The brain lateralization and development of math functions: progress since Sperry, 1974 — TEI-tagged view

SalillaspersName, Benavides-VarelapersName, SemenzapersName (2023date). “The brain lateralization and development of math functions: progress since Sperry, 1974.” Frontiers in Human Neurosciencetitle·j.

Object of study — which hemisphere sustains which mathematical function, and how that division changes from infancy to school age

Research question — Fifty years after Sperry concluded that calculation is almost exclusively a left-hemisphere function, how are math functions actually lateralized in the adult brain, and how does that lateralization develop?

Contribution — Reviewing lesion, neuroimaging, cortical-stimulation, TMSterm·mth and developmental evidence - and adding an ALEterm·mth meta-analysis with laterality indices for child fMRIterm·mth studies - it argues that the right hemisphereterm holds specific (not merely spatial) arithmetic functions and that the left IPSterm becomes dominant only for symbolicterm material at school age, while non-symbolicterm quantity processing stays right-lateralised from infancy.

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Abstract. In 1974, Roger Sperry, based on his seminal studies on the split-brainterm·mth condition, concluded that math was almost exclusively sustained by the language dominant left hemisphereterm. The right hemisphereterm could perform additionsterm·dom up to sums less than 20, the only exception to a complete left hemisphereterm dominance. Studies on lateralized focal lesions came to a similar conclusion, except for written complex calculation, where spatial abilities are needed to display digits in the right location according to the specific requirements of calculation procedures. Fifty years later, the contribution of new theoretical and instrumental tools lead to a much more complex picture, whereby, while left hemisphereterm dominance for math in the right-handed is confirmed for most functions, several math related tasks seem to be carried out in the right hemisphereterm. The developmental trajectory in the lateralization of math functions has also been clarified. This corpus of knowledge is reviewed here. The right hemisphereterm does not simply offer its support when calculation requires generic space processing, but its role can be very specific. For example, the right parietal lobe seems to store the operation-specific spatial layout required for complex arithmetical procedures and areas like the right insulaterm are necessary in parsing complex numbers containing zeroterm·dom. Evidence is found for a complex orchestration between the two hemispheres even for simple tasks: each hemisphere has its specific role, concurring to the correct result. As for development, data point to right dominance for basic numerical processes. The picture that emerges at school age is a bilateral pattern with a significantly greater involvement of the right-hemisphere, particularly in non-symbolicterm tasks. The intraparietal sulcus shows a left hemisphereterm preponderance in response to symbolicterm stimuli at this age. Introduction Roger Sperry and colleagues, in their seminal article on the split-brainterm·mth condition ( Sperry et al., 1969 ) concluded that calculation must be considered, along with speech and writing, a left hemisphereterm function and that the contribution of the right hemisphereterm to calculation was almost nil. In fact, they wrote, “tests for mathematical performance in the minor hemisphere with nonverbal readout and with the sensory input restricted to the left visual field or the left hand, indicate … that the capacity for calculation on the minor side is almost negligible. By manipulating marbles or dowel sticks, watching spots of light flashed to the left field and pointing with the left hand, … (split brainterm·mth) patients may succeed in matching numbers or in adding one to numbers below 10, but they fail when required to add or subtract two or higher numbers and they fail also at the simplest tasks in multiplicationterm·dom and division.” However, Sperry (1974) later observed how the right hemisphereterm could, in fact, perform additionsterm·dom up to sums less than 20, but that was the only exception to a complete left hemisphereterm dominance. Sperry’s conclusions were consistent with traditional wisdom. His contemporaries, in fact, considering the outcome of lateralized focal lesions, all agreed that primary acalculiaterm·def, the authentic deficit in arithmetic, was found only after left hemisphereterm lesions, while a right hemisphereterm lesion could only lead to calculation problems secondary to visuospatial disorders. Observed acalculiaterm·dom was thus classified in three main categories ( Berger, 1926 ; Hécaen et al., 1961 ; Hécaen and Angelergues, 1961 ): (1) “primary acalculiaterm·def” (“anarithmethiaterm·dom”), the disturbance of core math functions, resulting from lesions of the left parietal areas; (2) secondary acalculiaterm·dom, determined by language problems (mostly reading and writing disorders), resulting from lesions in left perisylvian, language-related, areas, and (3) secondary, “spatial” acalculiaterm·dom, following lesions of the posterior areas of the right hemisphereterm, related to spatial disorders, like, for instance, unilateral spatial neglectterm. In this classification, therefore, there was no primary role for the right hemisphereterm. Fifty years after Sperry’s article, the notions about brain laterality of calculation are radically changed. The contribution of new theoretical and instrumental tools leads to a much more complex picture, whereby, while a left hemisphereterm dominance for math in the right-handed is confirmed for most functions, several math related tasks seem to be carried out primarily in the right hemisphereterm. Moreover, even simple calculation, it is recognized, is sustained by complex networks where each of the two hemispheres may have a role of its own. Importantly, the developmental trajectory in the brain lateralization of math functions has also been clarified. The aim of this article is to summarize the state of the art about the lateralization of math functions, including its development under the influence of growth and education. In this last respect, existent meta-analyses will be scrutinized in terms of lateralization. The sources of evidence are lesion cases and neuroimaging techniques in adults as well as in developmental populations. Lesion cases Focal brain lesions may provoke so called “acalculiaterm·dom.” As mentioned in the introduction, since the earliest observations, a tripartite classification was proposed. Rather than being an exclusive result of a right or a left lateralized lesion, however, these different types of acalculiaterm·dom have a different frequency in left and in right hemisphereterm lesions ( Hécaen et al., 1961 ; Hécaen and Angelergues, 1961 ; Hécaen, 1962 ). Although different proportions are reported in various studies (see the reviewterm·mth by SemenzapersName, Benavides-VarelapersName and SalillaspersName, in press), anarithmethiaterm·dom and alexia/agraphia were always predominant after left hemisphereterm lesions and spatial acalculiaterm·dom was found predominant in right hemisphereterm lesions. In spatial acalculiaterm·dom patients are unable to respect the order and the position of digits in relation to each other; when the cause is neglectterm, one side of the calculation space is ignored. Notably, in the earlier literature, simple mental calculation, like tables, in which the possibility that errors originate from a spatial disorder is very unlikely, was occasionally found to be affected also after right hemisphereterm lesions ( Hécaen, 1972 ). The nature of such errors, however, was never discussed. Warrington and James (1967) addressed the issue of lateralization using very basic numerical tasks. They compared left and right brain damaged patients on tachistoscopic estimation of number of dots with untimed counting of dots. This last task did not show lateralization effects, while the estimation of number of dots was worse in the right parietal patients, as a consequence of a disturbance of approximationterm·dom abilities. Dehaene and Cohen (1991 , 1997) later appealed to this hypothesis in reporting three cases of acalculiaterm·dom who featured a double dissociation between calculation and approximationterm·dom abilities. Importantly, they proposed that simple single digit calculation can be solved either via a “direct” route or via an “indirect,” semantic route. The direct route (mainly used for additionterm·dom and multiplicationterm·dom and sustained by a left-sided cortico-subcortical circuit) would elicit the rote memory for the operation. The indirect route (preferentially used in subtractionterm·dom and located bilaterally in the inferior parietal cortex and in the left perisylvian network) would monitor the plausibility of a result retrieved by the direct route by referring to approximate magnitude knowledge. The anatomical correlates of the main acalculiaterm·dom types were the object of several group studies conducted via extensive batteries of math tasks. Grafman et al. (1982) compared left anterior, left posterior, right anterior, and right posterior patients on written additionsterm·dom, subtractionsterm·dom, multiplicationsterm·dom, and divisions, including multidigit ones. The worst performance was found in posterior groups, the left one being by far the most affected. This result still held when the influence of impairments of intelligence, visuospatial disorders, and aphasia was considered. No laterality effect was shown in the quality of errors. Similar results were found by Rosselli and Ardila (1989) in a more comprehensive study, including number reading and writing, number transcoding from Arabic codeterm to alphabetical code and vice versa, number size judgements, reading of arithmetical signs, mental and written calculation, successive additionsterm·dom, and subtractionsterm·dom, aligning of numbers for complex additionsterm·dom, and orally presented numerical problems. The left posterior group committed the highest number of errors, the quality of which seemed to vary according to the concomitant aphasia category; the right anterior and posterior groups did not differ from each other. Errors in the right hemisphereterm groups were analyzed in a later study ( Ardila and Rosselli, 1994 ).They appeared mostly in written calculation, where however the strategies and sequencies required to add, subtract, multiply and divide were preserved; moreover, arithmetical signs were correctly interpreted. In reading and writing numbers, the same spatial difficulties observed in reading and writing in general were observed. Disturbances of arithmetic reasoning and in simple calculation were also found. The authors attributed even these last errors to a spatial deficit. They argued, without further explanation, that they were related to the “general loss of automatisms” reported by Luria (1966) . Langdon and Warrington (1997) interestingly contrasted right and left lesions in calculation and arithmetical reasoning. They found that, unlike for calculation, the right hemisphereterm is involved in arithmetical reasoning as much as the left hemisphereterm. In Basso et al. (2000) only a small proportion of right hemisphereterm patients were found to be affected by acalculiaterm·dom if not affected by neglectterm: no report on the nature of their errors is provided. In their left hemisphereterm group with aphasia, almost half of the patients did not show signs of acalculiaterm·dom. The proportion of aphasic patients without acalculiaterm·dom was reported to be about a quarter of the group studied in Delazer et al. (1999) , where specific failures in specific math functions were related to specific aphasic syndromes. Thus, multiplicationterm·dom was especially hard for Broca’s aphasics, while calculation procedures were mostly affected in Wernicke’s aphasia. Confirming an earlier finding by Seron and Deloche (1983) , syntactic errors (substitution of multipliers, e.g., 4,000 instead of 400) were more frequent in Broca’s aphasia, whereas lexical errors (substitution of digits within position, e.g., 103 instead of 102) were mainly observed in Wernicke’s aphasia. More recent studies investigated the specific role of the right hemisphereterm more directly. A single case reported by Granà et al. (2006) provided evidence for a previously unknown specific function of the right hemisphereterm. The patient’s lesion was limited to the posterior areas of the right hemisphereterm. The only domain where he committed errors was that of procedures in multidigit written multiplicationterm·dom. In contrast, he was able to describe the procedures in words and knew all the steps necessary to perform the operation. His errors were not determined by a generic inability to deal with spatial material, or deficits like neglectterm. For example, he added the carryterm·dom to the leftmost side of the multiplicand, or of the partial product, or to the partial product in the row below. He seemed to know when and how the carryterm·dom must be added but he clearly forgot where . The authors concluded that he was lacking knowledge of the visuo-spatial layout representation specific to multiplicationterm·dom, that is learned at school and guides written multiplicationterm·dom. Reading aloud and writing on dictation multidigit numbers containing zeroterm·dom has also been found to be a right hemisphereterm specific function ( Benavides-VarelapersName et al., 2016 ). Surprisingly, right hemisphereterm patients, who are free from language disorders, committed many errors in these tasks, and not in numbers that do not contain zeroterm·dom. No relation was found of such errors with neglectterm or with generic cognitive impairment. These errors seem to reveal the existence of a basic mechanism entailing parsing and the ability to set-up empty-slot structures required for processing zerosterm·dom in complex numbers. As also confirmed in a subsequent study on a huge group of stroke patients ( Haupt et al., 2017 ), this ability can be located in the right insulaterm and its surroundings. Benavides-VarelapersName et al. (2014) further investigated the influence of neglectterm on calculation deficits. Right hemisphereterm patients without neglectterm still showed an impairment of math. Importantly, these patients failed in one-digit mental subtractionterm·dom and multiplicationterm·dom, tasks that do not require written visuospatial abilities. Thus, the authors concluded, patients with unilateral right hemisphereterm lesions did not just ignore the spatial arrangement of multi-digit written operations but were affected by specific representational deficits in simple mental calculation. Similar conclusions were reached by Dormal et al. (2014) : neglectterm patients performed worse in subtractionterm·dom, while they performed well on matched additionsterm·dom. According to the authors this result demonstrated a causal relationship between attending to the left side of space and solving subtractionsterm·dom. Benavides-VarelapersName et al. (2017) studied right hemisphereterm acalculiaterm·dom by administering NADL, a battery for numerical abilities ( SemenzapersName et al., 2014 ). Impairments were found in number comprehension, transcoding, and written operations. Interestingly, pure arithmetical errors (failure with number facts, carrying, borrowing, etc.) were more numerous than errors of spatial origin and were associated with lower parietal lesions; they were not predicted by visuo-spatial abilities. In contrast, spatial errors (misalignment, omissions of the left-most digits, number inversions, etc., often accompanied by neglectterm) were associated with lesions in fronto-temporoparietal areas; they were predicted by composite measures of visuo-spatial attentional and representational abilities. The respective role of the two hemispheres in the retrieval of arithmetical facts and other simple operations was clarified using direct cortical electrostimulation (DCEterm·mth) during tumor neurosurgery. Stimulation of the right parietal lobe impaired simple subtractionterm·dom ( Yu et al., 2011 ). Later studies identified positive sites in the right hemisphereterm also in additionterm·dom, in the supramarginal gyrus, and in multiplicationterm·dom, in the angular gyrusterm, the supramarginal gyrus, the interparietal sulcus and the superior parietal lobule ( Della Puppa et al., 2013 , 2015 ). Crucial information came from the analysis of substitution errors (omissions were less than 5%; SemenzapersName et al., 2017 ). Disruption on right parietal areas provoked multiplicationterm·dom errors, mostly consisting in replacing the correct solution with another table solution (e.g., 8×3 = 32 or 8 × 3 = 16). The authors attributed this effect to the left hemisphereterm, where the retrieval of tables is supported, taking over the operation. In contrast, disruption of the left hemisphereterm resulted in approximationterm·dom errors (e.g., 8 × 3 = 25). This would be due to the activity of the right hemisphereterm, where approximationterm·dom takes place. No individual site was positive for both additionterm·dom and multiplicationterm·dom. Errors therefore do not simply result from shortage of processing resources, which would have not provoked operation-specific deficits. Stimulation on the left hemisphereterm during simple additionterm·dom led to approximationterm·dom errors. Underestimation of the correct result was found after inhibition in both hemispheres: however, a larger deviation from correct was found after right hemisphereterm inhibition, reflecting a deficit in the approximationterm·dom mechanism. Neuroimaging studies of numerical processing in adults Studies on lateralization conducted via neuroimaging have been mostly inspired by the Triple Code Modelterm (TCMterm, Dehaene, 1992 ; Dehaene and Cohen, 1995 ), a theoretical framework encompassing three main numerical representations and the corresponding brain areas. The first proposed numerical representation is the Analogic Magnitude Representationterm·def ( Analogical Codeterm ), a pre-verbal representation, common to non-human species and pre-verbal infants, involved in virtually all numerical processes. It carries the numerical meaning, a “mental number lineterm” where numerosity is represented in a compressed manner, according to Weber’s law. It allows for the approximate contrast between sets of objects differing in numerosity. An approximate numerosity estimation system ( Approximate Number System – ANS) is referred to in some studies (e.g., Piazza, 2010 ). This analogical codeterm is located (according to a meta-analysis of neuroimaging data, Dehaene et al., 2003 ) bilaterally in the horizontal intraparietal sulcus (hIPSterm). Further studies confirmed this location using adaptation paradigms (e.g., Piazza et al., 2004 , 2007 ; Cantlon et al., 2006 ; Cohen Kadosh et al., 2007 ; Kadosh et al., 2011 ) and comparison tasks (e.g., Pinel et al., 1999 , 2001 ) where the ratio, or the distance, between numerosities is computed. A higher reliance on the right parietal areas for analogue quantities has also been proposed ( Faye et al., 2019 ). Cohen Kadosh et al. (2007) proposed that while the left parietal areas might process magnitude independently of format, the right parietal areas would process magnitude in a format dependent manner. The pattern of lateralization, is believed, may change when symbols are attached to numerical meanings. Vogel et al. (2015) showed hemispheric differences in the IPSterm using symbolicterm vs. non-symbolicterm stimuli. In a recent meta-analysis by Escobar-Magariño et al. (2022) lateralization indexes suggested a prevalent left IPSterm dominance when the stimuli were symbolicterm and a right IPSterm dominance when the stimuli where non-symbolicterm. A second numerical representation proposed by the TCMterm is the Visual Arabic Formterm·def (or Arabic Codeterm ), which works in the recognition of Arabic digits. It is located in the occipito-temporal cortices. The specific site of the so-called Number Form Area (NFAterm) has been the object of several studies in contrast to the visual word form area (VWFAterm). Electrocorticography studies ( Shum et al., 2013 ) seem to suggest a bilateral location. However, Hannagan et al. (2015) showed an asymmetry in favor of the right inferior temporal gyrus, and Yeo et al. (2017) meta-analysis indicated the right inferior temporal cortex as specific for the NFAterm. An Arabic number, unlike letters or letter strings, carries indeed numerical semantic information: this fact makes it likely a wider bilateral location of this recognition system. A complex network would be at work, encompassing the parietal regions bilaterally, and right lateralized superior and inferior frontal regions. Hannagan et al. (2015) suggested that the left NFAterm could be less differentiated from the VWFAterm, and less specific to number symbols. Nemmi et al. (2018) suggested that the right predominance of NFAterm could be explained by the default functional connectivity between inferior temporal gyrus (ITG) and IPSterm in the right hemisphereterm before symbols are learned. The connectivity with left parietal areas, they propose, would be established later, with the acquisition of symbols. Finally, the Verbal Word Frame ( Auditory-Verbal Codeterm ) organizes numbers as word sequences, supporting counting. Importantly, it sustains the retrieval of arithmetic factsterm·dom, which is achieved phonologically through rote verbal memory. Consistently with its verbal nature, it is lateralized ( Burbaud et al., 1995 ; Dehaene et al., 1999 ) in the left perisylvian areas and, specifically, in the left angular gyrusterm (AG). A training study of Delazer et al. (2003) showed a shift from IPSterm to left AG when learning of new arithmetic facts is achieved. This reflected a shift from quantity-based processes in IPSterm, to automatic retrieval of arithmetic factsterm·dom in left AG. Additional studies converged with these results with the additionterm·dom of the left hippocampusterm (e.g., Delazer et al., 2005 ; Ischebeck et al., 2006 ; Grabner et al., 2009 ; Bloechle et al., 2016 ). The TCMterm still constitutes a valid framework for the location of math functions. However, after over a quarter of a century, it needs additionsterm·dom. In particular, new important neuroimaging and electrophysiological findings have clarified the role of the right hemisphereterm, in keeping with the abovementioned research in the clinical domain. A meta-analysis by Arsalidou and Taylor (2011) evidenced how parietal areas are bilaterally relevant for additionterm·dom, subtractionterm·dom and multiplicationterm·dom. While additionterm·dom showed left hemisphereterm dominance, subtractionterm·dom appears to be sustained bilaterally and a right hemisphereterm dominance was found for multiplicationterm·dom (this last finding, surprising in consideration of a vast literature), was nonetheless confirmed in Rosenberg-Lee et al. (2011b) . The specific role of each hemisphere in simple calculation has been investigated by means of Magnetoencephalography (MEG). As stated by TCMterm, and in keeping with DCEterm·mth findings ( SemenzapersName et al., 2017 ), table retrieval seems to rely on a left frontoparietal circuit, while an analogous right frontoparietal circuit appears to support approximationterm·dom processes during calculation ( Arcara et al., 2021 ). Moreover, in SalillaspersName et al. (2021) the verification of incorrect multiplicationterm·dom solutions related to the operands (3 × 4 = 16) required a left hemisphereterm network, while the verification of multiplicationterm·dom solutions unrelated to the operands (3 × 4 = 13) needed a right hemisphereterm network. In the first case there is an interference of stored memories for arithmetic facts that is absent in the second case, hence the difference. Connectivity measures showed evidence for a loop between the left dorsolateral areas and the left AG, which might play a crucial role in resolving the interference of incorrect, yet related solutions. Inferior frontal areas, bilaterally, are probably used for final selection. Consistently with these findings Arcara et al. (2021) showed how retrieval of easy items (fastest responses) need the left AG in a first stage. The right dorsolateral prefrontal cortex as well right parietal areas, later contribute to identifying the correct solution. The lateralization of the mental number lineterm One important aspect of numerical cognition addressed with only a few neuroimaging studies is that of the lateralization of the “mental number lineterm,” a representation whereby, in left to right readers, small numbers are on the left and large numbers are on the right. The best demonstration of such representation is the so called SNARCterm (Spatial Numerical Association of Response Codes, Dehaene et al., 1993 ) effect: within a given interval, small numbers are responded faster with the left hand and larger numbers are responded faster with the right hand. Using Functional Near-Infrared Spectroscopy (fNIRS), Cutini et al. (2014) applied a comparison task and contrasted right and left responses to small and large numbers. Hence, they could contrast the hemodynamic response to SNARCterm compatible responses vs. SNARCterm incompatible responses. Bilateral HIPSterm and left AG appeared related to the SNARC effectterm·def and hIPSterm overlapped with the response to distance between numbers. The distance effect is a marker of the access to magnitude. Thus, these authors suggested a close link between space and the core number process during numerical comparison. Another recent study addressed the mental number lineterm with a different approach ( Liu et al., 2019 ). A previous work ( Zorzi et al., 2002 ) had shown how neglectterm patients tend to displace the center of number intervals to the right. That is, when asked to tell the middle number between two numbers (1–5), neglectterm patients shift the center of the interval to the right (responding 4 instead of 3), in the same way as they do with a line bisection task. Using fMRIterm·mth, Liu et al. (2019) applied the number bisection task and contrasted it with line bisection in healthy participants. The conjunction test for both tasks showed common activations mainly located bilaterally in parietal–frontal areas. They showed a bias towards the left hemisphereterm when contrasting number bisection minus physical bisection. This entailed a left hemisphereterm network: lingual gyrus, inferior frontal gyrus, precentral, inferior parietal lobule, the supplementary motor area, insulaterm, caudate, inferior temporal gyrus and thalamus. The authors highlighted a pivotal role of the left supplementary motor area (SMA) which is relevantly coupled with the bilateral frontoparietal networks, especially during number bisection. Hence, this work unveiled bilaterality for number bisection. However, it stressed that that number bisection, more than line bisection, requires a left lateralized network. Neurostimulation studies of numerical processing in adults While MRI was used in most studies, the electrophysiological responses were recorded in a few investigations conducted in epilepsy patients implanted with subdural electrodes. Thus Baek et al. (2018) found an increase in the high frequency broadband (HFB) activity in both the posterior inferior temporal gyrus and the intraparietal sulcus for equations presented in either digits or in number words. In the temporal gyrus the HFB activations were similar for digits and number words in the time of activation but differed in magnitude. In the intraparietal sulcus the activity was significantly delayed for number words in comparison to digits regardless of the hemisphere. A specific site in the posterior inferior temporal cortex was found by Pinheiro-Chagas et al. (2018) that activates during visual perception of numerals, with widespread adjacent responses when numerals are used in calculation. An initial burst of HFB activity decreased as the operands got larger. The authors concluded that while parietal sites appear to have a more sustained function in arithmetic computations, the inferior posterior inferior parietal area may contribute to early identification of the problem difficulty. These studies, however, do not seem to show any hemispheric asymmetry. TMSterm·mth has shown a role for both parietal lobes in processing quantity, including the left IPL ( Sandrini et al., 2004 ). Not all results were consistent with fMRIterm·mth studies ( SalillaspersName and SemenzapersName, 2015 ). In a number comparison task between two-digit numbers and a reference, Göbel et al. (2001) found a stronger effect for closer distances larger than the references after left AG stimulation. In Andres et al. (2005) the stimulation of the posterior parietal cortices (PPC) impaired comparison for close numbers, while only left PPC stimulation disrupted the comparison between far numbers. Cappelletti et al. (2007) found that, while the left IPSterm was crucial for both symbolicterm with non-symbolicterm stimuli, facilitation appeared only with stimulation of the right IPSterm. Sasanguie et al. (2013) the other hand, showed the crucial role of the left IPSterm in the mapping between small symbolicterm and non-symbolicterm numerosities. Cohen Kadosh et al. (2012) highlighted a role of the right IPSterm in the facilitation effect during a numerical Stroop task for physical judgments. Grotheer et al. (2016) showed a causal involvement of the right temporo-occipital cortex in the processing of masked Arabic numbers. Number magnitude tends to be contralaterally compatible with the MNL: right hemisphereterm with small numbers, and left hemisphereterm with big numbers. Cattaneo et al. (2009) found a variation in visual cortex excitability caused by the presentation of numbers: while small numbers increased the proportion of trials in which TMSterm·mth induced phosphenes after right occipital stimulation, large numbers increased this proportion after left occipital stimulation. Rusconi et al. (2007) showed bilaterally a SNARC effectterm·def in the posterior parietal lobes. Later, Rusconi et al. (2011) underlined the importance of right IFG and the frontal eye fields in the SNARC effectterm·def. Finally, SalillaspersName et al. (2009) , see also Renzi et al. (2011) showed that the ventral IPSterm, in the occipital part of IPSterm and within the network of motion perception ( Vanduffel et al., 2002 ; Orban et al., 2006 ), was causally linked to motion perception as well as to number comparison. A right hemisphereterm involvement was shown for small numbers, while large numbers seemed to be more bilateral. This motion-quantity association suggests that attention to motion may be a component of attention along the MNL ( McCrink et al., 2007 ). Most TMSterm·mth studies on calculation showed lateralization effects: additionterm·dom ( Göbel et al., 2006 ; SalillaspersName et al., 2012 ; Maurer et al., 2016 ; Montefinese et al., 2017 ), subtractionterm·dom ( Maurer et al., 2016 ; Montefinese et al., 2017 ; Fresnoza et al., 2020 ), multiplicationterm·dom ( Andres et al., 2011 ; SalillaspersName et al., 2012 ; Maurer et al., 2016 ; Fresnoza et al., 2020 ) and division ( Maurer et al., 2016 ) were studied. Bilaterality was shown for subtractionterm·dom but left lateralization for simple additionterm·dom and multiplicationterm·dom. Göbel et al. (2006) showed a role of the anterior and posterior left IPSterm for double digit additionterm·dom, and no effect on the right hemisphereterm. Montefinese et al. (2017) however showed a stronger role of the right hIPSterm for additionterm·dom, and a lesser asymmetry for the ventral IPSterm (vIPS). They showed, however, that bilateral hIPSterm and vIPS subserve additionterm·dom and subtractionterm·dom to different degrees. AG and supramarginal gyrus (SMG) bilaterally support additionterm·dom and subtractionterm·dom. The effects on the right SMG were stronger. ANG was more important for in additionterm·dom, while SMG was more involved in subtractionterm·dom. Fresnoza et al. (2020) distinguished retrieval from calculation strategies: the left AG was activated for both retrieval and calculation in multiplicationterm·dom, while it was only involved in retrieval during subtractionterm·dom. No detrimental effect was found for left hIPSterm. Andres et al. (2011) had also contrasted subtractionterm·dom and multiplicationterm·dom, showing a bilateral role of the hIPSterm for both operations. SalillaspersName et al. (2012) explored additionterm·dom and multiplicationterm·dom and found additionterm·dom to be supported by the horizontal part of the IPSterm (hIPSterm) bilaterally, while multiplicationterm·dom was supported by the left hIPSterm and, bilaterally, by the ventral IPSterm (vIPS). Maurer et al. (2016) stimulated more than 50 brain sites evidencing the probability of error for additionterm·dom, subtractionterm·dom, multiplicationterm·dom and division. The higher error rates in additionterm·dom appeared after inhibition of the right middle frontal gyrus, right AG, and superior temporal gyrus, as well as of the anterior superior temporal gyrus. In subtractionterm·dom, the highest proportion of errors appeared after inhibition of the right AG, as well as of the right SMG and the middle frontal gyrus. In multiplicationterm·dom, errors were more frequent after inhibition of the left AG and of the middle frontal gyrus. Finally, in division the highest error rates were provoked by inhibition of the left inferior parietal lobe, the left middle frontal gyrus, the posterior superior temporal cortex bilaterally, and the right middle precentral gyrus. The developmental changes of laterality The adult pattern of laterality is the result of a complex process in development. This section will summarize studies that concern the brain networks supporting numerical representations in the first stages of development, with a particular focus on lateralization and how it changes with neural maturation and enculturation. The differential role of the left IPSterm and the right IPSterm is evidenced through a meta-analysis at the end of this revision. Comprehensive and detailed reviewsterm·mth including other areas and functions (although not focused on lateralization) can be found in Arsalidou et al. (2018) , Peters and De Smedt (2018) , and Vogel and De Smedt (2021) . Magnitude representation abilities Behavioral studies (e.g., Izard et al., 2009 ; Benavides-VarelapersName and Reoyo-Serrano, 2021 ) report that children are equipped with the ability to represent number nonverbally from an early age. Two basic abilities are distinguished when analyzing numerical capacities in development. The first ability, present since birth and independent from language, consists in encoding and processing non-symbolicterm numerical representations ( Gelman and Butterworth, 2005 ; Dehaene, 2011 ). It implies distinguishing differences in the number of objects/dots in different sets. The second ability, at least partially independent from the first, consists of comprehending and using symbolicterm representation of numbers, for instance Arabic numbers and number words. Both abilities are gradually acquired and strongly rely on education and other capacities such as verbal counting or reading. Non-symbolicterm numerical abilities seem to be processed in the same areas in adults and young children. Clear asymmetries in the parietal regions are however evident in the first period of life. In fact, the left IPSterm does not have a strong involvement in sustaining basic numerical abilities early in life, while the right IPSterm readily encodes numerical magnitude independently of the amount of experience, mathematical knowledge, or age. For example, in the fMRIterm·mth study of Cantlon et al. (2006) , 4-year-old children and adults were exposed to a stream of dot arrays which occasionally changed in numerosity. Both groups showed stronger BOLD responses to novel than to familiar numerosities in the IPSterm. However, a stronger asymmetry towards the right hemisphereterm (i.e., resulting from lesser activity in the left IPSterm) was shown in children. Consistently, Holloway and Ansari (2010) tested older children (7- to 9-year-olds) and adults on both symbolicterm and non-symbolicterm number comparison. They showed that only a right-lateralized IPSterm activity was common to both groups. Studies with younger infants have also reported right lateralized brain responses to numerosity changes. For example, Izard et al. (2008) compared ERPs to changes in numerosity with those to changes in shape in 3-month-old infants. The response to numerical information originated primarily from right fronto-parietal regions. This study was consistent with an EEG study by Berger (2011) in 6–9-month-old infants, showing a right parietal activity related to the evaluation of numerosity in simple arithmetic equations. Likewise, in Libertus et al. (2009) , parametric variations were found in neural oscillations as a function of numerical ratio in 7-month-old infants: alpha-band (6–8 Hz) oscillations over midline and right posterior scalp sites were found to be modulated by the ratio between familiar and novel numerosities Studies using fNIRS, also found that only the right parietal cortex of 6-month-olds was sensitive to numerosity ( Hyde et al., 2010 ; Edwards et al., 2016 ). See Figure 1 for a graphical summary. Figure 1 Graphical summary on studies on quantity processing in infants. Studies using EEG and fNIRS are joined according to the NIRS channels and EEG electrodes where effects have been found. All tasks imply numerosity processing. The scale indexes the percentage of studies (6 studies) showing an effect on the channel. All data collection systems have been transformed to the standard 10–20 system location. See Supplementary Table S1 for details on the studies. The lateralization of numerical processing changes throughout development with maturation and the exposure to education. Rivera et al. (2005) showed an age-related increment in the recruitment of the left SMG during a task with symbolicterm digits. No such increment was observed contralaterally. Likewise, Ansari and Dhital (2006) showed greater effects of numerical distance on the left IPSterm in adults with respect to children. Thus, the involvement of left IPSterm seems to develop as a function of age and of experience with Arabic numerals and number words (e.g., Ansari, 2008 ). Emerson and Cantlon (2015) found that neural responses in the left IPSterm change systematically as a function of children’s numerical discrimination acuity whereas right IPSterm responses are constant over a 1–2-year period in young children. The sustained activation of the right IPSterm and the incremental takeover of the left inferior parietal areas eventually change into a more bilateral pattern observed in adults (see above sections). Approximate judgments, for example, correlate with stronger activation in the right than in the left IPSterm, while exact judgments correlate with a larger activation in the left ( Piazza et al., 2004 , 2007 ). Coordination between hemispheres may also gradually increase and sustain more efficient numerical processing throughout development. Cantlon et al. (2011) used fiber-based tractography to examine the relation between the integrity of the fibers of the corpus callosumterm connecting the left and right parietal lobes and performance on magnitude comparisonterm·mth tasks. Less integrity of these fibers was found in children compared with adults, with a correlation between integrity and the performance on the tasks. Thus, the interhemispheric connection seems to play an important role in the maturation of numerical representations. A later fMRIterm·mth study by Park et al. (2014) showed that the degree of the effective connectivity between the right parietal and the left parietal cortex can predict individual scores in a test of mathematical achievement. In general, better white matter integrity in connections of the prefrontal cortex and the posterior parietal cortex or the occipitotemporal cortex coincides with better arithmetic performance ( Matejko and Ansari, 2015 ). Other non-parietal areas also change their pattern of lateralization during life. ( Ansari et al., 2005 ) showed a right-lateralized frontal activity in a group of children while adults showed the typical bilateral IPSterm activation. This age-dependent frontal to parietal shift was replicated by Cantlon et al. (2009) . Monitoringterm·def, the process of continuously evaluating the internal or external contingencies to optimize behavior, which is right-lateralized in the frontal lobe ( Vallesi, 2012 ) could be working in children but gradually decrease in importance with age or practices. Arithmetic skills in typical development Learning of arithmetic, the ability to add, subtract, multiply and divide symbolicterm whole numbers, has been shown to depend on a widespread set of interconnected brain areas which include the IPSterm as a key region, but also areas involved in domain-specific and domain-general processes such as language, working memory, long term memory and visuo-spatial abilities: the dorsolateral and ventrolateral prefrontal cortex, the posterior superior parietal lobule (PSPLterm), the fusiform gyrus, the angular gyrusterm, the supramarginal gyrus, and the hippocampusterm ( Arsalidou et al., 2018 ). Activity associated with additionterm·dom and subtractionterm·dom increases over development in the right PSPLterm ( Rosenberg-Lee et al., 2011a ; Cho et al., 2012 ; Prado et al., 2014 ). Unlike for the IPSterm, the right PSPLterm is not considered to be specific to quantity-based processing, but to mechanisms of visuo-spatial attention, which might be progressively engaged or “recycled” in these tasks during arithmetic education ( Hubbard et al., 2005 ; Dehaene and Cohen, 2007 ; Knops et al., 2009 ; Prado et al., 2014 ). Learning arithmetic facts in multiplicationsterm·dom and additionsterm·dom, might rely on different strategies and developmental correlates ( Suárez-Pellicioni et al., 2022 ). Interestingly, activation in language-related areas, is not consistently evidenced in developmental studies (e.g., Rosenberg-Lee et al., 2011a , b ; Prado et al., 2014 ; Soltanlou et al., 2018 ; Declercq et al., 2022 ). Learning arithmetical facts in school-age children have been correlated with activity in the left-middle temporal gyrus ( Prado et al., 2014 ) and more consistently with the hippocampusterm ( Rivera et al., 2005 ; De Smedt et al., 2011 ). Reduced brain activity in the prefrontal cortex and increased activity in the right hippocampusterm were shown with the shift from the use of counting to memory-based strategies ( Qin et al., 2014 ). Cho et al. (2012) found that children who frequently used a retrieval strategy exhibited enhanced activity and connectivity from the right hippocampusterm and other areas in the frontal cortex, when compared to children who used procedural strategies. De Smedt et al. (2011) reported that the left hippocampusterm showed increased brain activity during fact retrieval problems in 10-to-12-year-olds ( De Smedt et al., 2011 ). Since adults seem to rely mainly on lower parietal areas, it has been suggested that the role of the hippocampusterm might be to encode new arithmetic facts before their representations can be transferred to language-related regions ( De Smedt et al., 2011 ; Peters and De Smedt, 2018 ). The lateralization of the response in the hippocampusterm, however, has not been clarified in the literature. Arithmetic skills in developmental dyscalculiaterm·dom One last issue connected with laterality concerns developmental dyscalculiaterm·dom (DDterm·dom). Differences between typically developing (TD) children and children with DDterm·dom have been reported in brain areas linked to general learning skills, including the hippocampal circuitry, the superior parietal lobule (SPL) and the prefrontal cortex ( Rotzer et al., 2008 ; Rykhlevskaia et al., 2009 ). Differences have also been found in the right IPSterm ( Molko et al., 2003 ; Rotzer et al., 2008 ), the left IPSterm ( Isaacs et al., 2001 ) or bilaterally ( Rykhlevskaia et al., 2009 ). A reduced white matter integrity of the superior longitudinal fasciculus is reported for DDterm·dom ( Rykhlevskaia et al., 2009 ). These tracts appeared to increase with age in the TD but not in the DDterm·dom children ( Ranpura et al., 2013 ). No clear differences between the anatomical alterations in the left and the right hemispheresterm emerge from these studies. Brain functional alterations have also been reported in DDterm·dom. Kucian et al. (2006) found that, when solving an approximate arithmetic task, children with DDterm·dom, compared to TD, had weaker activation in the left IPSterm as well as right inferior frontal gyrus and right medial frontal gyrus. Price et al. (2007) found that children with DDterm·dom showed significantly less brain activity in the right IPSterm compared to age- and IQ-matched TD children during a non-symbolicterm magnitude comparisonterm·mth task. Right or bilateral IPSterm differences compared to controls were also observed in further symbolicterm comparison tasks ( Soltész et al., 2007 ; Mussolin et al., 2010 ). In contrast, Michels et al. (2018) revealed increased activation in the left IPSterm, frontal cortex, and visual areas in DDterm·dom during number processing, as well as functional hyperconnectivity in parietal, frontal, visual, and temporal regions. This finding has been attributed to compensatory mechanisms and the increment of cognitive control resources in DDterm·dom ( Kaufmann et al., 2009 ). Children with DDterm·dom, differently from TD children, recruit the fronto-parietal network to the same extent for both easy and hard problems ( De Smedt et al., 2011 ; Ashkenazi et al., 2012 ). A recent meta-analysis by Tablante et al. (2023) considered the findings of 24 studies with 728 children, revealed that the most consistent dysfunction across studies was in the right parietal lobe along the intraparietal sulcus (IPSterm), suggesting a core deficit in quantity processing. Laterality patterns of neuroimaging studies in children In this section we systematically assess the degree of lateralization of brain areas associated with number comprehension and in simple calculation (additionterm·dom) in children. There are recent meta-analyses focusing on this issue ( Arsalidou et al., 2018 ; Peters and De Smedt, 2018 ), yet concrete measures of lateralization across studies were not included. Based on the literature compiled by those meta-analysis, homogeneity in the tasks and the concrete dependent measures of the studies is emphasized. First, the literature on quantity was split in two subsets, attending to the use of symbolicterm or non-symbolicterm material. Then, laterality indexes (LIs)term·stat were obtained from each of the two subsets. Second, the literature on calculation was studied for lateralization too. Because studies focusing on subtractionterm·dom and multiplicationterm·dom are sparse, they did not provide enough statistical power for the analyses. Thus, only additionterm·dom problems were analyzed. To achieve further homogeneity, only studies that involved neuroimaging (fMRIterm·mth) on school-age children over 6 years were included. fMRIterm·mth studies with younger children were excluded because they are scarce ( Cantlon et al., 2006 ; Park et al., 2014 ; Kersey and Cantlon, 2017 ). All correlational analysis with other variablesterm·var were not considered, given the variability in measures across studies. See Supplementary material for details on the included studies. Within the non-symbolicterm studies subset , all the tasks involved quantity comparison ( Ansari and Dhital, 2006 ; Kaufmann et al., 2008 ; Kucian et al., 2011 ; Berteletti et al., 2014 , 2015 ; Demir-Lira et al., 2016 ). The attended contrast was ratio or distance in all of them. The average age between studies was 10.67 y.o. (SD: 1.09) and the total number of participants was 128.Within the symbolicterm subset of studies , the tasks involved the comparison of two Arabic digits ( Ansari et al., 2005 ; Meintjes et al., 2010 ; Bugden et al., 2012 ; Gullick and Wolford, 2013 ), the matching between symbolicterm and non-symbolicterm formats ( Emerson and Cantlon, 2012 , 2015 ), and the adaptation to symbolicterm numerical stimuli ( Vogel et al., 2015 ). The attended contrast were ratio or distance effects ( Ansari et al., 2005 ; Meintjes et al., 2010 ; Bugden et al., 2012 ; Gullick and Wolford, 2013 ; Vogel et al., 2015 ) or a contrast to non-numerical stimuli ( Meintjes et al., 2010 ; Emerson and Cantlon, 2012 , 2015 ). Differing from Arsalidou et al. (2018) , and again with the main goal of increasing homogeneity across studies, the contrasts for negative numbers in Gullick and Wolford (2013) were not included. The average age between studies was 9.77 y.o. (SD: 1.84) and the total number of participants was 136. Within the additionterm·dom studies , all except one study involving passive mental calculation ( Kawashima et al., 2004 ) involved a verification task with one solution ( Rosenberg-Lee et al., 2011a ; Ashkenazi et al., 2012 ; Cho et al., 2012 ; Metcalfe et al., 2013 ; Qin et al., 2014 ), a selection between two ( Meintjes et al., 2010 ; De Smedt et al., 2011 ) or three solutions ( Davis et al., 2009 ). Most of the used contrasts involved one-digit operands that were contrasted to the sum +1 ( Rosenberg-Lee et al., 2011a ; Ashkenazi et al., 2012 ; Cho et al., 2012 ; Metcalfe et al., 2013 ; Qin et al., 2014 ). Meintjes et al. (2010) and Davis et al. (2009) implied the contrast to equivalent non-numeric symbolicterm tasks. The contrast from De Smedt et al. (2011) involved additionterm·dom > subtractionterm·dom, and Kawashima et al. (2004) involved the contrast additionterm·dom > fixation. The average age between studies was 9.06 y.o. (SD: 1.57) and the total number of participants was 136. Supplementary Table S2 for details the included studies in each of the three sets. The meta-analysis was performed with Ginger-Ale ( http://brainmap.org/aleterm·mth/; Research Imaging Center of the University of Texas in San Antonio), which estimates the likelihood that at least one of the coordinates falls in the template stereotaxic space, in activation likelihood estimated (ALE) valuesterm·stat. All the coordinates were transformed to the MNI space, considering the method used by the authors for normalization. Then the meta-analysis was conducted in the MNI space. ALEterm·mth maps were calculated with a corrected value of p < 0.001. Figures 2 – 4 shows the ALEterm·mth maps for the non-symbolicterm, symbolicterm subsets, and for additionterm·dom, respectively. Figure 2 Laterality pattern for non-symbolicterm quantity processing in school age children. Right: Results of meta-analysis displaying supra-threshold ALEterm·mth values (corrected p valueterm·stat < 0.001). Left: LIs values computed on those ALEterm·mth values. Range −1 to +1. Negative values mean right hemisphereterm (RH) predominance. Positive means left hemisphereterm (LH) predominance. Age range: 8.6–11.5 y.o. See Supplementary Table S3 for details on the suprathreshold clusters. Figure 3 Laterality pattern for symbolicterm quantity processing in school age children. Right: Results of meta-analysis displaying supra-threshold ALEterm·mth values (corrected p valueterm·stat < 0.001). Left: LIs values computed on those ALEterm·mth values. Range −1 to +1. Negative values mean right hemisphereterm (RH) predominance. Positive means left hemisphereterm (LH) predominance. Age range: 6.6–12.7 y.o. See Supplementary Table S3 for details on the suprathreshold clusters. Figure 4 Laterality pattern for simple additionterm·dom in school age children. Right: Results of meta-analysis displaying supra-threshold ALEterm·mth values (corrected p valueterm·stat < 0.001). Left: LIs values computed on those ALEterm·mth values. Range −1 to +1. Negative values mean right hemisphereterm (RH) predominance. Positive means left hemisphereterm (LH) predominance. Age range: 7.7–11.9 y.o. See Supplementary Table S3 for details on the suprathreshold clusters. To examine the hemispheric asymmetries, the MATLAB script AveLI ( Matsuo et al., 2012 ; http://aveli.web.fc2.com ) was used. This program considers not only the extension in voxels falling within two masks (left and right hemisphereterm mask), but also the intensity of the ALEterm·mth value in our case. The masks used were selected after observing the areas with suprathreshold in each of the ALEterm·mth maps (see Figures 2 – 4 and Supplementary material ). The masks were derived from a Freesurfer atlas. Then, the three suprathreshold ALEterm·mth values maps (symbolicterm, non-symbolicterm and additionterm·dom) were entered in the analysis, considering each of the selected masks. The non-symbolicterm quantity subset analysis showed suprathreshold ALEterm·mth values in the bilateral superior parietal lobe and the right IPSterm. The laterality indexesterm show a clear right asymmetry in the IPSterm, the involvement of bilateral SPLs (see Figure 2 ). symbolicterm quantity subset analyses showed significant clusters in the bilateral IPSterm, middle frontal gyrus (MFG), superior frontal gyrus (SFG). Moreover, the putamen, claustrum, the insular cortices and precentral SFG, MFG, Middle Cingulate cortex, showed also significant ALEterm·mth values. Attending to the LIs, and clearly differing from the non-symbolicterm subset, the IPSterm showed a left hemisphereterm preponderance. All the rest of areas showed a dominance for the right hemisphereterm (see Figure 3 ). The data on quantity processing confirm that the parietal areas used by children for processing numerical quantity differ in lateralization for symbolicterm and non-symbolicterm stimuli, especially for the IPSterm: the left IPSterm is driving the process with symbolicterm numbers while the right IPSterm drives quantity processing when the stimuli are non-symbolicterm. Moreover, the processing of symbolicterm stimuli involves of a wider cortical network that is bilateral, but with a right hemisphereterm dominance. This wider network involves a higher processing weight of the right putamen, insulaterm, middle cingulate gyrus, precentral gyrus, MFG, and SFG, which seem not necessary for the non-symbolicterm material. Supplementary Figure S1 shows the analysis performed including also studies on children from 4 years. Frontal areas loose relevance in the non-symbolicterm subset with age. Yet insulaterm and putamen are still irrelevant areas on non-symbolicterm quantity processing in younger children. As per exact calculation (additionterm·dom), the ALE-maps show suprathreshold values in the right occipital pole, bilateral insulaterm and IFG, bilateral MFG, the right middle cingulate cortex, the left SMA and the left parietal cortex only. LIs shows a clear left dominance for the IPSterm. And a tendency for bilaterality, yet with slighter bigger dominance for the right frontal hemisphere (IFG, MFG and SFG), as well as bilateral insular cortex, with a similar slight right predominance (see Figure 4 ). To summarize, the results indicate that, at school age, the laterality pattern changes as a function of the numerical stimuli presented. The use of non-symbolicterm stimuli in magnitude comparisonterm·mth tasks entails a clear involvement of the parietal areas in the right hemisphereterm. Tasks with number symbols instead, shift the laterality pattern with significantly stronger activation in the left IPSterm. This pattern resembles the one recently reported by Escobar-Magariño et al. (2022) in adults. It is also somehow in agreement with the proposal of Cohen Kadosh et al. (2007) that parietal areas would process magnitude in a format dependent manner. Thus, the overall right lateralization in children reported in previous meta-analyses (e.g., Arsalidou et al., 2018 ) have been influenced by the non-symbolicterm literature. Non-symbolicterm quantity processing in school-age overall seems to be already rely mainly on the parietal cortex. Besides parietal areas, symbolicterm quantity processing and additionsterm·dom in children rely on more extended brain activity. Areas in the frontal, insular and occipital cortex are also recruited in these tasks and might be related with effortful control, learning and generally less automatized processing mechanisms compared to adults (see also Arsalidou and Taylor, 2011 ; Arsalidou et al., 2018 ) These areas show clear lateralization to the right hemisphereterm. Notably, children show a more extended and less specialized network. Finally, in processing symbolicterm stimuli, the insular cortex and the cingulate are active during both quantity and additionterm·dom processes. This agrees with Arsalidou and Taylor (2011) and Arsalidou et al. (2018) , however these areas seem to play a role only with symbolicterm stimuli. More studies should address the exact function of these areas both in calculation and numerical quantity processing. Conclusion Lateralization of math in the brain has been investigated in several ways and considerable progress has been made since Sperry’s times. Besides clinical observations, still very important in several respects, new methodologies, unknown before the end of the last century, have been employed. The notion emerges of an interaction of the two hemispheres involving complex brain networks. However, each hemisphere seems to maintain its own role. An important, perhaps the newest, result is that there is more than a simple difference along the verbal/spatial dimensions distinguishing the work of each hemisphere. Very specific arithmetical functions like remembering the spatial templates for complex operations, or processing of zeroterm·dom in complex numbers, are indeed sustained in specific right sided areas. Importantly, the numerical brain undergoes a complex pattern of development. The ability to represent numbers nonverbally is supported mainly by right IPSterm and seems to be present from a very early age. This area is shown to be dysfunctional in developmental acalculiaterm·dom. Growth and education then shape less mature networks into more efficient ones. Later, at school ages, with the exposure to numerical codes like the Arabic codeterm and written number words, a more extended set of brain areas appears involved, while the role of the left IPSterm becomes dominant. Author contributions ES: Conceptualization, Formal analysis, Methodology, Writing – original draft, Writing – reviewterm·mth & editing. SB-V: Conceptualization, Funding acquisition, Validation, Writing – original draft, Writing – reviewterm·mth & editing. CS: Conceptualization, Validation, Writing – original draft, Writing – reviewterm·mth & editing.