Number processing in posterior cortical atrophy--a neuropsycholgical case study

Differential effects from cognitive rehabilitation and high-definition tDCS in posterior cortical atrophy: A single-case experimental design

Posterior cortical atrophy (PCA) is a progressive neurodegenerative syndrome characterized by visual-perceptual deficits, which impact daily life. Recent research has focused on non-pharmacological techniques to ameliorate these deficits, with the most common being cognitive rehabilitation. The present study investigates the differential effects of high definition-transcranial direct current stimulation (HD-tDCS) and cognitive rehabilitation in a single-case experimental design with two separate experimental phases in a patient with PCA. Experimental Phase 1 consisted of 10 sessions of HD-tDCS targeting the pre-SMA/dACC and Phase 2 consisted of 10 sessions of cognitive rehabilitation. Normed and standardized scores from figure copy and recall tests served as the primary outcome measures for visuospatial processing. The participant showed no immediate or long-term changes in visuospatial measures following HD-tDCS intervention. However, cognitive rehabilitation showed immediate improvement in visuospatial memory (figure recall) and clinically significant improvement in visuospatial construction (figure copy). Visuospatial construction gains remained in the low average range in the 10-week follow-up while visuospatial memory returned to baseline. Results indicated differential effects between HD-tDCS and cognitive rehabilitation with cognitive rehabilitation showing clinically significant improvement in primary outcome measures with sustained improvement in the long-term follow-up measure. Additional research is warranted to confirm these effects.

Aphasia and Math: Deficits with Basic Number Comprehension and in Numerical Activities of Daily Living

OBJECTIVE

In the present study, we explored numerical problems in individuals with aphasia. We investigate whether numerical deficits, usually accompanying aphasia, can be observed on number comprehension tasks that do not necessarily require an oral response.

METHOD

Individuals with aphasia were classified into anterior, posterior, and global subgroups according to the lesion type. To investigate numerical cognition, we used a relatively recent tool, the Numerical Activities of Daily Living (NADL).

RESULTS

The results showed that individuals with aphasia have problems with tasks of basic number comprehension as well as in most NADL. In the formal part of the NADL, anterior aphasic patients made comparatively more errors than the posterior aphasic patients. Global aphasic patients presented an invariably poor performance on almost all tasks.

CONCLUSION

The results provide insight into how numerical deficits may impair an individual with aphasia in activities of daily living. This study is a preliminary attempt to start the validation process of the NADL for the Greek population.

Numerical activities of daily living: a short version

Specific impairments in numerical functions may cause severe problems in everyday life that cannot be inferred from the available scales evaluating instrumental activities of daily living. The Numerical Activities of Daily living (NADL) is a battery designed to assess the patient's performance in everyday activities involving numbers (Informal Test) and in more scholastic capacities (Formal Test). A downside of this battery is its duration (45 min). The aim of the present study is to build a shorter version of NADL to make it more suitable for clinical and research purposes. The shortening procedure involved only the Formal test, and followed two steps: (i) a correlation of subtests with the general scores, and (ii) an item-analysis within the subtests previously showing higher correlations. Correlations between NADL-Short and NADL original version, and the new cut-offs were calculated. Lastly, the relationship between NADL-Short and other brief cognitive screening tests used in the clinical practice was evaluated in neurological patients and healthy controls. The NADL-Short includes the original Informal Test and the shortened Formal Test. It is a quick and easy clinical tool (15 min) to assess numerical abilities applied to informal and formal situations. It correlates highly with the original battery (Kendall's tau greater than 0.6 across tasks) and the cut-offs correctly identify impaired performance (accuracy of 95% or above). Correlation analysis showed a low positive correlation between NADL-Short and other brief cognitive scales. These findings suggest that it is appropriate to use specific tools to make inferences about a person's numerical abilities.

Examining the relevance of basic numerical skills for mathematical achievement in secondary school using a within-task assessment approach

Previous research repeatedly found basic numerical abilities (e.g., magnitude understanding, arithmetic fact knowledge, etc.) to predict young students' current and later arithmetic achievement as assessed by achievement tests - even when controlling for the influence of domain-general abilities (e.g., intelligence, working memory). However, to the best of our knowledge, previous studies hardly addressed this issue in secondary school students. Additionally, they primarily assessed basic numerical abilities in a between-task approach (i.e., using different tasks for different abilities). Finally, their relevance for real-life academic outcomes such as mathematics grades has only rarely been investigated. The present study therefore pursued an approach using one and the same task (i.e., a within-task approach) to reduce confounding effects driven by between-task differences. In particular, we evaluated the relevance of i) number magnitude understanding, ii) arithmetic fact knowledge, and iii) conceptual and procedural knowledge for the mathematics grades of 81 students aged between ten and thirteen (i.e., in Grades 5 and 6) employing the number bisection task. Results indicated that number magnitude understanding, arithmetic fact knowledge, and conceptual and procedural knowledge contributed to explaining mathematics grades even when controlling for domain-general cognitive abilities. Methodological and practical implications of the results are discussed.

Impairments of auditory scene analysis in posterior cortical atrophy

Although posterior cortical atrophy is often regarded as the canonical 'visual dementia', auditory symptoms may also be salient in this disorder. Patients often report particular difficulty hearing in busy environments; however, the core cognitive process-parsing of the auditory environment ('auditory scene analysis')-has been poorly characterized. In this cross-sectional study, we used customized perceptual tasks to assess two generic cognitive operations underpinning auditory scene analysis-sound source segregation and sound event grouping-in a cohort of 21 patients with posterior cortical atrophy, referenced to 15 healthy age-matched individuals and 21 patients with typical Alzheimer's disease. After adjusting for peripheral hearing function and performance on control tasks assessing perceptual and executive response demands, patients with posterior cortical atrophy performed significantly worse on both auditory scene analysis tasks relative to healthy controls and patients with typical Alzheimer's disease (all P < 0.05). Our findings provide further evidence of central auditory dysfunction in posterior cortical atrophy, with implications for our pathophysiological understanding of Alzheimer syndromes as well as clinical diagnosis and management.

Damage to the Intraparietal Sulcus Impairs Magnitude Representations of Results of Complex Arithmetic Problems

Past research investigating the role of the intraparietal sulcus (IPS) in numerical processes focused mainly on quantity and numerical comparisons as well on single digit arithmetic. The present study investigates the involvement of the IPS in estimating the results of multi-digit multiplication problems. For this purpose, the performance a 24-year-old female (JD) with brain damage in the left IPS was compared to an age-matched control group in the computation estimation task. When required to estimate whether the results of multi-digit multiplication problems are smaller or larger than given reference numbers, JD, in contrast to controls, did not show the common patterns of distance and size effects. Her strategy use was also atypical. Most control participants used both the approximated calculation strategy that involves rounding and calculation procedures and the sense of magnitude strategy that relies on an intuitive approximated magnitude representation of the results. In contrast, JD used only the former but not the latter strategy. Together, these findings suggest that the damage to the IPS impaired JD's representations of magnitude that play an important role in this computation estimation task.

Impaired perception of simultaneous stimuli in a patient with posterior cortical atrophy: an attentional account

We assessed visuospatial abilities in PCA. Sequential display of two simple geometric figures enhanced detection and discrimination relative to simultaneous display (Exps 1 & 2). Comparing edges of a single object enhanced discrimination relative to comparing edges of two separate objects, consistent with object-based attention (Exp. 3). Recognition of complex line drawings was spared for a single object but disrupted by an attention-grabbing small circle (Exp. 4). A covert orienting task showed difficulty disengaging from previous locations and attentional bias toward the right visual field (Exp. 5). These findings shed light on the role of visual attention in perceptual awareness.

Prevalence of Mathematical and Visuospatial Learning Disabilities in Patients With Posterior Cortical Atrophy

Importance

Increased prevalence of language-based learning disabilities (LDs) has been previously reported in patients with primary progressive aphasia (PPA). This study hypothesized that patients with focal neurodegenerative syndromes outside the language network, such as posterior cortical atrophy (PCA), would have a higher rate of nonlanguage LDs, congruent with their mainly visuospatial presentation.

Objective

To investigate the prevalence and type of LD (language and/or mathematical and visuospatial) in a large cohort of patients with PCA compared with patients with logopenic variant PPA (lvPPA) and amnestic Alzheimer disease (AD).

Design, Setting, and Participants

This case-control study reviewed 279 medical records from a university-based clinic and research center for patients with neurodegenerative diseases for LD history, including patients with PCA (n = 95), patients with lvPPA (n = 84), and a matched cohort with amnestic AD (n = 100). No records were excluded. The study compared cognitive and neuroimaging features of patients with PCA with and without LDs. A review of the records of patients presenting from March 1, 1999, to August 31, 2014, revealed 95 PCA cases and 84 lvPPA cases. Then 100 patients with amnestic AD from this same period were chosen for comparison, matching against the groups for age, sex, and disease severity. Data analysis was performed from September 8, 2013, to November 6, 2017.

Main Outcomes and Measures

Prevalence of total LD history and prevalence of language and mathematical or visuospatial LD history across all cohorts.

Results

A total of 179 atypical AD cases (95 with PCA and 84 with lvPPA) and 100 disease control cases (amnestic AD) were included in the study. The groups were not statistically different for mean (SD) age at first visit (PCA, 61.9 [7.0] years; lvPPA, 65.1 [8.7] years; amnestic AD, 64.0 [12.6] years; P = .08), mean (SD) age at first symptom (PCA, 57.5 [7.0] years; lvPPA, 61.1 [9.0] years; amnestic AD, 59.6 [13.7] years; P = .06), or sex (PCA, 66.3% female; lvPPA, 56.0% female; amnestic AD, 57.0% female; P = .30) but differed on non-right-hand preference (PCA, 18.3%; lvPPA, 20.2%; amnestic AD, 7.7%; P = .04), race/ethnicity (PCA, 88.3% white; lvPPA, 99.0% white; amnestic AD, 80.0% white; P < .001), and mean (SD) educational level (PCA, 15.7 [3.2] years; lvPPA, 16.2 [3.3] years; amnestic AD, 14.8 [3.5] years; P = .02). A total of 18 of the 95 patients with PCA (18.9%) reported a history of LD, which is greater than the 3 of 100 patients (3.0%) in the amnestic AD cohort (P < .001) and the 10.0% expected rate in the general population (P = .007). In the PCA cohort, 13 of 95 patients (13.7%) had a nonlanguage mathematical and/or visuospatial LD; this rate was greater than that in the amnestic AD (1 of 100 [1.0%]; P < .001) and lvPPA (2 of 84 [2.4%]; P = .006) cohorts and greater than the 6.0% expected general population rate of mathematical LD (P = .003). Compared with the patients with PCA without LDs, the group with LDs had greater preservation of global cognition and a more right-lateralized pattern of atrophy.

Conclusions and Relevance

Nonlanguage mathematical and visuospatial LDs were associated with focal, visuospatial predominant neurodegenerative clinical syndromes. This finding supports the hypothesis that neurodevelopmental differences in specific brain networks are associated with phenotypic manifestation of later-life neurodegenerative disease.

The Progressive Acalculia Presentation of Parietal Variant Alzheimer's Disease

BACKGROUND

Many patients with early-onset Alzheimer's disease (EOAD; age of onset <65 years) have non-amnestic presentations involving language (logopenic primary progressive aphasia, lvPPA), visuospatial abilities (posterior cortical atrophy, PCA), and even asymmetric symptoms consistent with corticobasal syndrome (CBS). An inferior parietal lobule variant of EOAD commonly presents with progressive difficulty with calculations.

METHODS

We reviewed 276 EOAD patients for presentations with predominant acalculia. These patients were diagnosed with clinically probable Alzheimer's disease (AD) verified by positron emission tomography (PET) or cerebrospinal fluid amyloid-β or tau biomarkers.

RESULTS

We identified 18 (9M/9F) (6.5%) EOAD patients with progressive acalculia that did not meet most criteria for lvPPA, visual PCA, or CBS. Their ages of onset and presentation were 56.6 (5.0) and 59.4 (6.5), respectively. Their acalculia was consistent with a primary acalculia ("anarithmetia") not explained by language or visuospatial impairments. Many also had anomia (14/18), ideomotor apraxia (13/18), and the complete Gerstmann's syndrome (7/18). Visual analysis of their diverse magnetic resonance imaging disclosed biparietal atrophy, disproportionately worse on the left.

CONCLUSIONS

Primary acalculia may be the most common manifestation of an inferior parietal presentation of EOAD affecting the left intraparietal sulcus. This parietal variant also commonly involves progressive anomia, ideomotor apraxia, and other elements of Gerstmann's syndrome. The early recognition of patients with this variant, which is distinguishable from lvPPA, visual PCA, or CBS, would be facilitated by its recognition as a unique subtype of EOAD.

Where words meet numbers: Comprehension of measurement unit terms in posterior cortical atrophy

Units of measurement (e.g., metre, week, gram) are critically important concepts in everyday life. Little is known about how knowledge of units is represented in the brain or how this relates to other forms of semantic knowledge. As unit terms are intimately connected with numerical quantity, we might expect knowledge for these concepts to be supported by parietally-mediated representations of space, time and magnitude. We investigated knowledge for measurement units in patients with posterior cortical atrophy (PCA), who display profound impairments of spatial and numerical cognition associated with occipital and parietal lobe atrophy. Relative to healthy controls, PCA patients displayed impairments for a range of unit-based knowledge, including the ability to specify the dimension which a unit refers to (e.g., grams measure mass), to select the appropriate units to measure everyday quantities (e.g., grams for sugar) and to determine the relative magnitudes of different unit terms (e.g., gram is smaller than kilogram). In most cases, their performance was also significantly poorer than a patient control group diagnosed with typical Alzheimer's disease. Our results suggest that impairment to systems that code numerical and spatial magnitudes has an effect on non-numerical verbal knowledge for measurement units. Units of measurement appear to lie at the intersection of the brain's verbal and numerical semantic systems, making them a critical class of concepts in which to investigate how magnitude-based codes contribute to verbal semantic representation.

Is an intact hippocampus necessary for answering 3 × 3? - Evidence from Alzheimer's disease

Recent evidence has suggested that the hippocampus supports learning and retrieval of arithmetic facts during childhood and adolescence. Whether the hippocampus is also involved in retrieving overlearned arithmetic facts (such as 3 × 5 = 15) during adult age is open for investigation. In this study, we assessed whether patients with hippocampal atrophy due to Alzheimer's disease (AD) are still able to retrieve overlearned arithmetic facts from memory. Sixteen patients (n = 13 with AD, n = 3 with Mild Cognitive Impairment - MCI) were evaluated using standard radiological, neurological, and neuropsychological test procedures. We adopted a multiple single-case analysis in order to acknowledge possible dissociations between hippocampal degeneration and intact arithmetic fact retrieval. All patients performed a neuropsychological screening battery assessing episodic memory as well as arithmetic processing, and underwent a 3-Tesla MRI procedure. A morphometric analysis comprising estimation of both cortical thickness and hippocampal volume, which also included a subfield analysis, was conducted. All patients had marked hippocampal atrophy (bilateral n = 15, unilateral n = 1) in comparison to healthy matched controls and showed deficits in episodic memory (delayed recall). However, 13 out of 16 patients performed in the average range of standardised norms during retrieval of overlearned arithmetic facts (i.e. multiplication tables). Our results suggest that intact retrieval of consolidated arithmetic facts from memory does not depend on the integrity of the hippocampus. This is in line with the view that the hippocampus plays a dynamic and time-limited role in arithmetic processing. While the hippocampus seems to be necessary for learning and consolidating new arithmetic facts in memory, it might not be critically involved in retrieving arithmetic facts when these are well consolidated in memory.

Visual and Imagery Magnitude Comparisons Are Affected Following Left Parietal Lesion

We describe Jane Dow (JD), a young right-handed female with acalculia following a cerebral infarction in the left intraparietal sulcus. We investigated automatic processing of different types of magnitudes that were presented visually or through imagery. We employed the size congruity task and the mental clock task that differ in stimuli presentation and in working memory load. In the size congruity task, for physical comparisons, JD presented a lack of facilitation effect, suggesting a deficit in the automatic processing of numerical values. In the mental clock task, JD performed as accurate as controls did but much slower. In both tasks, JD presented a steeper distance effect compared to controls, suggesting a deficit in a domain-general comparison process. Our findings present an atypical pattern of magnitude processing following a left parietal lesion that appears not only for visually presented stimuli but also for imagery-based magnitudes. These finding support recent theories suggesting different types of magnitudes are interconnected with each other.

Semantic word category processing in semantic dementia and posterior cortical atrophy

There is general agreement that perisylvian language cortex plays a major role in lexical and semantic processing; but the contribution of additional, more widespread, brain areas in the processing of different semantic word categories remains controversial. We investigated word processing in two groups of patients whose neurodegenerative diseases preferentially affect specific parts of the brain, to determine whether their performance would vary as a function of semantic categories proposed to recruit those brain regions. Cohorts with (i) Semantic Dementia (SD), who have anterior temporal-lobe atrophy, and (ii) Posterior Cortical Atrophy (PCA), who have predominantly parieto-occipital atrophy, performed a lexical decision test on words from five different lexico-semantic categories: colour (e.g., yellow), form (oval), number (seven), spatial prepositions (under) and function words (also). Sets of pseudo-word foils matched the target words in length and bi-/tri-gram frequency. Word-frequency was matched between the two visual word categories (colour and form) and across the three other categories (number, prepositions, and function words). Age-matched healthy individuals served as controls. Although broad word processing deficits were apparent in both patient groups, the deficit was strongest for colour words in SD and for spatial prepositions in PCA. The patterns of performance on the lexical decision task demonstrate (a) general lexicosemantic processing deficits in both groups, though more prominent in SD than in PCA, and (b) differential involvement of anterior-temporal and posterior-parietal cortex in the processing of specific semantic categories of words.

Non-pharmacological intervention for posterior cortical atrophy

Posterior cortical atrophy (PCA) is a rare neurodegenerative condition characterized by progressive visual-perceptual deficits. Although the neurocognitive profile of PCA is a growing and relatively well-established field, non-pharmacological care remains understudied and to be widely established in clinical practice. In the present work we review the available literature on non-pharmacological approaches for PCA, such as cognitive rehabilitation including individual cognitive exercises and compensatory techniques to improve autonomy in daily life, and psycho-education aiming to inform people with PCA about the nature of their visual deficits and limits of cognitive rehabilitation. The reviewed studies represented a total of 7 patients. There is a scarcity of the number of studies, and mostly consisting of case studies. Results suggest non-pharmacological intervention to be a potentially beneficial approach for the partial compensation of deficits, improvement of daily functionality and improvement of quality of life. Clinical implications and future directions are also highlighted for the advancement of the field, in order to clarify the possible role of non-pharmacological interventions, and its extent, in PCA.

Knowing what and where: TMS evidence for the dual neural basis of geographical knowledge

All animals acquire knowledge about the topography of their immediate environment through direct exploration. Uniquely, humans also acquire geographical knowledge indirectly through exposure to maps and verbal information, resulting in a rich database of global geographical knowledge. We used transcranial magnetic stimulation to investigate the structure and neural basis of this critical but poorly understood component of semantic knowledge. Participants completed tests of geographical knowledge that probed either information about spatial locations (e.g., France borders Spain) or non-spatial taxonomic information (e.g., France is a country). TMS applied to the anterior temporal lobe, a region that codes conceptual knowledge for words and objects, had a general disruptive effect on the geographical tasks. In contrast, stimulation of the intraparietal sulcus (IPS), a region involved in the coding of spatial and numerical information, had a highly selective effect on spatial geographical decisions but no effect on taxonomic judgements. Our results establish that geographical concepts lie at the intersection of two distinct neural representation systems, and provide insights into how the interaction of these systems shape our understanding of the world.

Patterns of linguistic and numerical performance in aphasia

BACKGROUND

Empirical research on the relationship between linguistic and numerical processing revealed inconsistent results for different levels of cognitive processing (e.g., lexical, semantic) as well as different stimulus materials (e.g., Arabic digits, number words, letters, non-number words). Information of dissociation patterns in aphasic patients was used in order to investigate the dissociability of linguistic and numerical processes. The aim of the present prospective study was a comprehensive, specific, and systematic investigation of relationships between linguistic and numerical processing, considering the impact of asemantic vs. semantic processing and the type of material employed (numbers compared to letters vs. words).

METHODS

A sample of aphasic patients (n = 60) was assessed with a battery of linguistic and numerical tasks directly comparable for their cognitive processing levels (e.g., perceptual, morpho-lexical, semantic).

RESULTS AND CONCLUSIONS

Mean performance differences and frequencies of (complementary) dissociations in individual patients revealed the most prominent numerical advantage for asemantic tasks when comparing the processing of numbers vs. letters, whereas the least numerical advantage was found for semantic tasks when comparing the processing of numbers vs. words. Different patient subgroups showing differential dissociation patterns were further analysed and discussed. A comprehensive model of linguistic and numerical processing should take these findings into account.

Novel brain imaging approaches to understand acquired and congenital neuro-ophthalmological conditions

PURPOSE OF REVIEW

The arrival of large datasets and the on-going refinement of neuroimaging technology have led to a number of recent advances in our understanding of visual pathway disorders. This work can broadly be classified into two areas, both of which are important when considering the optimal management strategies. The first looks at the delineation of damage, teasing out subtle changes to (specific components of) the visual pathway, which may help evaluate the severity and extent of disease. The second uses neuroimaging to investigate neuroplasticity, via changes in connectivity, cortical thickness, and retinotopic maps within the visual cortex.

RECENT FINDINGS

Here, we give consideration to both acquired and congenital patients with damage to the visual pathway, and how they differ. Congenital disorders of the peripheral visual system can provide insight into the large-scale reorganization of the visual cortex: these are investigated with reference to disorders of the optic chiasm and anophthalmia (absence of the eyes). In acquired conditions, we consider the recent work describing patterns of degeneration, both following single insult and in neurodegenerative conditions. We also discuss the developments in functional neuroimaging, with particular reference to work on hemianopia and the controversial suggestion of cortical reorganization following acquired retinal injury.

SUMMARY

Techniques for comparing neuro-ophthalmological conditions with healthy visual systems provide sensitive metrics to uncover subtle differences in grey and white matter structure of the brain. It is now possible to compare the massive reorganization present in congenital conditions with the apparent lack of plasticity following acquired damage.

A new clinical tool for assessing numerical abilities in neurological diseases: numerical activities of daily living

The aim of this study was to build an instrument, the numerical activities of daily living (NADL), designed to identify the specific impairments in numerical functions that may cause problems in everyday life. These impairments go beyond what can be inferred from the available scales evaluating activities of daily living in general, and are not adequately captured by measures of the general deterioration of cognitive functions as assessed by standard clinical instruments like the MMSE and MoCA. We assessed a control group (n = 148) and a patient group affected by a wide variety of neurological conditions (n = 175), with NADL along with IADL, MMSE, and MoCA. The NADL battery was found to have satisfactory construct validity and reliability, across a wide age range. This enabled us to calculate appropriate criteria for impairment that took into account age and education. It was found that neurological patients tended to overestimate their abilities as compared to the judgment made by their caregivers, assessed with objective tests of numerical abilities.

Single-digit arithmetic processing-anatomical evidence from statistical voxel-based lesion analysis

Different specific mechanisms have been suggested for solving single-digit arithmetic operations. However, the neural correlates underlying basic arithmetic (multiplication, addition, subtraction) are still under debate. In the present study, we systematically assessed single-digit arithmetic in a group of acute stroke patients (n = 45) with circumscribed left- or right-hemispheric brain lesions. Lesion sites significantly related to impaired performance were found only in the left-hemisphere damaged (LHD) group. Deficits in multiplication and addition were related to subcortical/white matter brain regions differing from those for subtraction tasks, corroborating the notion of distinct processing pathways for different arithmetic tasks. Additionally, our results further point to the importance of investigating fiber pathways in numerical cognition.

Semantic knowledge fractionations: verbal propositions vs. perceptual input? Evidence from a child with Klinefelter syndrome

This paper addresses the relative independence of different types of lexical- and factually-based semantic knowledge in JM, a 9-year-old boy with Klinefelter syndrome (KS). JM was matched to typically developing (TD) controls on the basis of chronological age. Lexical-semantic knowledge was investigated for common noun (CN) and mathematical vocabulary items (MV). Factually-based semantic knowledge was investigated for general and number facts. For CN items, JM's lexical stores were of a normal size but the volume of correct 'sensory feature' semantic knowledge he generated within verbal item descriptions was significantly reduced. He was also significantly impaired at naming item descriptions and pictures, particularly for fruit and vegetables. There was also weak object decision for fruit and vegetables. In contrast, for MV items, JM's lexical stores were elevated, with no significant difference in the amount and type of correct semantic knowledge generated within verbal item descriptions and normal naming. JM's fact retrieval accuracy was normal for all types of factual knowledge. JM's performance indicated a dissociation between the representation of CN and MV vocabulary items during development. JM's preserved semantic knowledge of facts in the face of impaired semantic knowledge of vocabulary also suggests that factually-based semantic knowledge representation is not dependent on normal lexical-semantic knowledge during development. These findings are discussed in relation to the emergence of distinct semantic knowledge representations during development, due to differing degrees of dependency upon the acquisition and representation of semantic knowledge from verbal propositions and perceptual input.

The "where" and "what" in developmental dyscalculia

Developmental dyscalculia (DD) is a congenital deficit that affects the ability to acquire arithmetical skills. Individuals with DD have problems learning standard number facts and procedures. Estimates of the prevalence rate of DD are similar to those of developmental dyslexia. Recent reports and discussions suggest that those with DD suffer from specific deficits (e.g., subitizing, comparative judgment). Accordingly, DD has been described as a domain-specific disorder that involves particular brain areas (e.g., intra-parietal sulcus). However, we and others have found that DD is characterized by additional deficiencies and may be affected by domain-general (e.g., attention) factors. Hence "pure DD" might be rather rare and not as pure as one would think. We suggest that the heterogeneity of symptoms that commonly characterize learning disabilities needs to be taken into account in future research and treatment.

Some is not enough: quantifier comprehension in corticobasal syndrome and behavioral variant frontotemporal dementia

Quantifiers are very common in everyday speech, but we know little about their cognitive basis or neural representation. The present study examined comprehension of three classes of quantifiers that depend on different cognitive components in patients with focal neurodegenerative diseases. Patients evaluated the truth-value of a sentence containing a quantifier relative to a picture illustrating a small number of familiar objects, and performance was related to MRI grey matter atrophy using voxel-based morphometry. We found that patients with corticobasal syndrome (CBS) and posterior cortical atrophy (PCA) are significantly impaired in their comprehension of cardinal quantifiers (e.g. "At least three birds are on the branch"), due in part to their deficit in quantity knowledge. MRI analyses related this deficit to temporal-parietal atrophy found in CBS/PCA. We also found that patients with behavioral variant frontotemporal dementia (bvFTD) are significantly impaired in their comprehension of logical quantifiers (e.g. "Some of the birds are on the branch"), associated with a simple form of perceptual logic, and this correlated with their deficit on executive measures. This deficit was related to disease in rostral prefrontal cortex in bvFTD. These patients were also impaired in their comprehension of majority quantifiers (e.g. "At least half of the birds are on the branch"), and this too was correlated with their deficit on executive measures. This was related to disease in the basal ganglia interrupting a frontal-striatal loop critical for executive functioning. These findings suggest that a large-scale frontal-parietal neural network plays a crucial role in quantifier comprehension, and that comprehension of specific classes of quantifiers may be selectively impaired in patients with focal neurodegenerative conditions in these areas.

Early place-value understanding as a precursor for later arithmetic performance--a longitudinal study on numerical development

It is assumed that basic numerical competencies are important building blocks for more complex arithmetic skills. The current study aimed at evaluating this interrelation in a longitudinal approach. It was investigated whether first graders' performance in basic numerical tasks in general as well as specific processes involved (e.g., place-value understanding) reliably predicted performance in an addition task in third grade. The results indicated that early place-value understanding was a reliable predictor for specific aspects of arithmetic performance. Implications of the role of basic numerical competencies for the acquisition of complex arithmetic are discussed.

Numerical Estimation in Deaf and Hearing Adults

Deaf students often lag behind hearing peers in numerical and mathematical abilities. Studies of hearing children with mathematical difficulties highlight the importance of estimation skills as the foundation for formal mathematical abilities, but research with adults is limited. Deaf and hearing college students were assessed on the Number-to-Position task as a measure of estimation, and completed standardised assessments of arithmetical and mathematical reasoning. Deaf students performed significantly more poorly on all measures, including making less accurate number-line estimates. For deaf students, there was also a strong relationship showing that those more accurate in making number-line estimates achieved higher scores on the math achievement tests. No such relationship was apparent for hearing students. Further insights into the estimation abilities of deaf individuals should be made, including tasks that require symbolic and non-symbolic estimation and which address the quality of estimation strategies being used.

Single-case research in neuropsychology: a comparison of five forms of t-test for comparing a case to controls

Five inferential methods employed in single-case studies to compare a case to controls are examined; all of these make use of a t-distribution. It is shown that three of these ostensibly different methods are in fact strictly equivalent and are not fit for purpose; they are associated with grossly inflated Type I errors (these exceed even the error rate obtained when a case's score is converted to a z score and the latter used as a test statistic). When used as significance tests, the two remaining methods (Crawford and Howell's method and a prediction interval method first used by Barton and colleagues) are also equivalent and achieve control of the Type I error rate (the two methods do differ however in other important aspects). A number of broader issues also arise from the present findings, namely: (a) they underline the value of accompanying significance test results with the effect size for the difference between a case and controls, (b) they suggest that less care is often taken over statistical methods than over other aspects of single-case studies, and (c) they indicate that some neuropsychologists have a distorted conception of the nature of hypothesis testing in single-case research (it is argued that this may stem from a failure to distinguish between group studies and single-case studies).

Numerosity impairment in corticobasal syndrome

OBJECTIVE

We assessed the representation of numerosity in corticobasal syndrome (CBS), a neurodegenerative condition affecting the parietal lobe.

METHOD

Patients judged whether a target numerosity (e.g., "3") falls between two bounding numerosities (e.g., "1" and "5"). We manipulated the format for representing numerosity (Arabic numerals or dot arrays), the size of the gap between the two bounding numerosities, the absolute magnitude of the numerosities, and the order for presenting the bounding numerosities. In a subset of patients with available imaging, we related performance to cortical atrophy using voxel-based morphometry.

RESULTS

CBS patients were significantly impaired overall (65.7% +/- 16.2 correct) compared to healthy seniors (96.6% +/- 2.4 correct), and required three times longer than controls to judge correct stimuli. This deficit was equally evident for Arabic numeral and dot array formats. Controls were significantly slower with smaller gaps than larger gaps, consistent with the greater challenge distinguishing between numerosities that are more similar to each other than very different numerosities. However, CBS patients were equally slow and inaccurate for all gap sizes. Controls also were significantly slower with larger numerosities than smaller numerosities, but CBS patients were equally slow and inaccurate with all numerosity magnitudes. Voxel-based morphometry revealed significant cortical atrophy in parietal and frontal regions in CBS compared to controls, including the intraparietal sulcus.

CONCLUSIONS

These observations are consistent with the claim that the representation of numerosity is degraded in CBS.

Understanding quantity in semantic dementia

Patients with semantic dementia (SD) show relative preservation of number skills, contrasting with their severe multimodal semantic impairment. Underpinning this preservation, it is argued, is spared understanding of numerical quantity, a competence likened to a spatial map and subserved by the parietal lobes. The study investigated quantity knowledge in 14 SD patients to determine whether it is consistently preserved irrespective of disease severity or whether there are constraints on this preserved knowledge domain. Performance was well preserved on Piagetian conservation tasks, estimating object numerosity, and understanding of basic numerical magnitude. However, patients showed impairment on real-world estimation tasks, increasing with semantic severity. More surprisingly, on an analogue scale task, they produced implausible responses, suggesting degraded knowledge of precise numerical relationships. The findings challenge the view that knowledge of quantity is totally preserved in SD and suggest that the temporal lobes have a contributory role in the conceptual understanding of quantity.

Neural basis of repetition priming during mathematical cognition: repetition suppression or repetition enhancement?

We investigated the neural basis of repetition priming (RP) during mathematical cognition. Previous studies of RP have focused on repetition suppression as the basis of behavioral facilitation, primarily using word and object identification and classification tasks. More recently, researchers have suggested associative stimulus-response learning as an alternate model for behavioral facilitation. We examined the neural basis of RP during mathematical problem solving in the context of these two models of learning. Brain imaging and behavioral data were acquired from 39 adults during novel and repeated presentation of three-operand mathematical equations. Despite wide-spread decreases in activation during repeat, compared with novel trials, there was no direct relation between behavioral facilitation and the degree of repetition suppression in any brain region. Rather, RT improvements were directly correlated with repetition enhancement in the hippocampus and the posteromedial cortex [posterior cingulate cortex, precuneus, and retrosplenial cortex; Brodmann's areas (BAs) 23, 7, and 30, respectively], regions known to support memory formation and retrieval, and in the SMA (BA 6) and the dorsal midcingulate ("motor cingulate") cortex (BA 24d), regions known to be important for motor learning. Furthermore, improvements in RT were also correlated with increased functional connectivity of the hippocampus with both the SMA and the dorsal midcingulate cortex. Our findings provide novel support for the hypothesis that repetition enhancement and associated stimulus-response learning may facilitate behavioral performance during problem solving.

Arithmetic procedural knowledge: a cortico-subcortical circuit

The disturbances of arithmetic procedural knowledge form a heterogeneous picture, in which we can distinguish "memory" impairments and "monitoring" problems. Patients with "memory" disturbances reported in the literature present left parietal lesions, while "monitoring" impairments have been assumed to be due to frontal damage. Procedural knowledge has been less investigated in basal ganglia lesions, in which there has been no analysis of procedural impairments. The present study investigates and compares the patterns of acalculia in two patients, one with a left parietal lesion and the other with a left basal ganglia lesion. The patients were tested on a broad range of neuropsychological abilities, with the main focus on number processing and calculation. The results show many similarities between their deficits, with some difficulties in simple arithmetic, arithmetical rules and mental and written complex calculations. The errors made in complex mental and written calculations were due to memory-based procedural impairments in both patients. These findings, corroborated with other studies reported in the literature, suggest the existence of a fronto-parieto-subcortical circuit responsible for arithmetic complex calculations and that procedural knowledge relies on a visuo-spatial sketchpad that contains a representation of each sub-step of the procedure.

Numerical representation in the parietal lobes: abstract or not abstract?

The study of neuronal specialisation in different cognitive and perceptual domains is important for our understanding of the human brain, its typical and atypical development, and the evolutionary precursors of cognition. Central to this understanding is the issue of numerical representation, and the question of whether numbers are represented in an abstract fashion. Here we discuss and challenge the claim that numerical representation is abstract. We discuss the principles of cortical organisation with special reference to number and also discuss methodological and theoretical limitations that apply to numerical cognition and also to the field of cognitive neuroscience in general. We argue that numerical representation is primarily non-abstract and is supported by different neuronal populations residing in the parietal cortex.

Numerical deficits in a single case of basal ganglia dysfunction

The present investigation assesses specific numerical difficulties in a patient (SJ) with basal ganglia (BG) dysfunction. While previous studies on number processing in BG disorders typically tested arithmetic facts by production tasks, the present study uses production, recognition (verification, multiple-choice) and indirect (number-matching) arithmetic tasks. Patient SJ was severely impaired in production and to a lesser extent in verification and multiple-choice tasks. In number-matching, an abnormal latency pattern was found. This study extends previous research by indicating that BG dysfunction may not only affect production processes and sequencing, as was found in previous investigations, but may lead to a breakdown of semantic relationships of arithmetic facts.

Eye fixation behaviour in the number bisection task: evidence for temporal specificity

Together with magnitude representations, knowledge about multiplicativity and parity contributes to numerical problem solving. In the present study, we used eye tracking to document how and when multiplicativity and parity are recruited in the number bisection task. Fourteen healthy adults evaluated whether the central number of a triplet (e.g., 21_24_27) corresponds to the arithmetic integer mean of the interval defined by the two outer numbers. We observed multiplicativity to specifically affect gaze duration on numbers, indicating that the information of multiplicative relatedness is activated at early processing stages. In contrast, parity only affected total reading time, suggesting involvement in later processing stages. We conclude that different representational features of numbers are available and integrated at different processing stages within the same task and outline a processing model for these temporal dynamics of numerical cognition.

Functional heterogeneity of inferior parietal cortex during mathematical cognition assessed with cytoarchitectonic probability maps

Although the inferior parietal cortex (IPC) has been consistently implicated in mathematical cognition, the functional roles of its subdivisions are poorly understood. We address this problem using probabilistic cytoarchitectonic maps of IPC subdivisions intraparietal sulcus (IPS), angular gyrus (AG), and supramarginal gyrus. We quantified IPC responses relative to task difficulty and individual differences in task proficiency during mental arithmetic (MA) tasks performed with Arabic (MA-A) and Roman (MA-R) numerals. The 2 tasks showed similar levels of activation in 3 distinct IPS areas, hIP1, hIP2, and hIP3, suggesting their obligatory role in MA. Both AG areas, PGa and PGp, were strongly deactivated in both tasks, with stronger deactivations in posterior area PGp. Compared with the more difficult MA-R task, the MA-A task showed greater responses in both AG areas, but this effect was driven by less deactivation in the MA-A task. AG deactivations showed prominent overlap with lateral parietal nodes of the default mode network, suggesting a nonspecific role in MA. In both tasks, greater bilateral AG deactivation was associated with poorer performance. Our findings suggest a close link between IPC structure and function and they provide new evidence for behaviorally salient functional heterogeneity within the IPC during mathematical cognition.

The processing and representation of fractions within the brain: an fMRI investigation

Little is known about how adults process fractions and how fractions are represented in the brain. The intraparietal sulcus is assumed to host an analogue representation of number magnitude. It is unknown, however, how the magnitude of fractions is represented in the brain. Fraction magnitude might be represented by the numerical value of the fraction as a whole or might involve separate representations of the values of the fractions' denominator and numerator. The present fMRI study investigated brain areas involved in fraction comparison. As a diagnostic for fraction processing, the numerical distance effect (reaction times and error rates increase as the distance between the numbers being compared decreases) was evaluated. If fractions are represented as their numerical value, a distance effect is expected for the distance between the numerical values of the two fractions being compared. If fractions are represented in parts, however, that is, as the separate values of their denominators and numerators, a distance effect is expected for the distances between the two fractions' numerators and denominators, respectively. Although both types of distance effects were observed in the behavioral data, only the distance between the numerical values of the two fractions was observed to modulate activation within the intraparietal sulcus (IPS). This indicates that, within the IPS, a fraction might be represented by its numerical value as a whole, rather than by the numerical values of its numerator and denominator.

Neuroscience of learning arithmetic--evidence from brain imaging studies

It is widely accepted that the human brain is remarkably adaptive not only in child development, but also during adulthood. Aim of this work is to offer an overview and a systematic analysis of neuroimaging studies on the acquisition of arithmetic expertise. In normally developing children and adults, the gain of arithmetic competence is reflected by a shift of activation from frontal brain areas to parietal areas relevant for arithmetic processing. A shift of activation is also observed within the parietal lobe from the intraparietal sulci to the left angular gyrus. Increases in angular gyrus activation with gaining of expertise have also been documented in other cognitive domains. It appears that the left angular gyrus activation is modulated by inter-individual differences in arithmetic performance. The comparison of normal individuals with exceptionally performing individuals (e.g., calculating prodigies) suggests that the experts' arithmetic proficiency relies on a more extended activation network than the network found in non-experts. In expert individuals with long-lasting, extensive mathematical training, specific structural brain modifications are also evident.

Are numbers special? Comparing the generation of verbal materials from ordered categories (months) to numbers and other categories (animals) in an fMRI study

Months, days of the week, and numbers differ from other verbal concepts because they are ordered in a sequence, whereas no order is imposed on members of other categories, such as animals or tools. Recent studies suggest that numbers activate a representation of their quantity within the intraparietal sulcus (IPS) automatically, that is, in tasks that do not require the processing of quantity. It is unclear, however, whether ordered verbal materials in general and not only numbers activate the IPS in such tasks. In the present functional magnetic resonance imaging study word generation of months, numbers, and animals were compared. Word generation of numbers and nonnumerical materials from an ordered category (months) activated the IPS more strongly than generating items from a not-ordered category such as animals or the verbal control conditions. An ROI analysis of three subregions within the anterior IPS revealed that the most anterior and lateral of these regions, human intraparietal area hIP2, shows a greater sensitivity to ordered materials than the other two areas, hIP1 and hIP3. Interestingly, no difference in activation was observed within the IPS between numbers and months suggesting that the activation of the IPS might not be modulated by the additional quantity information carried by numbers.