Abstract
The search for genetic factors associated with disease is complicated by the complexity of the biological pathways linking genotype and phenotype. This analytical complexity is particularly concerning in diseases historically lacking reliable diagnostic biological markers, such as schizophrenia and other mental disorders. We investigate the use of functional magnetic resonance imaging (fMRI) as an intermediate phenotype (endophenotype) to identify physiogenomic associations to schizophrenia. We screened 99 subjects, 30 subjects diagnosed with schizophrenia, 13 unaffected relatives of schizophrenia patients, and 56 unrelated controls, for gene polymorphisms associated with fMRI activation patterns at two locations in temporal and frontal lobes previously implied in schizophrenia. A total of 22 single nucleotide polymorphisms (SNPs) in 15 genes from the dopamine and serotonin neurotransmission pathways were genotyped in all subjects. We identified three SNPs in genes that are significantly associated with fMRI activity. SNPs of the dopamine beta-hydroxylase (DBH) gene and of the dopamine receptor D4 (DRD4) were associated with activity in the temporal and frontal lobes, respectively. One SNP of serotonin-3A receptor (HTR3A) was associated with temporal lobe activity. The results of this study support the physiogenomic analysis of neuroimaging data to discover associations between genotype and disease-related phenotypes.
References
Assaf M., Rivkin P. R., Kuzu C. H., Calhoun V. D., Kraut M. A., Groth K. M., et al (2006). Abnormal object recall and anterior cingulate overactivation correlate with formal thought disorder in schizophrenia. Biol. Psychiatry 59: 452–459
Bath K. G., Lee F. S. (2006). Variant BDNF (Val66Met) impact on brain structure and function. Cogn. Affect. Behav. Neurosci. 6: 79–85
Beasley C. L., Pennington K., Behan A., Wait R., Dunn M. J., Cotter D. (2006). Proteomic analysis of the anterior cingulate cortex in the major psychiatric disorders: evidence for disease-associated changes. Proteomics 6: 3414–3425
Benjamini Y., Hochberg Y. (1995). Controlling the false discovery rate: a practical and powerful approach to multiple testing. J. Roy. Stat. Soc. Ser. B 57: 289–300
Benjamini Y., Hochberg Y.(2000). On the adaptive control of the false discovery rate in multiple testing with independent statistics. J. Edu. Behav. Stat. 25: 60–83
Blair J., Spreen O. (1989). New Adult Reading Test—Revised Manual. VIC., Canada: University of Victoria
Blair J., Spreen O. (1989). Predicting premorbid IQ: a revision of the National Adult Reading Test. Clin. Neuropsychol. 3: 129–136
Brahmbhatt S. B., Haut K., Csernansky J. G., Barch D. M. (2006): Neural correlates of verbal and nonverbal working memory deficits in individuals with schizophrenia and their high-risk siblings. Schizophr. Res. 87: 191–204
Braver T. S., Barch D. M., Gray J. R., Molfese D. L., Snyder A. (2001): Anterior cingulate cortex and response conflict: effects of frequency, inhibition and errors. Cereb. Cortex 11: 825–836
Calhoun V. D., Adali T., Kiehl K. A., Astur R., Pekar J. J., Pearlson G. D. (2006): A method for multitask fMRI data fusion applied to schizophrenia. Hum. Brain Mapp. 27: 598–610
Calhoun V. D., Kiehl K. A., Liddle P. F., Pearlson G. D. (2004): Aberrant localization of synchronous hemodynamic activity in auditory cortex reliably characterizes schizophrenia. Biol. Psychiatry 55: 842–849
Calhoun, V. D., P. K. Maciejewski, G. D. Pearlson, and K. A. Kiehl. Temporal lobe and “default” hemodynamic brain modes discriminate between schizophrenia and bipolar disorder. Hum. Brain Mapp., 2007 [Epub ahead of print].
Callicott J. H. (2003). An expanded role for functional neuroimaging in schizophrenia. Curr. Opin. Neurobiol. 13: 256–260
Cardon L. R., Bell J. I. (2001). Association study designs for complex diseases. Nat. Rev. Genet. 2: 91–99
Casey B. J., Forman S. D., Franzen P., Berkowitz A., Braver T. S., Nystrom L. E. et al (2001): Sensitivity of prefrontal cortex to changes in target probability: a functional MRI study. Hum. Brain Mapp. 13: 26–33
Clark, D., I. Dedova, S. Cordwell, and I. Matsumoto. A proteome analysis of the anterior cingulate cortex gray matter in schizophrenia. Mol. Psychiatry 11:459–470, 423, 2006
Cleveland W. S. (1979): Robust locally weighted regression and smoothing scatterplots. J. Am. Stat. Assoc. 74: 829–836
Cleveland W. S., Devlin S. J. (1988): Locally weighted regression: an approach to regression analysis by local fitting. J. Am. Stat. Assoc. 83: 596–610
Colhoun H. M., McKeigue P. M., Davey S. G. (2003): Problems of reporting genetic associations with complex outcomes. Lancet 361: 865–872
Cubells J. F., Zabetian C. P. (2004): Human genetics of plasma dopamine beta-hydroxylase activity: applications to research in psychiatry and neurology. Psychopharmacology (Berl) 174: 463–476
Dalgaard P. (2002): Introductory Statistics with R. New York: Springer
Detera-Wadleigh S. D., McMahon F. J. (2006): G72/G30 in schizophrenia and bipolar disorder: review and meta-analysis. Biol. Psychiatry 60: 106–114
Dupuis J., O’Donnell C. J. (2007): Interpreting results of large-scale genetic association studies: separating gold from fool’s gold. JAMA 297: 529–531
Faerber L., Drechsler S., Ladenburger S., Gschaidmeier H., Fischer W. (2007): The neuronal 5-HT3 receptor network after 20 years of research-evolving concepts in management of pain and inflammation. Eur. J. Pharmacol. 560: 1–8
Fan J. B., Oliphant A., Shen R., Kermani B. G., Garcia F., Gunderson K. L. et al (2003): Highly parallel SNP genotyping. Cold Spring Harb. Symp. Quant. Biol. 68: 69–78
Fanous A. H., Neale M. C., Straub R. E., Webb B. T., O’Neill A. F., Walsh D. et al (2004): Clinical features of psychotic disorders and polymorphisms in HT2A, DRD2, DRD4, SLC6A3 (DAT1), and BDNF: a family based association study. Am. J. Med. Genet. B Neuropsychiatr. Genet. 125: 69–78
Faraway J. J. (2004): Linear Models with R. Boca Raton, FL: Chapman & Hall/CRC
First M. B., Spitzer R. L., Gibbon illiams B. (1995) Structured Clinical Interview for DSM-IV Axis I Disorders: Patient Edition (SCID-I/P, Version 2.0). New York: Biometrics Research Department, New York State Psychiatric Institute
Freire L., Mangin J. F. (2001): Motion correction algorithms may create spurious brain activations in the absence of subject motion. Neuroimage 14: 709–722
Friston J. A. (1995). Spatial registration and normalization of images. Human Brain Mapp. 3: 165–189
Gallinat J., Heinz A. (2006). Combination of multimodal imaging and molecular genetic information to investigate complex psychiatric disorders. Pharmacopsychiatry 31(Suppl 1): S76–S79
Gambaro G., Anglani F., D’Angelo A. (2000): Association studies of genetic polymorphisms and complex disease. Lancet 355: 308–311
Garrity A. G., Pearlson G. D., McKiernan K., Lloyd D., Kiehl K. A., Calhoun V. D. (2007): Aberrant “default mode” functional connectivity in schizophrenia. Am. J. Psychiatry 164: 450–457
Glahn D. C., Bearden C. E., Niendam T. A., Escamilla M. A. (2004): The feasibility of neuropsychological endophenotypes in the search for genes associated with bipolar affective disorder. Bipolar. Disord. 6: 171–182
Glahn D. C., Therman S., Manninen M., Huttunen M., Kaprio J., Lonnqvist J. et al (2003): Spatial working memory as an endophenotype for schizophrenia. Biol. Psychiatry 53: 624–626
Goldberg T. E., Straub R. E., Callicott J. H., Hariri A., Mattay V. S., Bigelow L. et al (2006): The G72/G30 gene complex and cognitive abnormalities in schizophrenia. Neuropsychopharmacology 31: 2022–2032
Goldman, A. L., L. Pezawas, V. S. Mattay, B. Fischl, B. A. Verchinski, B. Zoltick et al (2007): Heritability of brain morphology related to schizophrenia: a large-scale automated magnetic resonance imaging segmentation study. Biol. Psychiatry, 11: 459–470
Guidotti A., Auta J., Davis J. M., Dong E., Grayson D. R., Veldic M., et al (2005): GABAergic dysfunction in schizophrenia: new treatment strategies on the horizon. Psychopharmacology (Berl) 180: 191–205
Hariri A. R., Weinberger D. R. (2003): Imaging genomics. Br. Med. Bull. 65: 259–270
Harrison P. J., Weinberger D. R. (2005): Schizophrenia genes, gene expression, and neuropathology: on the matter of their convergence. Mol. Psychiatry 10: 40–68
Ho B. C., Milev P., O’Leary D. S., Librant A., Andreasen N. C., Wassink T. H. (2006): Cognitive and magnetic resonance imaging brain morphometric correlates of brain-derived neurotrophic factor Val66Met gene polymorphism in patients with schizophrenia and healthy volunteers. Arch. Gen. Psychiatry 63: 731–740
Ho, B. C., T. H. Wassink, D. S. O’Leary, V. C. Sheffield, and N. C. Andreasen. Catechol-O-methyl transferase Val158Met gene polymorphism in schizophrenia: working memory, frontal lobe MRI morphology and frontal cerebral blood flow. Mol. Psychiatry 10:229, 287–229, 298, 2005
Holford T. R., Windemuth A., Ruano G. (2006): Designing physiogenomic studies. Pharmacogenomics 7: 157–158
Johnson M. R., Morris N. A., Astur R. S., Calhoun V. D., Mathalon D. H., Kiehl K. A., et al (2006): A functional magnetic resonance imaging study of working memory abnormalities in schizophrenia. Biol. Psychiatry 60: 11–21
Kalayasiri R., Sughondhabirom A., Gueorguieva R., Coric V., Lynch W. J., Lappalainen J. et al (2007): Dopamine beta-hydroxylase gene (DbetaH)-1021C->T influences self-reported paranoia during cocaine self-administration. Biol. Psychiatry 61: 1310–1313
Keshavan M. S., Prasad K. M., Pearlson G. (2007): Are brain structural abnormalities useful as endophenotypes in schizophrenia? Int. Rev. Psychiatry 19: 397–406
Keshavan, M. S., K. M. Prasad, and G. Pearlson. (2007): Are brain structural abnormalities useful as endophenotypes in schizophrenia? Intl. Psychiatr. Rev. 19: 397–406
Kiehl K. A., Liddle P. F. (2001): An event-related functional magnetic resonance imaging study of an auditory oddball task in schizophrenia. Schizophr. Res. 48: 159–171
Kiehl K. A., Liddle P. F. (2003): Reproducibility of the hemodynamic response to auditory oddball stimuli: a six-week test–retest study. Hum. Brain Mapp. 18: 42–52
Kiehl K. A., Stevens M. C., Celone K., Kurtz M., Krystal J. H. (2005): Abnormal hemodynamics in schizophrenia during an auditory oddball task. Biol. Psychiatry 57: 1029–1040
Kiehl K. A., Stevens M. C., Laurens K. R., Pearlson G., Calhoun V. D., Liddle P. F. (2005): An adaptive reflexive processing model of neurocognitive function: supporting evidence from a large scale (n = 100) fMRI study of an auditory oddball task. Neuroimage 25: 899–915
Kim C. H., Zabetian C. P., Cubells J. F., Cho S., Biaggioni I., Cohen B. M., et al (2002): Mutations in the dopamine beta-hydroxylase gene are associated with human norepinephrine deficiency. Am. J. Med. Genet. 108: 140–147
Lander E. S., Linton L. M., Birren B., Nusbaum C., Zody M. C., Baldwin J. et al (2001): Initial sequencing and analysis of the human genome. Nature 409: 860–921
Lee C., McGlashan T. H., Woods S. W. (2005): Prevention of schizophrenia: can it be achieved? CNS. Drugs 19: 193–206
Lewis D. A. (2000): GABAergic local circuit neurons and prefrontal cortical dysfunction in schizophrenia. Brain Res. Brain Res. Rev. 31: 270–276
Liddle P. F. (1996): Functional imaging-schizophrenia. Br. Med. Bull. 52: 486–494
Lieberman J. A., Sheitman B. B., Kinon B. J. (1997): Neurochemical sensitization in the pathophysiology of schizophrenia: deficits and dysfunction in neuronal regulation and plasticity. Neuropsychopharmacology 17: 205–229
Linden D. E., Prvulovic D., Formisano E., Vollinger M., Zanella F. E., Goebel R. et al (1999): The functional neuroanatomy of target detection: an fMRI study of visual and auditory oddball tasks. Cereb. Cortex 9: 815–823
Lo W. S., Lau C. F., Xuan Z., Chan C. F., Feng G. Y., He L. et al (2004): Association of SNPs and haplotypes in GABAA receptor beta2 gene with schizophrenia. Mol. Psychiatry 9: 603–608
Losoncz M. F., Davidson M., Davis K. L. (1987): The dopamine hypothesis of schizophrenia. In: Eltzer H. Y., (Ed), Psychopharmacology: The Third Generation of Progress. New York: Raven Press, pp 715–726
Maindonald J., Braun J. (2003): Data Analysis and Graphics Using R. Cambridge: Cambridge University Press
Maldjian J. A., Laurienti P. J., Kraft R. A., Burdette J. H. (2003): An automated method for neuroanatomic and cytoarchitectonic atlas-based interrogation of fMRI data sets. Neuroimage 19: 1233–1239
Malek R. L., Wang H. Y., Kwitek A. E., Greene A. S., Bhagabati N., Borchardt G. et al (2006): Physiogenomic resources for rat models of heart, lung and blood disorders. Nat. Genet. 38: 234–239
Marchini J., Cardon L. R., Phillips M. S., Donnelly P. (2004): The effects of human population structure on large genetic association studies. Nat. Genet. 36: 512–517
McCarley R. W., Shenton M. E., O’Donnell B. F., Faux S. F., Kikinis R., Nestor P. G. et al (1993): Auditory P300 abnormalities and left posterior superior temporal gyrus volume reduction in schizophrenia. Arch. Gen. Psychiatry 50: 190–197
McCarthy G., Luby M., Gore J., Goldman-Rakic P. (1997): Infrequent events transiently activate human prefrontal and parietal cortex as measured by functional MRI. J. Neurophysiol. 77: 1630–1634
Menon V., Ford J. M., Lim K. O., Glover G. H., Pfefferbaum A. (1997): Combined event-related fMRI and EEG evidence for temporal-parietal cortex activation during target detection. Neuroreport 8: 3029–3037
Meyer-Lindenberg A., Poline J. B., Kohn P. D., Holt J. L., Egan M. F., Weinberger D. R. et al (2001): Evidence for abnormal cortical functional connectivity during working memory in schizophrenia. Am. J. Psychiatry 158: 1809–1817
Meyer-Lindenberg A., Weinberger D. R. (2006): Intermediate phenotypes and genetic mechanisms of psychiatric disorders. Nat. Rev. Neurosci. 7: 818–827
Nakajima M., Hattori E., Yamada K., Iwayama Y., Toyota T., Iwata Y. et al (2007): Association and synergistic interaction between promoter variants of the DRD4 gene in Japanese schizophrenics. J. Hum. Genet. 52: 86–91
Numata S., Ueno S., Iga J., Yamauchi K., Hongwei S., Kinouchi S., et al (2007): Interaction between catechol-O-methyltransferase (COMT) Val108/158Met and brain-derived neurotrophic factor (BDNF) Val66Met polymorphisms in age at onset and clinical symptoms in schizophrenia. J. Neural. Transm. 114: 255–259
Numata S., Ueno S., Iga J., Yamauchi K., Hongwei S., Ohta K., et al (2006): Brain-derived neurotrophic factor (BDNF) Val66Met polymorphism in schizophrenia is associated with age at onset and symptoms. Neurosci. Lett. 401: 1–5
Nyholt D. R. (2001): Genetic case–control association studies-correcting for multiple testing. Hum. Genet. 109: 564–567
Oak J. N., Oldenhof J., Van Tol H. H. (2000): The dopamine D(4) receptor: one decade of research. Eur. J. Pharmacol. 405: 303–327
Ohnishi T., Hashimoto R., Mori T., Nemoto K., Moriguchi Y., Iida H., et al (2006): The association between the Val158Met polymorphism of the catechol-O-methyl transferase gene and morphological abnormalities of the brain in chronic schizophrenia. Brain 129: 399–410
Oliphant, A., D. L. Barker, J. R. Stuelpnagel, and M. S. Chee. BeadArray technology: enabling an accurate, cost-effective approach to high-throughput genotyping. Biotechniques Suppl: 56–57, 2002
Oliver Josephs R. T. K. F. (1997): Event-related fMRI. Human Brain Mapp. 5: 243–248
Opitz B., Mecklinger A., Von Cramon D. Y., Kruggel F. (1999): Combining electrophysiological and hemodynamic measures of the auditory oddball. Psychophysiology 36: 142–147
Owen M. J., Craddock N., O’Donovan M. C. (2005): Schizophrenia: genes at last? Trends Genet. 21: 518–525
Pearlson G. D., Calhoun V. (2007): Structural and functional magnetic resonance imaging in psychiatric disorders. Can. J. Psychiatry 52: 158–166
R Core Development Team (2004): A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing
Redden D. T., Allison D. B. (2003): Nonreplication in genetic association studies of obesity and diabetes research. J. Nutr. 133: 3323–3326
Reinere A., Yekutiele D., Benjamini Y. (2003): Identifying differentially expressed genes using false discovery rate controlling procedures. Bioinformatics 19: 368–375
Rosen B. R., Buckner R. L., Dale A. M. (1998): Event-related functional MRI: past, present, and future. Proc. Natl. Acad. Sci. USA 95: 773–780
Ruano, G. Physiogenomic method for predicting clinical outcomes of treatments in patients. Patent, USPTO # 20060278241. 12-14-2006
Ruano, G., J. W. Goethe, C. Caley, S. Woolley, T. R. Holford, M. Kocherla, et al. (2007) Physiogenomic comparison of weight profiles of olanzapine- and risperidone-treated patients. Mol. Psychiatry, 12(5): 474–482
Ruano G., Seip R. L., Windemuth A., Zollner S., Tsongalis G. J., Ordovas J. et al (2006): Apolipoprotein A1 genotype affects the change in high density lipoprotein cholesterol subfractions with exercise training. Atherosclerosis 185: 65–69
Ruano G., Thompson P. D., Windemuth A., Smith A., Kocherla M., Holford T. R., et al. (2005): Physiogenomic analysis links serum creatine kinase activities during statin therapy to vascular smooth muscle homeostasis. Pharmacogenomics 6: 865–872
Ruano, G., A. Windemuth, and T. Holford. Physiogenomics: integrating systems engineering and nanotechnology for personalized medicine. In: The Biomedical Engineering Handbook, 3rd edn, edited by J. D. Bronzino. CRC Press, 2005, pp. 28-1–28-9
Ruano G., Windemuth A., Kocherla M., Holford T., Fernandez M. L., Forsythe C. E. et al (2006): Physiogenomic analysis of weight loss induced by dietary carbohydrate restriction. Nutr. Metab (Lond) 3: 20
Salanti G., Sanderson S., Higgins J. P. (2005): Obstacles and opportunities in meta-analysis of genetic association studies. Genet. Med. 7: 13–20
Saltelli A., Chan K., Scott E. M. (2000): Sensitivity Analysis. Chichester: John Wiley and Sons
Saperstein A. M., Fuller R. L., Avila M. T., Adami H., McMahon R. P., Thaker G. K., et al (2006): Spatial working memory as a cognitive endophenotype of schizophrenia: assessing risk for pathophysiological dysfunction. Schizophr. Bull. 32: 498–506
Sarter M., Berntson G. G., Cacioppo J. T. (1996) Brain imaging and cognitive neuroscience. Toward strong inference in attributing function to structure. Am. Psychol. 51: 13–21
Schroder J., Buchsbaum M. S., Siegel B. V., Geider F. J., Lohr J., Tang C. et al (1996): Cerebral metabolic activity correlates of subsyndromes in chronic schizophrenia. Schizophr. Res. 19: 41–53
Sherry S. T., Ward M., Sirotkin K. (1999): dbSNP-database for single nucleotide polymorphisms and other classes of minor genetic variation. Genome Res. 9: 677–679
Soares J. C. (2003) Contributions from brain imaging to the elucidation of pathophysiology of bipolar disorder. Int. J. Neuropsychopharmacol. 6: 171–180
Spitzer R. L., Williams J. B., Gibbon M. (1996): Structured Clinical Interview for DSM-IV: Non-patient Edition (SCID-NP). New York: Biometrics Research Department, New York State Psychiatric Institute
Sternberg D. E., VanKammen D. P., Lerner P., Bunney W. E. (1982): Schizophrenia: dopamine beta-hydroxylase activity and treatment response. Science 216: 1423–1425
Strange B. A., Dolan R. J. (2001): Adaptive anterior hippocampal responses to oddball stimuli. Hippocampus 11: 690–698
Sundgren P. C., Dong Q., Gomez-Hassan D., Mukherji S. K., Maly P., Welsh R. (2004): Diffusion tensor imaging of the brain: review of clinical applications. Neuroradiology 46: 339–350
Tamminga C. A., Holcomb H. H. (2005): Phenotype of schizophrenia: a review and formulation. Mol. Psychiatry 10: 27–39
Tang Y., Buxbaum S. G., Waldman I., Anderson G. M., Zabetian C. P., Kohnke M. D., et al (2006): A single nucleotide polymorphism at DBH, possibly associated with attention-deficit/hyperactivity disorder, associates with lower plasma dopamine beta-hydroxylase activity and is in linkage disequilibrium with two putative functional single nucleotide polymorphisms. Biol. Psychiatry 60: 1034–1038
Tarazi F. I., Baldessarini R. J. (1999): Brain dopamine D(4) receptors: basic and clinical status. Int. J. Neuropsychopharmcol. 2: 41–58
Tarazi F. I., Baldessarini R. J. (1999): Dopamine D4 receptors: significance for molecular psychiatry at the millennium. Mol. Psychiatry 4: 529–538
Thaker G. K. (2000): Defining the schizophrenia phenotype. Curr. Psychiatry Rep. 2: 398–403
The International HapMap Consortium. A haplotype map of the human genome. Nature 437:1299–1320, 2005
Thompson P. M., Cannon T. D., Narr K. L., van Erp T., Poutanen V. P., Huttunen M. et al (2001): Genetic influences on brain structure. Nat. Neurosci. 4: 1253–1258
Vawter M. P., Shannon W. C., Ferran E., Matsumoto M., Overman K., Hyde T. M. et al (2004): Gene expression of metabolic enzymes and a protease inhibitor in the prefrontal cortex are decreased in schizophrenia. Neurochem. Res. 29: 1245–1255
Waldemar G., Hogh P., Paulson O. B. (1997): Functional brain imaging with single-photon emission computed tomography in the diagnosis of Alzheimer’s disease. Int. Psychogeriatr. 9(Suppl 1):223–227
Yamamoto K., Cubells J. F., Gelernter J., Benkelfat C., Lalonde P., Bloom D., et al (2003): Dopamine beta-hydroxylase (DBH) gene and schizophrenia phenotypic variability: a genetic association study. Am. J. Med. Genet. B Neuropsychiatr. Genet. 117: 33–38
Yu Z., Chen J., Shi H., Stoeber G., Tsang S. Y., Xue H. (2006): Analysis of GABRB2 association with schizophrenia in German population with DNA sequencing and one-label extension method for SNP genotyping. Clin. Biochem. 39: 210–218
Acknowledgments
This work was supported in part by grants from the National Institutes of Health, under RO1 grants MH60504, MH43775, MH52886, EB000840, EB005846, and an NIMH MERIT award (to GP), as well as SBIR R43 grant MH075481 (to GR).
Financial Disclosures
Dr. Windemuth, Dr. Ruaño, and Mr. Kocherla report financial interest in Genomas Inc. in the form of salary, stock, and stock options. Dr. Calhoun and Dr. Pearlson report no financial interests in companies or potential conflicts of interest.
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Windemuth, A., Calhoun, V.D., Pearlson, G.D. et al. Physiogenomic Analysis of Localized fMRI Brain Activity in Schizophrenia. Ann Biomed Eng 36, 877–888 (2008). https://doi.org/10.1007/s10439-008-9475-2
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DOI: https://doi.org/10.1007/s10439-008-9475-2