate one-hit neuronal death kinetics, Brain Res. Bull., 65, 1, 59-67, (2005)
[14] Clarke, G.; Lumsden, C. J., Scale-free neurodegeneration: cellular heterogeneity and the stretched exponential kinetics of cell death, J. Theor. Biol., 233, 4, 515-525, (2005)
[15] Clarke, G.; Lumsden, C. J.; McInnes, R. R., Inherited neurodegenerative diseases: the one-hit model of neurodegeneration, Hum. Mol. Genet., 10, 20, 2269-2275, (2001)
[16] Coleman, H. R.; Chan, C. C.; Ferris III, F. L.; Chew, E. Y., Age-related macular degeneration, Lancet, 372, 9652, 1835-1845, (2008)
[17] Colón Vélez, M. A.; Hernández, D. J.; Bernier, U. R.; van Laarhoven, J.; Camacho, E. T., Mathematical models for photoreceptor interactions, Technical Report, (2003), Cornell University, Department of Biological Statistics and Computational Biology
[18] Curcio, C. A.; Millican, C. L.; Allen, K. A.; Kalina, R. E., Aging of the human photoreceptor mosaic: evidence for selective vulnerability of rods in central retina, Invest. Ophthalmol. Vis. Sci., 34, 12, 3278-3296, (1993)
[19] Curcio, C. A.; Sloan, K. R.; Kalina, R. E.; Hendrickson, A. E., Human photoreceptor topography, J. Comp. Neurol., 292, 4, 497-523, (1990)
[20] Del Priore, L. V.; Kaplan, H. J.; Hornbeck, R.; Jones, Z.; Swinn, M., Retinal pigment epithelial debridement as a model for the pathogenesis and treatment of macular degeneration, Am. J. Ophthalmol., 122, 5, 629-643, (1996)
[21] Dong, A.; Shen, J.; Krause, M.; Akiyama, H.; Hackett, S. F.; Lai, H.; Campochiaro, P. A., Superoxide dismutase 1 protects retinal cells from oxidative damage, J. Cell Physiol., 208, 3, 516-526, (2006)
[22] Escher, P.; Tran, H. V.; Vaclavik, V.; Borruat, F. X.; Schorderet, D. F.; Munier, F. L., Double concentric autofluorescence ring in NR2e3-p.G56R-linked autosomal dominant retinitis pigmentosa, Invest. Ophthalmol. Vis. Sci., 53, 8, 4754-4764, (2012)
[23] Fintz, A. C.; Audo, I.; Hicks, D.; Mohand-Saïd, S.; Léveillard, T.; Sahel, J., Partial characterization of retina-derived cone neuroprotection in two culture models of photoreceptor degeneration, Invest. Ophthalmol. Vis. Sci., 44, 2, 818-825, (2003)
[24] García-Ayuso, D.; Ortín-Martínez, A.; Jiménez-López, M.; Galindo-Romero, C.; Cuenca, N.; Pinilla, I.; Vidal-Sanz, M.; Agudo-Barriuso, M.; Villegas-Pérez, M. P., Changes in the photoreceptor mosaic of P23H-1 rats during retinal degeneration: implications for rod-cone dependent survival, Invest. Ophthalmol. Vis. Sci., 54, 8, 5888-5900, (2013)
[25] Grover, S.; Fishman, G. A.; Brown Jr, J., Patterns of visual field progression in patients with retinitis pigmentosa, Ophthalmology, 105, 6, 1069-1075, (1998)
[26] Gupta, N.; Brown, K. E.; Milam, A. H., Activated microglia in human retinitis pigmentosa, late-onset retinal degeneration, and age-related macular degeneration, Exp. Eye Res., 76, 4, 463-471, (2003)
[27] Hamel, C., Retinitis pigmentosa, Orphanet. J. Rare Dis., 1, 1, 40, (2006)
[28] Hamel, C., Cone rod dystrophies, Orphanet. J. Rare Dis., 2, 1, 7, (2007)
[29] Hartong, D. T.; Berson, E. L.; Dryja, T. P., Retinitis pigmentosa, Lancet, 368, 9549, 1795-1809, (2006)
[30] Jager, R. D.; Mieler, W. F.; Miller, J. W., Age-related macular degeneration, N. Engl. J. Med., 358, 24, 2606-2617, (2008)
[31] Ji, Y.; Zhu, C. L.; Grzywacz, N. M.; Lee, E. J., Rearrangement of the cone mosaic in the retina of the rat model of retinitis pigmentosa, J. Comp. Neurol., 520, 4, 874-888, (2012)
[32] Kohen, R.; Nyska, A., Invited review: oxidation of biological systems: oxidative stress phenomena, antioxidants, redox reactions, and methods for their quantification, Toxicol. Pathol., 30, 6, 620-650, (2002)
[33] Komeima, K.; Rogers, B.; Lu, L.; Campochiaro, P., Antioxidants reduce cone cell death in a model of retinitis pigmentosa, Proc. Natl. Acad. Sci., 103, 30, 11300-11305, (2006)
[34] Komeima, K.; Rogers, B. S.; Campochiaro, P. A., Antioxidants slow photoreceptor cell death in mouse models of retinitis pigmentosa, J. Cell Physiol., 213, 3, 809-815, (2007)
[35] Lee, D. C.; Vazquez-Chona, F. R.; Ferrell, W. D.; Tam, B. M.; Jones, B. W.; Marc, R. E.; Moritz, O. L., Dysmorphic photoreceptors in a P23H mutant rhodopsin model of retinitis pigmentosa are metabolically active and capable of regenerating to reverse retinal degeneration, J. Neurosci., 32, 6, 2121-2128, (2012)
[36] Lee, E. J.; Ji, Y.; Zhu, C. L.; Grzywacz, N. M., Role of Müller cells in cone mosaic rearrangement in a rat model of retinitis pigmentosa, Glia, 59, 7, 1107-1117, (2011)
[37] Léveillard, T.; Mohand-Saïd, S.; Lorentz, O.; Hicks, D.; Fintz, A. C.; Clérin, E.; Simonutti, M.; Forster, V.; Cavusoglu, N.; Chalmel, F.; Dollé, P.; Poch, O.; Lambrou, G.; Sahel, J. A., Identification and characterization of rod-derived cone viability factor, Nat. Genet., 36, 7, 755-759, (2004)
[38] Li, Z. Y.; Possin, D. E.; Milam, A. H., Histopathology of bone spicule pigmentation in retinitis pigmentosa, Ophthalmology, 102, 5, 805-816, (1995)
[39] Lima, L. H.; Burke, T.; Greenstein, V. C.; Chou, C. L.; Cella, W.; Yannuzzi, L. A.; Tsang, S. H., Progressive constriction of the hyperautofluorescent ring in retinitis pigmentosa, Am. J. Ophthalmol., 153, 4, 718-727, (2012)
[40] Lima, L. H.; Cella, W.; Greenstein, V. C.; Wang, N. K.; Busuioc, M.; Smith, R. T.; Yannuzzi, L. A.; Tsang, S. H., Structural assessment of hyperautofluorescent ring in patients with retinitis pigmentosa, Retina, 29, 7, 1025-1031, (2009)
[41] Lomasko, T.; Clarke, G.; Lumsden, C. J., One-hit stochastic decline in a mechanochemical model of cytoskeleton-induced neuron death i: cell-fate arrival times, J. Theor. Biol., 249, 1, 1-17, (2007)
[42] Lomasko, T.; Clarke, G.; Lumsden, C. J., One-hit stochastic decline in a mechanochemical model of cytoskeleton-induced neuron death II: transition state metastability, J. Theor. Biol., 249, 1, 18-28, (2007)
[43] Lomasko, T.; Lumsden, C. J., One-hit stochastic decline in a mechanochemical model of cytoskeleton-induced neuron death III: diffusion pulse death zones, J. Theor. Biol., 256, 1, 104-116, (2009) · Zbl 1400.92100
[44] Milam, A. H.; Zong, Y. L.; Fariss, R. N., Histopathology of the human retina in retinitis pigmentosa, Prog. Retin. Eye Res., 17, 2, 175-205, (1998)
[45] Mohand-Saïd, S.; Deudon-Combe, A.; Hicks, D.; Simonutti, M.; Forster, V.; Fintz, A. C.; Léveillard, T.; Dreyfus, H.; Sahel, J. A., Normal retina releases a diffusible factor stimulating cone survival in the retinal degeneration mouse, Proc. Natl. Acad. Sci., 95, 14, 8357-8362, (1998)
[46] Mohand-Saïd, S.; Hicks, D.; Dreyfus, H.; Sahel, J. A., Selective transplantation of rods delays cone loss in a retinitis pigmentosa model, Arch. Ophthalmol., 118, 6, 807-811, (2000)
[47] Mohand-Saïd, S.; Hicks, D.; Simonutti, M.; Tran-Minh, D.; Deudon-Combe, A.; Dreyfus, H.; Silverman, M. S.; Ogilvie, J. M.; Tenkova, T.; Sahel, J., Photoreceptor transplants increase host cone survival in the retinal degeneration (rd) mouse, Ophthalmic Res., 29, 290-297, (1997)
[48] Mullins, R. F.; Kuehn, M. H.; Radu, R. A.; Enriquez, G. S.; East, J. S.; Schindler, E. I.; Travis, G. H.; Stone, E. M., Autosomal recessive retinitis pigmentosa due to ABCA4 mutations: clinical, pathologic, and molecular characterization, Invest. Ophthalmol. Vis. Sci., 53, 4, 1883-1894, (2012)
[49] Murakami, T.; Akimoto, M.; Ooto, S.; Suzuki, T.; Ikeda, H.; Kawagoe, N.; Takahashi, M.; Yoshimura, N., Association between abnormal autofluorescence and photoreceptor disorganization in retinitis pigmentosa, Am. J. Ophthalmol., 145, 4, 687-694, (2008)
[50] Musarella, M. A.; MacDonald, I. M., Current concepts in the treatment of retinitis pigmentosa, J. Ophthalmol., 2011, 753547, (2011)
[51] Okoye, G.; Zimmer, J.; Sung, J.; Gehlbach, P.; Deering, T.; Nambu, H.; Hackett, S.; Melia, M.; Esumi, N.; Zack, D. J.; Campochiaro, P. A., Increased expression of brain-derived neurotrophic factor preserves retinal function and slows cell death from rhodopsin mutation or oxidative damage, J. Neurosci., 23, 10, 4164-4172, (2003)
[52] Orosz, K. E.; Gupta, S.; Hassink, M.; Abdel-Rahman, M.; Moldovan, L.; Davidorf, F. H.; Moldovan, N. I., Delivery of antiangiogenic and antioxidant drugs of ophthalmic interest through a nanoporous inorganic filter, Mol. Vis., 10, 555-565, (2004)
[53] Oyster, C. W., The human eye: structure and function, (1999), Sinauer Associates Inc
[54] Padnick-Silver, L.; Derwent, J. J.K.; Giuliano, E.; Narfström, K.; Linsenmeier, R. A., Retinal oxygenation and oxygen metabolism in Abyssinian cats with a hereditary retinal degeneration, Invest. Ophthalmol. Vis. Sci., 47, 8, 3683-3689, (2006)
[55] Popović, P.; Jarc-Vidmar, M.; Hawlina, M., Abnormal fundus autofluorescence in relation to retinal function in patients with retinitis pigmentosa, Graefes Arch. Clin. Exp. Ophthalmol., 243, 1018-1027, (2005)
[56] Ripps, H., Cell death in retinitis pigmentosa: gap junctions and the ‘bystander’ effect, Exp. Eye Res., 74, 3, 327-336, (2002)
[57] Roberts, P. A., Mathematical Models of the Retina in Health and Disease D. Phil. thesis, (2015), University of Oxford
[58] Roberts, P. A.; Gaffney, E. A.; Luthert, P. J.; Foss, A. J.E.; Byrne, H. M., Mathematical and computational models of the retina in health, development and disease, Prog. Retin. Eye. Res., 53, 48-69, (2016)
[59] Robson, A. G.; Egan, C. A.; Luong, V. A.; Bird, A. C.; Holder, G. E.; Fitzke, F. W., Comparison of fundus autofluorescence with photopic and scotopic fine-matrix mapping in patients with retinitis pigmentosa and normal visual acuity, Invest. Ophthalmol. Vis. Sci., 45, 11, 4119-4125, (2004)
[60] Robson, A. G.; El-Amir, A.; Bailey, C.; Egan, C. A.; Fitzke, F. W.; Webster, A. R.; Bird, A. C.; Holder, G. E., Pattern ERG correlates of abnormal fundus autofluorescence in patients with retinitis pigmentosa and normal visual acuity, Invest. Ophthalmol. Vis. Sci., 44, 8, 3544-3550, (2003)
[61] Robson, A. G.; Michaelides, M.; Saihan, Z.; Bird, A. C.; Webster, A. R.; Moore, A. T.; Fitzke, F. W.; Holder, G. E., Functional characteristics of patients with retinal dystrophy that manifest abnormal parafoveal annuli of high density fundus autofluorescence; a review and update, Doc. Ophthalmol., 116, 2, 79-89, (2008)
[62] Robson, A. G.; Saihan, Z.; Jenkins, S. A.; Fitzke, F. W.; Bird, A. C.; Webster, A. R.; Holder, G. E., Functional characterisation and serial imaging of abnormal fundus autofluorescence in patients with retinitis pigmentosa and normal visual acuity, Br. J. Ophthalmol., 90, 4, 472-479, (2006)
[63] Robson, A. G.; Tufail, A.; Fitzke, F.; Bird, A. C.; Moore, A. T.; Holder, G. E.; Webster, A. R., Serial imaging and structure-function correlates of high-density rings of fundus autofluorescence in retinitis pigmentosa, Retina, 10(10), 1-10, (2011)
[64] Sahaboglu, A.; Paquet-Durand, O.; Dietter, J.; Dengler, K.; Bernhard-Kurz, S.; Ekstrom, P. A.R.; Hitzmann, B.; Ueffing, M.; Paquet-Durand, F., Retinitis pigmentosa: rapid neurodegeneration is governed by slow cell death mechanisms, Cell Death. Dis., 4, e488, (2013)
[65] Sanz, M. M.; Johnson, L. E.; Ahuja, S.; Ekström, P. A.R.; Romero, J.; van Veen, T., Significant photoreceptor rescue by treatment with a combination of antioxidants in an animal model for retinal degeneration, Neuroscience, 145, 3, 1120-1129, (2007)
[66] Shen, J.; Yang, X.; Dong, A.; Petters, R. M.; Peng, Y. W.; Wong, F.; Campochiaro, P. A., Oxidative damage is a potential cause of cone cell death in retinitis pigmentosa, J. Cell Physiol., 203, 3, 457-464, (2005)
[67] Shintani, K.; Shechtman, D. L.; Gurwood, A. S., Review and update: current treatment trends for patients with retinitis pigmentosa, Optometry, 80, 7, 384-401, (2009)
[68] Stone, J.; Maslim, J.; Valter-Kocsi, K.; Mervin, K.; Bowers, F.; Chu, Y.; Barnett, N.; Provis, J.; Lewis, G.; Fisher, S. K.; Bistid, S.; Gargini, C.; Cervetto, L.; Merin, S.; Pe’er, J., Mechanisms of photoreceptor death and survival in Mammalian retina, Prog. Retin. Eye Res., 18(6), 689-735, (1999)
[69] Tao, W., Application of encapsulated cell technology for retinal degenerative diseases, Expert Opin. Biol. Ther., 6, 7, 717-726, (2006)
[70] Tao, W.; Wen, R.; Goddard, M. B.; Sherman, S. D.; O’Rourke, P. J.; Stabila, P. F.; Bell, W. J.; Dean, B. J.; Kauper, K. A.; Budz, V. A.; Tsiaras, W. G.; Acland, G. M.; Pearce-Kelling, S.; Laties, A. M.; Aguirre, G. D., Encapsulated cell-based delivery of CNTF reduces photoreceptor degeneration in animal models of retinitis pigmentosa, Invest. Ophthalmol. Vis. Sci., 43, 10, 3292-3298, (2002)
[71] Travis, G. H.; Sutcliffe, J. G.; Bok, D., The retinal degeneration slow (rds) gene product is a photoreceptor disc membrane-associated glycoprotein, Neuron, 6, 1, 61-70, (1991)
[72] Valter, K.; Maslim, J.; Bowers, F.; Stone, J., Photoreceptor dystrophy in the RCS rat: roles of oxygen, debris, and bfgf, Invest. Ophthalmol. Vis. Sci., 39, 12, 2427-2442, (1998)
[73] Wang, X.; Ryter, S. W.; Dai, C.; Tang, Z. L.; Watkins, S. C.; Yin, X. M.; Song, R.; Choi, A. M.K., Necrotic cell death in response to oxidant stress involves the activation of the apoptogenic caspase-8/bid pathway, J. Biol. Chem., 278, 31, 29184-29191, (2003)
[74] Wangsa-Wirawan, N. D.; Linsenmeier, R. A., Retinal oxygen: fundamental and clinical aspects, Arch. Ophthalmol., 121, 4, 547-557, (2003)
[75] Wellard, J.; Lee, D.; Valter, K.; Stone, J., Photoreceptors in the rat retina are specifically vulnerable to both hypoxia and hyperoxia, Vis. Neurosci., 22, 4, 501-507, (2005)
[76] Wen, R.; Tao, W.; Li, Y.; Sieving, P. A., CNTF and retina, Prog. Retin. Eye Res., 31, 2, 136-151, (2012)
[77] Yamada, H.; Yamada, E.; Ando, A.; Esumi, N.; Bora, N.; Saikia, J.; Sung, C.-H.; Zack, D. J.; Campochiaro, P. A., Fibroblast growth factor-2 decreases hyperoxia-induced photoreceptor cell death in mice, Am. J. Pathol., 159, 3, 1113-1120, (2001)
[78] Yamada, H.; Yamada, E.; Hackett, S. F.; Ozaki, H.; Okamoto, N.; Campochiaro, P. A., Hyperoxia causes decreased expression of vascular endothelial growth factor and endothelial cell apoptosis in adult retina, J. Cell Physiol., 179, 2, 149-156, (1999)
[79] Young, R. W., The renewal of photoreceptor cell outer segments, J. Cell Biol., 33, 1, 61-72, (1967)
[80] Young, R. W., The renewal of rod and cone outer segments in the rhesus monkey, J. Cell Biol., 49, 303-318, (1971)
[81] Young, R. W., The daily rhythm of shedding and degradation of rod and cone outer segment membranes in the chick retina, Invest. Ophthalmol. Vis. Sci., 17, 2, (1978)
[82] Young, R. W.; Bok, D., Participation of the retinal pigment epithelium in the rod outer segment renewal process, J. Cell Biol., 42, 392-403, (1969)
[83] Yu, D. Y.; Cringle, S.; Valter, K.; Walsh, N.; Lee, D.; Stone, J., Photoreceptor death, trophic factor expression, retinal oxygen status, and photoreceptor function in the P23H rat, Invest. Ophthalmol. Vis. Sci., 45, 6, 2013-2019, (2004)
[84] Yu, D. Y.; Cringle, S. J., Oxygen distribution and consumption within the retina in vascularised and avascular retinas and in animal models of retinal disease, Prog. Retin. Eye Res., 20, 2, 175-208, (2001)
[85] Yu, D. Y.; Cringle, S. J., Retinal degeneration and local oxygen metabolism, Exp. Eye Res., 80, 6, 745-751, (2005)
[86] Yu, D. Y.; Cringle, S. J.; Su, E. N.; Yu, P. K., Intraretinal oxygen levels before and after photoreceptor loss in the RCS rat, Invest. Ophthalmol. Vis. Sci., 41, 12, 3999-4006, (2000)
[87] Zhu, C. L.; Ji, Y.; Lee, E.-J.; Grzywacz, N. M., Spatiotemporal pattern of rod degeneration in the S334ter-line-3 rat model of retinitis pigmentosa, Cell Tissue Res., 351, 1, 29-40, (2013)
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