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. Author manuscript; available in PMC: 2016 Jan 1.
Published in final edited form as: Clin Neurophysiol. 2014 May 9;126(1):39–46. doi: 10.1016/j.clinph.2014.04.015

Mapping Mental Calculation Systems with Electrocorticography

Keisuke Ueda 1, Erik C Brown 3,4, Katsuaki Kojima 1, Csaba Juhász 1,2, Eishi Asano 1,2,*
PMCID: PMC4225188  NIHMSID: NIHMS593777  PMID: 24877680

Abstract

Objective

We investigated intracranially-recorded gamma activity during calculation tasks to better understand the cortical dynamics of calculation.

Methods

We studied 11 patients with focal epilepsy (age range: 9–28 years) who underwent measurement of calculation- and naming-related gamma-augmentation during extraoperative electrocorticography (ECoG). The patients were instructed to overtly verbalize a one-word answer in response to auditorily-delivered calculation and naming questions. The assigned calculation tasks were addition and subtraction involving integers between 1 and 17.

Results

Out of the 1001 analyzed cortical electrode sites, 63 showed gamma-augmentation at 50–120 Hz elicited by both tasks, 88 specifically during naming, and 7 specifically during calculation. Common gamma-augmentation mainly took place in the Rolandic regions. Calculation-specific gamma-augmentation, involving the period between the question-offset and response-onset, was noted in the middle-temporal, inferior-parietal, inferior post-central, middle-frontal, and premotor regions of the left hemisphere. Calculation-specific gamma-augmentation in the middle-temporal, inferior-parietal, and inferior post-central regions peaked around the question offset, while that in the frontal lobe peaked after the question offset and before the response onset. This study failed to detect a significant difference in calculation-specific gamma amplitude between easy trials and difficult ones requiring multi-digit operations.

Conclusions

Auditorily-delivered stimuli can elicit calculation-specific gamma-augmentation in multiple regions of the left hemisphere including the parietal region. However, the additive diagnostic value of measurement of gamma-augmentation related to a simple calculation task appears modest.

Significance

Further studies are warranted to determine the functional significance of calculation-specific gamma-augmentation in each site, and to establish the optimal protocol for mapping mental calculation.

Keywords: Epilepsy surgery, Intracranial ECoG recording, Ripples, High-frequency oscillations (HFOs), Number, Numeral, Speech, Language, Functional brain mapping

INTRODUCTION

Mental calculation, performed in mind without the help of a pen, paper, or fingers, is an essential skill in our daily activities. Mental calculation relies on a highly complex set of processes, many of which are not strictly specific to the number domain (Ashcraft, 1992; Dehaene et al., 2003). For example, the verbal processing required to answer “Thirteen” for an audible task “Four plus nine” includes (1) phonological and semantic analyses of each word and (2) syntactic analysis of a given equation. Such phonological, semantic, and syntactic analyses are needed not only during calculation but also during object naming. Conversely, retrieval of memorized arithmetic facts is a central calculation-specific process for solving addition and subtraction problems involving single-digit or teen integers (McCloskey et al., 1991; Ashcraft, 1992; Dehaene et al., 2003; Klein et al., 2010). By the fourth grade, children generally secure a memory retrieval strategy for simple problems, while very young children still heavily reply on overt or covert counting strategy (Ashcraft and Fierman, 1982). Older children and adults can effortlessly retrieve a correct answer for easy problems (such as “Three plus two”). Conversely, more difficult and less familiar problems involving multi-digit operations (such as “Four plus nine”) might require some additional strategies such as counting or referring to related operations (Campbell and Xue, 2001; Grabner et al., 2009).

We believe that mapping of the cortical sites involved in mental calculation including arithmetic fact retrieval is highly justified in epilepsy surgery. Yet, not many investigators have incorporated a calculation task in functional cortical mapping using direct cortical stimulation or measurement of task-related signal changes on electrocorticography (ECoG). In the present study, thus, we attempted to explore if intracranial measurement of event-related gamma activity would reveal the spatial-temporal characteristics of cortical activation specific to mental calculation and not to object naming. Augmentation of gamma activity at 50–120 Hz is an excellent summary measure of in situ cortical activation (Lachaux et al., 2012; Kojima et al., 2013a; 2013c). Since equation stimuli were presented auditorily in the present study, we expected that calculation-specific gamma-augmentation would involve the period between the offset of auditory stimuli and the onset of overt responses and that such delayed gamma augmentation cannot be simply explained by difference in the physical property of auditory stimuli. We also tested the hypothesis that relatively difficult calculation problems, compared to easy ones, would elicit larger calculation-specific gamma augmentation.

We expected that calculation-specific gamma-augmentation would at least involve the left parietal region. Previous lesion studies suggested that the left parietal lobe may be crucial for calculation (Gerstmann, 1940; Grafman et al., 1982; Dehaene and Cohen, 1991). A more recent study reported patients with isolated acalculia resulting from strokes involving the left intraparietal sulcus (Takayama et al., 1994). A study using functional MRI (fMRI) and transcranial magnetic stimulation (TMS) showed that the left and right parietal lobes were hemodynamically activated during a calculation task and that stimulation of the activated areas increased the response time (Andres et al., 2011). A recent ECoG study of three adult patients with focal epilepsy showed augmentation of gamma activity in the left or right parietal lobe (Dastjerdi et al., 2013). While the aforementioned fMRI, TMS, and ECoG studies with equation stimuli presented visually, the uniqueness of the present study was that both calculation and naming questions were delivered auditorily. Replication of parietal gamma augmentation in a calculation task with stimuli of a different modality would further clarify the causal role of parietal lobe in mental calculation.

1. METHODS

1.1. Patients

We studied 11 native English-speaking patients with focal epilepsy (age range: 9–28 years; 3 males, 8 females; Table 1) who satisfied the following inclusion and exclusion criteria. The inclusion criteria included: (i) history of focal epilepsy scheduled for extraoperative ECoG recording as part of the presurgical evaluation at Children’s Hospital of Michigan or Harper University Hospital, Detroit, between August 2009 and November 2013, and (ii) completion of both calculation and naming tasks during extraoperative ECoG recording. The exclusion criteria consisted of: (i) presence of massive brain malformations (such as perisylvian polymicrogyria or megalencephaly) altering the major anatomical landmarks, (ii) severe cognitive dysfunction reflected by verbal comprehension index or verbal IQ of <70, and (iii) diagnosis of acalculia. This study has been approved by the Institutional Review Board at Wayne State University, and written informed consent was obtained from each adult patient or the legal guardian of each pediatric patient. Written assent was obtained from children above 13.

Table 1.

Patient profile.

Patient
number		 Age at
surgery
(year)		 Age of
seizure
onset
(year)		 Antiepileptic
medications		 Seizure onset
zone		 Sampled
hemisphere
1 14 13 LCM, LEV, OXC Not captured Left
2 9 9 OXC Temporal Left
3 17 15 LCM, LMG Temporal Left *
4 21 19 LEV, PHT Temporal Left
5 28 5 LCM, VPA Temporal Right
6 12 9 LCM, LMG Temporal Left
7 14 12 LMG, OXC, TPM Temporal Left
8 27 14 LEV Frontal Left
9 13 9 LEV, OXC Frontal Right
10 16 13 OXC, PGB Temporal Right
11 13 1 LEV, OXC Temporal Left
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*

: ECoG signals in the parietal region were included in analysis in all patients but patient #3.

LCM: lacosamide, LEV: levetiracetam, LMG: lamotrigine, OXC: oxcarbazepine, PGB: pregabalin, PHT: phenytoin, VPA: valproate, TPM: topiramate.

1.2. Subdural electrode placement

Subdural platinum grid and strip electrodes (10-mm inter-contact distance; 4-mm diameter) were surgically placed on the presumed epileptogenic hemisphere (left-sided in eight and right-sided in three patients). Placement of subdural electrodes was clinically guided by the results of Phase-I presurgical evaluation including: scalp video-EEG recording, MRI, and 2-deoxy-2-[18F] fluoro-D-glucose positron emission tomography (FDG PET) (Asano et al., 2009). The total number of analyzed electrodes per patient ranged from 86 to 138. All electrode plates were stitched to adjacent plates or the edge of dura mater, to avoid movement of subdural electrodes after placement. In all patients, intraoperative photographs were taken with a digital camera before dural closure as well as after re-opening during the second stage of surgery. All electrodes were displayed on the three-dimensional brain surface reconstructed from high-resolution MRI (Alkonyi et al., 2009; Wu et al., 2011). We confirmed the spatial accuracy of electrode display on the three-dimensional brain surface by comparison to the intraoperative digital photographs.

1.3. Extraoperative video-ECoG recording

Extraoperative video-ECoG recordings were obtained for 3 to 5 days, using a 192-channel Nihon Kohden Neurofax 1100A Digital System (Nihon Kohden America Inc., Foothill Ranch, CA, USA) at a sampling frequency of 1,000 Hz and an amplifier band pass of 0.08 to 300 Hz. The averaged voltage of ECoG signals derived from the fifth and sixth subdural electrodes of the ECoG amplifier was used as the original reference (Wu et al., 2011). ECoG signals were then re-montaged to a common average reference. Channels contaminated with artifacts or large interictal epileptiform discharges were excluded from the common average reference to minimize their influence on the results (Fukuda et al., 2008). Surface electromyography electrodes were placed on the left and right deltoid muscles, and electrooculography electrodes were placed 2.5 cm below and 2.5 cm lateral to the left and right outer canthi. ECoG traces were visually inspected with a time-constant of 0.003 s and a sensitivity of 20 µV/mm; thereby, irregular broadband signals synchronized with facial and ocular muscle activities seen on electrooculography electrodes were treated as artifacts (Otsubo et al., 2008; Jerbi et al., 2009; Kovach et al., 2011; Kojima et al., 2013c). Seizure onset sites were clinically determined (Asano et al., 2009) and excluded from further analysis.

1.4. Mental calculation task

During extraoperative ECoG recording, patients were assigned a series of 96 calculation trials, each of which was either simple addition or subtraction. All questions were delivered via playback of an audio recording of a native English speaking researcher’s (E.C.B.) voice using Presentation version 9.81 software (Neurobehavioral Systems Inc., Albany, CA, USA). Integers between 1 and 17 were used as stimuli in the calculation tasks; tie problems (e.g.: ‘Two plus two’) were excluded and solutions of the tasks did not include 10 and did not exceed 17. Within ‘addition’ trials, easy questions were defined as those with the correct answers not more than 9 (e.g.: ‘Six plus two’), while difficult ones between 11 and 17 (e.g.: ‘Five plus seven’). Within ‘subtraction’ trials, easy trials were defined as those with the stimuli consisting of single-digits alone (e.g.: ‘Nine minus five’), while difficult ones consisted of double-digit and single-digit numbers (e.g.: ‘Eleven minus four’). Thereby, all difficult trials commonly involved a multi-digit operation, while easy ones did not. Twenty-four easy addition, 24 difficult addition, 24 easy subtraction and 24 difficult subtraction trials were presented in a pseudorandom order. Patients were instructed to overtly verbalize a one-word answer (e.g.: ‘Eight’ for ‘Six plus two’) or ‘I don't know’ when they were unable to provide an answer. Patients were also instructed not to overtly count or to use their fingers for counting. The entire audible session was recorded and integrated with ECoG as previously described (Brown et al., 2008). Subsequently, the onset and offset of auditory stimuli as well as the onset of the patient's vocalization of the response were marked for each trial. Cool-Edit Pro Software (Syntrillium Software Corp., Phoenix, AZ, USA) was used to visually and audibly aid in the manual determination of these time points (Brown et al., 2008). The response time, defined as the period between offset of stimulus presentation and onset of the respective overt response, was measured for each trial.

1.5. Object naming task

Patients were also assigned an auditory naming task as previously reported (Brown et al., 2008; Kojima et al., 2013c). Patients received 85–100 question-and-answer trials. All questions were likewise delivered auditorily and were designed to elicit one- or two-word answers with nouns; e.g., “What flies in the sky?” Patients were instructed to answer: “I don't know” when they did not know the answer or did not understand a given question.

1.6. Measurement of task-related gamma-activity

We determined the spatial-temporal characteristics of task-related gamma-augmentation as previously validated (Wu et al., 2011; Kojima et al., 2013a; 2013c). In short, each ECoG trial containing both the question and the correct answer was transformed into the time-frequency domain using a complex demodulation technique incorporated in BESA® EEG V.5.1.8 software (BESA GmbH, Gräfelfing, Germany) (Hoechstetter et al., 2004). The ECoG signal at each channel was assigned an amplitude (a measure proportional to the square root of power) as a function of time and frequency (in steps of 10 ms and 5 Hz, respectively). The time-frequency transform was obtained by multiplication of the time-domain signal with a complex exponential, followed by a band-pass filter. The band-pass filter used here was a finite impulse response filter of Gaussian shape, making the complex demodulation effectively equivalent to a Gabor transform. The filter had a full width at half maximum of 2 × 15.8 ms in the temporal domain and 2 × 7.1 Hz in the frequency domain. The corresponding time-frequency resolution was ±15.8 ms and ±7.1 Hz (defined as the 50% power drop of the finite impulse response filter). ECoG traces were aligned to: (i) stimulus (question) onset; (ii) stimulus offset; and (iii) response (answer) onset. We systematically determined ‘when,’ ‘where,’ and ‘how much’ gamma activity at 50–120 Hz averaged across trials was augmented compared to the silent/resting periods between given trials within each task (see the methodological details in Supplementary Figure S1; Kojima et al., 2013c). ECoG traces aligned to the stimulus onset were used to assess cortical activation elicited by auditory stimuli, while those aligned to the stimulus offset were used to assess cortical activation not attributed to perception of the auditory stimuli but rather that elicited by cognitive activities following auditory perception. Those aligned to the response onset were used to assess cortical activation elicited by preparation and execution of overt responses.

We subsequently determined whether the degree of task-related gamma augmentation in each time-frequency bin reached significance using studentized bootstrap statistics followed by Simes’ correction (see the methodological details and discussion in Wu et al., 2011; Kojima et al., 2013c). Sites showing significant gamma-augmentation50–120 Hz (corrected p-value <0.05) spanning (i) at least 20 Hz in width and (ii) at least 20 ms in duration were defined as ‘task-related gamma sites’ (Figures 1 and 2). We previously reported that concordant clinical symptoms were elicited by electrical stimulation of ‘sensory and motor-related gamma sites50–120 Hz’ as defined above (Fukuda et al., 2008; Nagasawa et al., 2010a; 2010b; Kojima et al., 2012). We also reported that resection of ‘naming-related gamma sites’ resulted in post-operative language deficits requiring speech therapy (Kojima et al., 2013a; 2013c).

Figure 1. Task-specific gamma-augmentation in a 14-year-old girl.

Figure 1

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(A) The results of time-frequency analyses relative to stimulus offset are shown. Red electrodes: ‘calculation-specific gamma sites’. Blue electrodes: ‘naming-specific gamma sites’. Yellow electrodes: ‘common gamma sites’. (B) The time-frequency plots relative to stimulus offset are shown. Red bins: amplitude augmentation. Blue bins: amplitude attenuation. At channel #1 in the left inferior parietal region (BA 39), mild but significant gamma-augmentation50–120Hz was noted between −190 ms and +470 ms relative to the stimulus offset during the calculation task. At channel #2 in the left middle temporal region (BA 21), significant gamma-augmentation50–120Hz was also noted during the calculation task between −1050 ms and +1980 ms relative to the stimulus offset. At channels #1 and #2, the magnitude of gamma-augmentation50–120Hz failed to reach significance during the naming task. Conversely, at channel #3 in the left superior-temporal region (BA 22), significant gamma-augmentation50–120Hz was noted during the naming task between −440 ms and +1240 ms relative to the stimulus offset, while the magnitude of gamma-augmentation50–120Hz failed to reach significance during the calculation task. At channel #4 in the Rolandic region (BA 4/3/1/2), gamma-augmentation50–120Hz reached significance during both calculation and naming tasks. Gamma-augmentation50–120Hz at channel #4 peaked around the onset of responses.

Figure 2. Task-specific gamma-augmentation in a 9-year-old girl.

Figure 2

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(A) The results of time-frequency analyses relative to stimulus offset are shown. Red electrodes: ‘calculation-specific gamma sites’. Blue electrodes: ‘naming-specific gamma sites’. Yellow electrodes: ‘common gamma sites’. (B) The time-frequency plots relative to stimulus offset are shown. Red bins: amplitude augmentation. Blue bins: amplitude attenuation. At channel #1 in the left Rolandic region (BA 6), significant gamma-augmentation50–120 Hz was noted between +760 ms and +2000 ms relative to the stimulus offset during the calculation task. At channel #2 in the left middle-frontal region (BA 46), significant gamma-augmentation50–120 Hz was also noted during the calculation task between −20 ms and +2000 ms relative to the stimulus offset. At channel #3 in the inferior post-central region (BA 3/1/2), significant gamma-augmentation50–120 Hz was noted during the calculation task between −460 ms and +1600 ms relative to the stimulus offset. At channels #1, #2, and #3, the magnitude of gamma-augmentation50–120 Hz failed to reach significance during the naming task. Conversely, at channel #4 in the left inferior-frontal region (BA 47), significant gamma-augmentation50–120 Hz was noted during the naming task between +315 ms and +1630 ms relative to the stimulus offset, while the magnitude of gamma-augmentation50–120 Hz failed to reach significance during the calculation task. At channels #5 in the Rolandic region (BA 4/3/1/2), gamma-augmentation50–120 Hz reached significance during both calculation and naming tasks. Gamma-augmentation50–120 Hz at channel #4 and that at channel #5 peaked around the onset of responses.

We described the spatial-temporal profiles of ‘calculation-specific gamma sites’, ‘naming-specific gamma sites’, and sites showing gamma-augmentation elicited by both tasks (defined as ‘common gamma sites’). Subsequently, the McNemar’s test was applied to a 2×2 contingency table, where each of the four cells contained the number of (1) ‘common gamma sites’, (2) ‘calculation-specific gamma sites’, (3) ‘naming-specific gamma sites’, and (4) ‘sites showing no significant gamma-augmentation’, respectively. We determined whether the observed frequency of ‘calculation-specific gamma sites’ or ‘naming-specific gamma sites’ differed from random chance frequency. We also determined whether the magnitude of calculation-specific gamma-amplitude50–120 Hz differed between easy and difficult trials using the studentized bootstrap statistics method previously reported by our team (Fukuda et al., 2010b; Kojima et al., 2013b). P<0.05 was considered to be significant.

In the present study, we specifically measured the spatial-temporal dynamics of event-related augmentation of gamma activity. Previous ECoG studies reported that sensorimotor tasks elicited augmentation of gamma activity as well as attenuation of alpha-beta activities (Crone et al., 1998a; 1998b; Fukuda et al., 2008; 2010a). Thereby, the onset of movement or somatosensory stimuli was more temporally locked with event-related gamma-augmentation than alpha-beta attenuation (Crone et al., 1998a; 1998b; Fukuda et al.,2010a). Our recent study of the effect of phoneme articulation on ECoG signals demonstrated that event-related alteration of gamma activity involved distinct sites within the left oral-sensorimotor area with a timing variable across 44 English phonemes, whereas alpha-beta attenuation nonspecifically and lingeringly involved the frontal-parietal-temporal regions (Toyoda et al., 2013). Furthermore, the effect of surgical resection of the sites showing event-related alpha-beta attenuation remains unclear, while resection of the sites showing language-related gamma augmentation was reported to often result in postoperative language impairments (Cervenka et al., 2013; Kojima et al., 2013a; 2013c).

2. RESULTS

2.1. Behavioral results

The response time for the calculation task was longer than that for the naming task (median across all patients: 2.1 s versus 1.5 s; p = 0.01 on Wilcoxon Signed Rank Test). Within the calculation task, the response time for the difficult trials was longer than that for the easy ones (median across all patients: 2.4 s versus 1.3 s; p = 0.003; Wilcoxon Signed Rank Test). The median percentage of correct answers in the calculation task was 0.77, which was smaller than 0.90 in the naming task (p = 0.04 on Wilcoxon Signed Rank Test).

2.2. Calculation- and naming-related gamma-augmentation

Figures 1 and 2 present the spatial-temporal profiles of calculation- and naming-related gamma-augmentation in two individual patients. Figure 3 summarizes the overall results obtained from all 11 patients, and demonstrates the spatial characteristics of gamma-augmentation specific to either task during the period between the offset of stimuli and the onset of responses as well as that elicited by both tasks commonly. Out of the 1001 analyzed cortical electrode sites, 63 was classified as ‘common gamma sites’, 7 as ‘calculation-specific gamma sites’, and 88 as ‘naming-specific gamma sites’. The remaining 843 analyzed sites failed to show significant gamma-augmentation during either task. The McNemar’s test suggested that the observed frequency of ‘calculation-specific gamma sites’ (7.4% [7/95]) was by far smaller than ‘naming-specific gamma sites’ (92.6% [88/95]) (p<0.0001). ‘Common gamma sites’ mainly involved the Rolandic regions on either hemisphere (Figure 3). ‘Calculation-specific gamma sites’, involving the period between the question offset and response onset (Figures 1 and 2), were noted in the middle-temporal (N=1; BA 21), inferior-parietal (N=1; Brodmann Area [BA] 39), post-central (N=2; BA 3/1/2), middle-frontal (N=2; BA 46), and premotor (N=1; BA 6) regions of the left hemisphere. Calculation-specific gamma-augmentation50–120 Hz in the middle-temporal, inferior-parietal, and inferior post-central regions peaked around the offset of the questions, while that in the frontal lobe peaked after the question offset but prior to the response onset; that in the post-central (sensorimotor face) area peaked around the onset of responses (Figure 4). None of the seven ‘calculation-specific gamma sites’ showed a significant difference in gamma amplitude50–120 Hz between easy and difficult trials (the latter requiring multi-digit operations). None of the 11 patients reported new deficits in mental calculation following epilepsy surgery

Figure 3. Summary of the spatial characteristics of task-related gamma-augmentation.

Figure 3

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(A) Regions of interest were color-coded as previously performed by our team (Kojima et al., 2013a). Blue: superior frontal region (superior-frontal gyrus involving BA 8/9). Orange: middle-frontal region (middle-frontal gyrus involving BA 10/46/9). Red: inferior-frontal region (inferior-frontal gyrus involving BA 47/44/45). Green: superior-temporal region (superior-temporal gyrus involving BA 22/41/42). Light-green: middle-temporal region (middle-temporal gyrus involving BA 21/37). Dark-green: inferior-temporal region (inferior-temporal gyrus involving BA 20). Light-blue: dorsolateral-premotor region (dorsolateral portion of BA 6). Pink: Rolandic region (Pre- and post-central gyri involving BA 4/3/1/2). Yellow: inferior-parietal region (supramarginal and angular gyrus involving BA 40/39). Purple: medial-temporal region (parahippocampal gyrus, hippocampus, and uncus involving BA 27/28/34/35/36). Brown: medial-frontal region (medial portion of superior-frontal and anterior-cingulate gyri involving the posterior portion of BA 24/32/33). Gray: occipital and occipital-temporal regions (BA 17/18/19/37). White: ‘other’ regions. (B) The overall results of time–frequency analysis relative to the stimulus offset are presented. The locations of subdural electrodes in 11 patients were superimposed on a common brain template (Kojima et al., 2013a). Red dots: ‘calculation-specific gamma sites’. Blue dots: ‘naming-specific gamma sites’. Yellow dots: ‘common gamma sites’. Black dots: sites not showing significant gamma-augmentation during either task. Seizure onset sites and sites showing artifacts were excluded from the analysis and not shown here.

Figure 4. Temporal characteristics of calculation-specific gamma-augmentation.

Figure 4

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Left: Time-frequency plots relative to the onset of stimuli. Middle: those relative to the offset of stimuli. Right: Those relative to the onset of responses. Red bins: amplitude augmentation. Blue bins: amplitude attenuation. (A) Patient #1. Calculation-specific gamma-augmentation50–120 Hz in the middle-temporal site (Channel #1) and in the inferior-parietal site (Channel #2) peaked around the offset of questions. (B) Patient #2. Calculation-specific gamma-augmentation50–120 Hz in the inferior post-central site (Channel #3) peaked around the offset of questions, while that in the middle-frontal (Channel #4) and premotor site (Channel #5) peaked afterwards but prior to the response onset. (C) Patient #7. Calculation-specific gamma-augmentation50–120 Hz in the middle-frontal site (Channel #6) peaked prior to the response onset. (D) Patient #6. Calculation-specific gamma-augmentation50–120 Hz in the post-central site (sensorimotor face area; Channel #7) peaked around the response onset.

3. DISCUSSION

3.1. Potential clinical utility of gamma-augmentation elicited by a simple calculation task

Only 7 out of the 1001 analyzed sites showed calculation-specific gamma-augmentation, while 88 sites showed naming-specific gamma-augmentation and 63 showed gamma-augmentation commonly elicited by both tasks. It seems that the calculation tasks mostly activated the cortical network shared by that involved in the object naming task. Some clinicians may suggest that the additive diagnostic value of measurement of gamma-augmentation elicited by a simple calculation task would be modest at best, especially if the goal of mapping is to efficiently localize the functionally-important cortex with a minimum number of mapping tasks. While the response time was longer during the calculation task, why did only a very small proportion of sites show calculation-specific gamma-augmentation in the present study? The plausible explanations include that the brain regions involved in retrieval of arithmetic fact were scarcely sampled in this ECoG study. Previous fMRI studies suggested that increased hemodynamic activations elicited by mental calculation tasks frequently involved the regions along the intraparietal sulci (Chochon et al., 1999; Delazer et al., 2003; Rivera et al., 2005; Grabner et al., 2009). None of our patients had depth electrodes placed in deep structures in the parietal regions, because there was no clinical indication for such ECoG sampling. Placement of subdural electrodes was also limited to one hemisphere in each patient; thus, our study was not designed to determine the co-activation or connectivity across hemispheres, while a previous fMRI study indicated that functional connectivity between the left and right parietal lobes was enhanced during a calculation task (Park et al., 2013). Another explanation for a small number of ‘calculation-specific gamma-sites’ is that many of the naming trials would inevitably require a mental-calculation process. For example, a question “What comes after April?” could have been covertly interpreted as “Four plus one”, while it is not possible to completely exclude the ‘number’ and ‘sequence’ domains from the naming tasks.

3.2. Functional significance of calculation-specific gamma-augmentation

Seven left-hemispheric sites showed calculation-specific gamma-augmentation. Calculation-specific gamma-augmentation in the left middle-temporal and inferior-parietal regions peaked around the offset of questions, while that in the frontal lobe peaked after the question offset but prior to the response onset. Our previous ECoG study of 56 patients using an auditory naming task likewise demonstrated that gamma-augmentation in the temporal and parietal regions preceded that in the frontal regions (Kojima et al., 2013a). Functional significance of calculation-specific gamma-augmentation may differ between the temporal-parietal and frontal regions.

In the present study, calculation-specific gamma-augmentation took place in the left middle-temporal region about 1 second before and lasted 2 second after the stimulus offset (Figure 1). This finding is consistent with the hypothesis that the left middle temporal region may be involved in the mental process of each of the calculation-specific lexicons such as numbers and symbols “plus” or “minus”. Previous fMRI studies using auditory stimuli consistently suggested that the lexical-semantic network involves the left middle-temporal region (Kotz et al., 2002; Prabhakaran et al., 2006). In a previous ECoG study, where numerals and letters were visually presented, the left inferior-temporal and fusiform gyri generated larger gamma-augmentation following presentation of numerals compared to that of letters (Shum et al., 2013). Further ECoG studies are warranted to determine whether auditorily-delivered numerals and letters can differentially elicit gamma-augmentation in the left temporal lobe structures.

In the present study, calculation-specific gamma-augmentation in the left middle-frontal and premotor regions peaked after the stimulus offset and before the response onset. This observation is consistent with the findings of previous fMRI studies reporting that mental calculation tasks elicited hemodynamic activation in the frontal lobe predominantly in the left hemisphere (Burbaud et al., 1995; Rueckert et al., 1996). It is possible that such calculation-specific gamma-augmentation may reflect cortical activation related to working memory exerted during the calculation task. Observation of the longer response time during calculation compared to naming supports this speculation, while statistical analysis failed to prove that such gamma-augmentation was greater on difficult trials compared to easy ones. The number of trials could have been too small to detect difference in gamma amplitudes between easy and difficult trials. Further ECoG studies, combining more complicated calculation trials such as: “Four plus three plus six”, may determine how much of calculation-specific gamma-augmentation in the frontal lobe can be explained by the calculation-specific demand of working memory.

Supplementary Material

01

HIGHLIGHTS.

  • -

    Calculation and naming tasks differentially elicited augmentation of gamma activity.

  • -

    Calculation-specific gamma activity involved the left parietal, temporal and frontal lobes.

  • -

    The timing of calculation-specific gamma activity differed across the regions.

Acknowledgement

This work was supported by NIH grants NS47550 and NS64033 (to E. Asano). We are grateful to Harry T. Chugani, MD, Sandeep Sood, MD, and Carol Pawlak, REEG/EPT at Children’s Hospital of Michigan, Wayne State University for the collaboration and assistance in performing the studies described above.

Footnotes

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REFERENCE

  1. Alkonyi B, Juhász C, Muzik O, Asano E, Saporta A, Shah A, et al. Quantitative brain surface mapping of an electrophysiologic/metabolic mismatch in human neocortical epilepsy. Epilepsy Res. 2009;87:77–87. doi: 10.1016/j.eplepsyres.2009.08.002. [DOI] [PMC free article] [PubMed] [Google Scholar]
  2. Andres M, Pelgrims B, Michaux N, Olivier E, Pesenti M. Role of distinct parietal areas in arithmetic: an fMRI-guided TMS study. Neuroimage. 2011;54:3048–3056. doi: 10.1016/j.neuroimage.2010.11.009. [DOI] [PubMed] [Google Scholar]
  3. Asano E, Juhász C, Shah A, Sood S, Chugani HT. Role of subdural electrocorticography in prediction of long-term seizure outcome in epilepsy surgery. Brain. 2009;132:1038–1047. doi: 10.1093/brain/awp025. [DOI] [PMC free article] [PubMed] [Google Scholar]
  4. Ashcraft MH, Fierman BA. Mental addition in third, fourth, and sixth graders. J Exp Child Psychol. 1982;33:216–234. [Google Scholar]
  5. Ashcraft MH. Cognitive arithmetic: A review of data and theory. Cognition. 1992;44:75–106. doi: 10.1016/0010-0277(92)90051-i. [DOI] [PubMed] [Google Scholar]
  6. Brown EC, Rothermel R, Nishida M, Juhász C, Muzik O, Hoechstetter K, et al. In vivo animation of auditory-language-induced gamma-oscillations in children with intractable focal epilepsy. Neuroimage. 2008;41:1120–1131. doi: 10.1016/j.neuroimage.2008.03.011. [DOI] [PMC free article] [PubMed] [Google Scholar]
  7. Burbaud P, Degreze P, Lafon P, Franconi JM, Bouligand B, Bioulac B, et al. Lateralization of prefrontal activation during internal mental calculation: a functional magnetic resonance imaging study. J Neurophysiol. 1995;74:2194–2200. doi: 10.1152/jn.1995.74.5.2194. [DOI] [PubMed] [Google Scholar]
  8. Campbell JI, Xue Q. Cognitive arithmetic across cultures. J Exp Psychol Gen. 2001;130:299–315. doi: 10.1037//0096-3445.130.2.299. [DOI] [PubMed] [Google Scholar]
  9. Cervenka MC, Corines J, Boatman-Reich DF, Eloyan A, Sheng X, Franaszczuk PJ, et al. Electrocorticographic functional mapping identifies human cortex critical for auditory and visual naming. Neuroimage. 2013;69:267–276. doi: 10.1016/j.neuroimage.2012.12.037. [DOI] [PMC free article] [PubMed] [Google Scholar]
  10. Chochon F, Cohen L, van de Moortele PF, Dehaene S. Differential contributions of the left and right inferior parietal lobules to number processing. J Cogn Neurosci. 1999;11:617–630. doi: 10.1162/089892999563689. [DOI] [PubMed] [Google Scholar]
  11. Crone NE, Miglioretti DL, Gordon B, Sieracki JM, Wilson MT, Uematsu S, et al. Functional mapping of human sensorimotor cortex with electrocorticographic spectral analysis. I. Alpha and beta event-related desynchronization. Brain. 1998a;121:2271–2299. doi: 10.1093/brain/121.12.2271. [DOI] [PubMed] [Google Scholar]
  12. Crone NE, Miglioretti DL, Gordon B, Lesser RP. Functional mapping of human sensorimotor cortex with electrocorticographic spectral analysis. II. Event-related synchronization in the gamma band. Brain. 1998b;121:2301–2315. doi: 10.1093/brain/121.12.2301. [DOI] [PubMed] [Google Scholar]
  13. Dastjerdi M, Ozker M, Foster BL, Rangarajan V, Parvizi J. Numerical processing in the human parietal cortex during experimental and natural conditions. Nat Commun. 2013 doi: 10.1038/ncomms3528. [DOI] [PMC free article] [PubMed] [Google Scholar]
  14. Dehaene S, Cohen L. Two mental calculation systems: a case study of severe acalculia with preserved approximation. Neuropsychologia. 1991;29:1045–1054. doi: 10.1016/0028-3932(91)90076-k. [DOI] [PubMed] [Google Scholar]
  15. Dehaene S, Piazza M, Pinel P, Cohen L. Three parietal circuits for number processing. Cogn Neuropsychol. 2003;20:487–506. doi: 10.1080/02643290244000239. [DOI] [PubMed] [Google Scholar]
  16. Delazer M, Domahs F, Bartha L, Brenneis C, Lochy A, Trieb T, et al. Learning complex arithmetic--an fMRI study. Brain Res Cogn Brain Res. 2003;18:76–88. doi: 10.1016/j.cogbrainres.2003.09.005. [DOI] [PubMed] [Google Scholar]
  17. Fukuda M, Nishida M, Juhász C, Muzik O, Sood S, Chugani HT, et al. Short-latency median-nerve somatosensory-evoked potentials and induced gamma-oscillations in humans. Brain. 2008;131:1793–1805. doi: 10.1093/brain/awn100. [DOI] [PMC free article] [PubMed] [Google Scholar]
  18. Fukuda M, Juhász C, Hoechstetter K, Sood S, Asano E. Somatosensory-related gamma-, beta- and alpha-augmentation precedes alpha- and beta-attenuation in humans. Clin Neurophysiol. 2010a;121:366–375. doi: 10.1016/j.clinph.2009.10.036. [DOI] [PMC free article] [PubMed] [Google Scholar]
  19. Fukuda M, Rothermel R, Juhász C, Nishida M, Sood S, Asano E. Cortical gamma-oscillations modulated by listening and overt repetition of phonemes. Neuroimage. 2010b;49:2735–2745. doi: 10.1016/j.neuroimage.2009.10.047. [DOI] [PMC free article] [PubMed] [Google Scholar]
  20. Gerstmann J. Syndrome of finger agnosia, disorientation for right and left, agraphia and acalculia. Arch Neurol Psychiatry. 1940;44:398–407. [Google Scholar]
  21. Grabner RH, Ansari D, Koschutnig K, Reishofer G, Ebner F, Neuper C. To retrieve or to calculate? Left angular gyrus mediates the retrieval of arithmetic facts during problem solving. Neuropsychologia. 2009;47:604–608. doi: 10.1016/j.neuropsychologia.2008.10.013. [DOI] [PubMed] [Google Scholar]
  22. Grafman J, Passafiume D, Faglioni P, Boller F. Calculation disturbances in adults with focal hemispheric damage. Cortex. 1982;18:37–49. doi: 10.1016/s0010-9452(82)80017-8. [DOI] [PubMed] [Google Scholar]
  23. Hoechstetter K, Bornfleth H, Weckesser D, Ille N, Berg P, Scherg M. BESA source coherence: a new method to study cortical oscillatory coupling. Brain Topogr. 2004;16:233–238. doi: 10.1023/b:brat.0000032857.55223.5d. [DOI] [PubMed] [Google Scholar]
  24. Jerbi K, Freyermuth S, Dalal S, Kahane P, Bertrand O, Berthoz A, et al. Saccade related gamma-band activity in intracerebral EEG: dissociating neural from ocular muscle activity. Brain Topogr. 2009;22:18–23. doi: 10.1007/s10548-009-0078-5. [DOI] [PubMed] [Google Scholar]
  25. Klein E, Moeller K, Dressel K, Domahs F, Wood G, Willmes K, et al. To carry or not to carry--is this the question? Disentangling the carry effect in multi-digit addition. Acta Psychol. 2010;135:67–76. doi: 10.1016/j.actpsy.2010.06.002. [DOI] [PubMed] [Google Scholar]
  26. Kojima K, Brown EC, Rothermel R, Carlson A, Matsuzaki N, Shah A, et al. Multimodality language mapping in patients with left-hemispheric language dominance on Wada test. Clin Neurophysiol. 2012;123:1917–1724. doi: 10.1016/j.clinph.2012.01.027. [DOI] [PMC free article] [PubMed] [Google Scholar]
  27. Kojima K, Brown EC, Matsuzaki N, Rothermel R, Fuerst D, Shah A, et al. Gamma activity modulated by picture and auditory naming tasks: Intracranial recording in patients with focal epilepsy. Clin Neurophysiol. 2013a;124:1737–1744. doi: 10.1016/j.clinph.2013.01.030. [DOI] [PMC free article] [PubMed] [Google Scholar]
  28. Kojima K, Brown EC, Matsuzaki N, Asano E. Animal category-preferential gamma-band responses in the lower- and higher-order visual areas: Intracranial recording in children. Clin Neurophysiol. 2013b;124:2368–2377. doi: 10.1016/j.clinph.2013.05.030. [DOI] [PMC free article] [PubMed] [Google Scholar]
  29. Kojima K, Brown EC, Rothermel R, Carlson A, Fuerst D, Matsuzaki N, et al. Clinical significance and developmental changes of auditory-language-related gamma activity. Clin Neurophysiol. 2013c;124:857–869. doi: 10.1016/j.clinph.2012.09.031. [DOI] [PMC free article] [PubMed] [Google Scholar]
  30. Kotz SA, Cappa SF, von Cramon DY, Friederici AD. Modulation of the lexical-semantic network by auditory semantic priming: an event-related functional MRI study. Neuroimage. 2002;17:1761–1772. doi: 10.1006/nimg.2002.1316. [DOI] [PubMed] [Google Scholar]
  31. Kovach CK, Tsuchiya N, Kawasaki H, Oya H, Howard MA, Adolphs R. Manifestation of ocular-muscle EMG contamination in human intracranial recordings. Neuroimage. 2011;54:213–233. doi: 10.1016/j.neuroimage.2010.08.002. [DOI] [PMC free article] [PubMed] [Google Scholar]
  32. Lachaux JP, Axmacher N, Mormann F, Halgren E, Crone NE. High-frequency neural activity and human cognition: past, present and possible future of intracranial EEG research. Prog Neurobiol. 2012;98:279–301. doi: 10.1016/j.pneurobio.2012.06.008. [DOI] [PMC free article] [PubMed] [Google Scholar]
  33. McCloskey M, Harley W, Sokol SM. Models of arithmetic fact retrieval: an evaluation in light of findings from normal and brain-damaged subjects. J Exp Psychol Learn Mem Cogn. 1991;17:377–397. [PubMed] [Google Scholar]
  34. Nagasawa T, Rothermel R, Juhász C, Fukuda M, Nishida M, Akiyama T, et al. Cortical gamma-oscillations modulated by auditory-motor tasks-intracranial recording in patients with epilepsy. Hum Brain Mapp. 2010a;31:1627–1642. doi: 10.1002/hbm.20963. [DOI] [PMC free article] [PubMed] [Google Scholar]
  35. Nagasawa T, Rothermel R, Juhász C, Nishida M, Sood S, Asano E. Cortical gamma-oscillations modulated by visuomotor tasks: Intracranial recording in patients with epilepsy. Epilepsy Behav. 2010b;18:254–261. doi: 10.1016/j.yebeh.2010.02.015. [DOI] [PMC free article] [PubMed] [Google Scholar]
  36. Otsubo H, Ochi A, Imai K, Akiyama T, Fujimoto A, Go C, et al. High-frequency oscillations of ictal muscle activity and epileptogenic discharges on intracranial EEG in a temporal lobe epilepsy patient. Clin Neurophysiol. 2008;119:862–868. doi: 10.1016/j.clinph.2007.12.014. [DOI] [PubMed] [Google Scholar]
  37. Park J, Park DC, Polk TA. Parietal functional connectivity in numerical cognition. Cereb Cortex. 2013;23:2127–2135. doi: 10.1093/cercor/bhs193. [DOI] [PMC free article] [PubMed] [Google Scholar]
  38. Prabhakaran R, Blumstein SE, Myers EB, Hutchison E, Britton B. An event-related fMRI investigation of phonological-lexical competition. Neuropsychologia. 2006;44:2209–2221. doi: 10.1016/j.neuropsychologia.2006.05.025. [DOI] [PubMed] [Google Scholar]
  39. Rivera SM, Reiss AL, Eckert MA, Menon V. Developmental changes in mental arithmetic: evidence for increased functional specialization in the left inferior parietal cortex. Cereb Cortex. 2005;15:1779–1790. doi: 10.1093/cercor/bhi055. [DOI] [PubMed] [Google Scholar]
  40. Rueckert L, Lange N, Partiot A, Appollonio I, Litvan I, Le Bihan D, Grafman J. Visualizing cortical activation during mental calculation with functional MRI. Neuroimage. 1996;3:97–103. doi: 10.1006/nimg.1996.0011. [DOI] [PubMed] [Google Scholar]
  41. Shum J, Hermes D, Foster BL, Dastjerdi M, Rangarajan V, Winawer J, et al. A brain area for visual numerals. J Neurosci. 2013;33:6709–6715. doi: 10.1523/JNEUROSCI.4558-12.2013. [DOI] [PMC free article] [PubMed] [Google Scholar]
  42. Takayama Y, Sugishita M, Akiguchi I, Kimura J. Isolated Acalculia due to Left Parietal Lesion. Arch Neurol. 1994;51:286–291. doi: 10.1001/archneur.1994.00540150084021. [DOI] [PubMed] [Google Scholar]
  43. Toyoda G, Brown EC, Matsuzaki N, Kojima K, Nishida M, Asano E. Electrocorticographic correlates of overt articulation of 44 English phonemes: Intracranial recording in children with focal epilepsy. Clin Neurophysiol. 2013 doi: 10.1016/j.clinph.2013.11.008. [DOI] [PMC free article] [PubMed] [Google Scholar]
  44. Wu H, Nagasawa T, Brown E, Juhasz C, Rothermel R, Hoechstetter K, et al. Gamma oscillations modulated by picture naming and word reading: intracranial recording in epileptic patients. Clin Neurophysiol. 2011;122:1929–1942. doi: 10.1016/j.clinph.2011.03.011. [DOI] [PMC free article] [PubMed] [Google Scholar]

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