Abstract
FMRI-based laterality index (LI) is widely used to assess relative left–right differences in brain function. Here we investigated objective ways to generate categorical LI. By defining left and right hemisphere contributions as discrete random variables, it was possible to depict the probability mass function of LI. Its distribution has a shape of a symmetrical truncated exponential function. We demonstrate that LI = ± 0.2 is an objective cut-off to categorize classification of hemispheric dominance. We then searched for parallels between LI and classic similarity or association indices. A parallel between LI and Sorensen–Dice index can be established under maximal voxel-wise overlap between left and right hemispheres. To redefine LI as a proper distance metric, we suggest instead to relate LI to Jaccard–Tanimoto similarity index. Accordingly, a new LI formula can be derived: LInew = LH–RH/max(LH,RH). Using this new formula, all LInew values follow a uniform-like distribution, and optimal categorization of hemispheric dominance can be achieved at cut-off LInew = ± 1/3. Overall, this study investigated some statistical properties of LI and revealed interesting parallels with classic similarity indices in taxonomy. The theoretical distribution of LI should be taken into account when quantifying any existing bias in empirical distributions of lateralization in healthy or clinical populations.
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Notes
Tanimoto distance is not always a synonym for Jaccard distance. For binary data, Tanimoto index can be defined as the ratio of the intersecting set to the union set (as in Equation [11], see also Todeschini et al. 2012). In that case, Equation [10] is a proper distance metric (Lipkus 1999). This distance is also called Soergel’s distance.
References
Abbott DF, Waites AB, Lillywhite L, Jackson GD (2010) fMRI assessment of language lateralization: an objective approach. Neuroimage 50:1446–1455
Albatineh AN (2010) Means and variances for a family of similarity indices used in cluster analysis. J Stat Plan Inference 140:2828–2838
Albatineh AN, Khan HMR, Zogheib B, Kibria GBM (2017) Effects of some design factors on the distribution of similarity indices in cluster analysis. Commun Stat Simul Comput 46:4018–4034
Barbosa AM (2015) fuzzySim: applying fuzzy logic to binary similarity indices in ecology. Methods Ecol Evol 6:853–858
Bauer PR, Reitsma JB, Houweling BM, Ferrier CH, Ramsey NF (2014) Can fMRI safely replace the Wada test for preoperative assessment of language lateralisation? A meta-analysis and systematic review. J Neurol Neurosurg Psychiatry 85:581–588
Binder JR, Rao SM, Hammeke TA, Frost JA, Bandettini PA, Jesmanowicz A, Hyde JS (1995) Lateralized human brain language systems demonstrated by task subtraction functional magnetic resonance imaging. Arch Neurol 52:593–601
Binder JR et al (1996) Determination of language dominance using functional MRI: a comparison with the Wada test. Neurology 46:978–984
Bishop DV (2013) Cerebral asymmetry and language development: cause, correlate, or consequence? Science 340:1230531
Bradshaw AR, Bishop DVM, Woodhead ZVJ (2017) Methodological considerations in assessment of language lateralisation with fMRI: a systematic review. PeerJ 5:e3557
Cai Q, Van der Haegen L, Brysbaert M (2013) Complementary hemispheric specialization for language production and visuospatial attention. Proc Natl Acad Sci USA 110:E322–E330
Cha S-H (2007) Comprehensive survey on distance/similarity measures between probability density functions. Int J Math Models Methods Appl Sci 1:300–307
Chao A, Chazdon RL, Colwell RK, Shen TJ (2006) Abundance-based similarity indices and their estimation when there are unseen species in samples. Biometrics 62:361–371
Cheetham AH, Hazel JE (1969) Binary (presence-absence) similarity coefficients. J Paleontol 43:1130–1136
Chlebus P, Mikl M, Brazdil M, Pazourkova M, Krupa P, Rektor I (2007) fMRI evaluation of hemispheric language dominance using various methods of laterality index calculation. Exp Brain Res 179:365–374
Choi SS, Cha SH, Tappert C (2010) A survey of binary similarity and distance measures. J Syst Cybern Inf 8:43–48
Corballis MC (2014) Left brain, right brain: facts and fantasies. PLoS Biol 12:e1001767
Desmond JE et al (1995) Functional MRI measurement of language lateralization in Wada-tested patients. Brain 118:1411–1419
Drane DL et al (2012) Cortical stimulation mapping and Wada results demonstrate a normal variant of right hemisphere language organization. Epilepsia 53:1790–1798
Fagard J, Chapelain A, Bonnet P (2015) How should “ambidexterity” be estimated? Laterality 20:543–570
Fligner MA, Verducci JS, Blower PE (2002) A modification of the Jaccard-Tanimoto similarity index for diverse selection of chemical compounds using binary strings. Technometrics 44:110–119
Geschwind N, Galaburda AM (1985) Cerebral lateralization: biological mechanisms, associations, and pathology: I. A hypothesis and a program for research. Arch Neurol 42:428–459
Gower JC, Legendre P (1986) Metric and Euclidean properties of dissimilarity coefficients. J Classif 3:5–48
Holliday JD, Hu CY, Willett P (2002) Grouping of coefficients for the calculation of inter-molecular similarity and dissimilarity using 2D fragment bit-strings. Comb Chem High Throughput Screen 5:155–166
Hubalek Z (1982) Coefficients of association and similarity, based on binary (presence-absence) data: an evaluation. Biol Rev 57:669–689
Hwang C-M, Yang M-S, Hung W-L (2018) New similarity measures of intuitionistic fuzzy sets based on the Jaccard index with its application to clustering. Int J Intell Syst 33:1672–1688
Ivchenko GI, Polpchuk OV, Khonov SA (1995) Concerning a class of similarity tests. Math Notes 58:1049–1056
Janecek JK, Swanson SJ, Sabsevitz DS, Hammeke TA, Raghavan ME, Rozman M, Binder JR (2013) Language lateralization by fMRI and Wada testing in 229 patients with epilepsy: rates and predictors of discordance. Epilepsia 54:314–322
Jansen A et al (2006) The assessment of hemispheric lateralization in functional MRI-robustness and reproducibility. Neuroimage 33:204–217
Johnston JW (1976) Similarity indices I: what do they measure? Battelle. Pacific Northwest Laboratories, Virginia
Knecht S et al (2000) Handedness and hemispheric language dominance in healthy humans. Brain 123:2512–2518
Kong XZ et al (2018) Mapping cortical brain asymmetry in 17,141 healthy individuals worldwide via the ENIGMA Consortium. Proc Natl Acad Sci USA 115:E5154–E5163
Kosub S (2019) A note on the triangle inequality for the Jaccard distance. Pattern Recog Lett 120:36–38
Lipkus AH (1999) A proof of the triangle inequality for the Tanimoto distance. J Math Chem 26:263–265
Mazoyer B et al (2014) Gaussian mixture modeling of hemispheric lateralization for language in a large sample of healthy individuals balanced for handedness. PLoS One 9:e101165
McCormick WP, Lyons NI, Hutcheson K (1992) Distributional properties of Jaccard’s index of similarity. Commun Stat 21:51–68
McHugh ML (2012) Interrater reliability: the kappa statistic. Biochem Med 22:276–282 (Zagreb)
Oldfield RC (1971) The assessment and analysis of handedness: the Edinburgh inventory. Neuropsychologia 9:97–113
Paradowski M (2015) On the order equivalence relation of binary association measures. Int J Appl Math Comp Sci 25:645–657
Pinel P, Dehaene S (2010) Beyond hemispheric dominance: brain regions underlying the joint lateralization of language and arithmetic to the left hemisphere. J Cogn Neurosci 22:48–66
Real R (1999) Tables of significant values of Jaccard’s index of similarity. Misc Zool 22:29–40
Real R, Vargas JM (1996) The probabilistic basis of Jaccard’s index of similarity. Syst Biol 45:380–385
Seghier ML (2008) Laterality index in functional MRI: methodological issues. Magn Res Imaging 26:594–601
Seghier ML, Kherif F, Josse G, Price CJ (2011) Regional and hemispheric determinants of language laterality: implications for preoperative fMRI. Hum Brain Mapp 32:1602–1614
Snijders TAB, Dormaar M, van Schuur WH, Dijkman-Caes C, Driessen G (1990) Distribution of some similarity coefficients for dyadic binary data in the case of associated attributes. J Classif 7:5–31
Stroobant N, Buijs D, Vingerhoets G (2009) Variation in brain lateralization during various language tasks: a functional transcranial Doppler study. Behav Brain Res 199:190–196
Taha AA, Hanbury A (2015) Metrics for evaluating 3D medical image segmentation: analysis, selection, and tool. BMC Med Imaging 15:29
Todeschini R, Consonni V, Xiang H, Holliday J, Buscema M, Willett P (2012) Similarity coefficients for binary chemoinformatics data: overview and extended comparison using simulated and real data sets. J Chem Inf Model 52:2884–2901
Warrens MJ (2008) Similarity coefficients for binary data: properties of coefficients, coefficient matrices, multi-way metrics and multivariate coefficients. Leiden University, Leiden
Whitehouse AJ, Bishop DV (2009) Hemispheric division of function is the result of independent probabilistic biases. Neuropsychologia 47:1938–1943
Wolda H (1981) Similarity indices, sample size and diversity. Oecologia 50:296–302
Zijdenbos AP, Dawant BM (1994) Brain segmentation and white matter lesion detection in MR images. Crit Rev Biomed Eng 22:401–465
Zou KH et al (2004) Statistical validation of image segmentation quality based on a spatial overlap index. Acad Radiol 11:178–189
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This work was funded by ECAE’s Research Office.
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Seghier, M.L. Categorical laterality indices in fMRI: a parallel with classic similarity indices. Brain Struct Funct 224, 1377–1383 (2019). https://doi.org/10.1007/s00429-019-01833-9
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DOI: https://doi.org/10.1007/s00429-019-01833-9