Béatrice Lemesle

Emmanuel J Barbeau

Emilie Milongo Rigal

Marie Denuelle

Luc Valton

Jérémie Pariente

Jonathan Curot

Hidden objective memory deficits behind subjective memory complaints in temporal lobe epilepsy

Keywords: EEG, Electroencephalogram FCSRT, Free and Cued Selective Reminding Test QAM, Self-assessment memory questionnaire (Questionnaire d'autoévaluation de la mémoire) STAI, State-Trait Anxiety Inventory TEA, Transient epileptic amnesia TLE, Temporal lobe epilepsy yr., year

Objective: To test the hypothesis that temporal lobe epilepsy (TLE) patients with subjective initial memory complaints (not confirmed by an objective standard assessment) and various phenotypes also show objective very long-term memory deficit with accelerated long-term forgetting, we tested TLE patients with two surprise memory tests after 3 weeks: (1) the standard Free and Cued Selective Reminding Test (FCSRT), and (2) Epireal, a new test specifically designed to capture more ecological aspects of autobiographical memory.

Methods: 47 TLE patients (12 hippocampal sclerosis, 12 amygdala enlargement, 11 extensive lesions, 12 normal MRI) who complained about their memory, but for whom the standard neuropsychological assessment did not reveal any memory impairment after a standard delay of 20 min, underwent two surprise memory tests after three weeks. They were compared to 35 healthy control subjects.

Results: After 3 weeks, FCSRT and Epireal recall scores were significantly lower in patients than in controls (p<0.001). There was no significant correlation between FCSRT and Epireal scores (p=0.99). Seventy-six percent of TLE patients had objective impairment on at least one of these very long-term memory tests, regardless of the existence and type of lesion or response to antiseizure medication. Easily applicable, Epireal had a higher effect size, detected deficits in 28 % more patients, and is a useful addition to the standard workup.

Conclusion:

Assessing long-term memory should be broadened to a wide spectrum of TLE patients with a memory complaint, regardless of the epileptic syndrome, and associated with a lesion or not. This could lead to rethinking TLE nosology associated with memory.

Introduction

More than fifty percent of epilepsy patients complain that their memory function moderately or severely limits their daily functioning. [START_REF] Corcoran | Epilepsy and poor memory: Who complains and what do they mean?[END_REF] Even if their complaints are taken seriously, i.e., they lead to a neuropsychological evaluation, they may not be confirmed, leading to the idea that the patient may have a purely subjective complaint related to, for example, anxiousness or neuroticism [START_REF] Hendriks | Memory complaints in medically refractory epilepsy: Relationship to epilepsy-related factors[END_REF] . This conclusion may be reinforced by the notion that some antiseizure medication may impair memory efficiency [START_REF] Motamedi | Antiepileptic drugs and memory[END_REF][START_REF] Hermann | Cognition across the lifespan: Antiepileptic drugs, epilepsy, or both? Epilepsy Behav[END_REF][START_REF] Meador | Cognitive outcomes and predictive factors in epilepsy[END_REF] and that, consequently, subjective memory impairment should not be taken too seriously.

Very long-term memory assessment, usually limited to specific autobiographical memory complaints, can, however, reveal accelerated long-term forgetting (ALF, normal learning of new information but accelerated forgetting of that information over subsequent days or weeks). ALF is particularly observed in transient epileptic amnesia (TEA, a syndrome primarily characterized by seizures with dense transient amnesia, in which there is also a high prevalence of interictal accelerated long-term forgetting and retrograde memory deficits) [START_REF] Felician | Transient epileptic amnesia: Update on a slowly emerging epileptic syndrome[END_REF][START_REF] Zeman | Transient epileptic amnesia[END_REF] . However, it is unclear whether or not other TLE patients [START_REF] Hendriks | Memory complaints in medically refractory epilepsy: Relationship to epilepsy-related factors[END_REF][START_REF] Illman | Assessment of everyday memory functioning in temporal lobe epilepsy and healthy adults using the multifactorial memory questionnaire (MMQ)[END_REF] not particularly suggestive of TEA [START_REF] Felician | Transient epileptic amnesia: Update on a slowly emerging epileptic syndrome[END_REF][START_REF] Zeman | Transient epileptic amnesia[END_REF] , with different phenotypes (such as syndromes related to hippocampal sclerosis, amygdala enlargement, etc.) also suffer from interictal accelerated long-term forgetting.

To test the hypothesis that these TLE patients with subjective memory complaint do, in fact, have an objective very long-term memory deficit related to accelerated long-term forgetting, 47 TLE patients who had a general complaint about their memory but for whom the standard neuropsychological assessment did not reveal memory impairment after a standard delay of 20 minutes, underwent two surprise memory tests after three weeks. One test, the Free and Cued Selective Reminding Test (FCSRT), was standard and adapted for very long-term assessment. The other, Epireal, was a new test specifically designed to capture more naturalistic components of autobiographical memory, such as episodes and recollection.

We thought that the combination of both tests would be needed to reveal if some patients showed accelerated long-term forgetting. Their performance was compared to that of 35 matched healthy control subjects.

Methods

Participants

Patients suffering from focal TLE were recruited between 2015 and 2017. Inclusion criteria were: (1) TLE diagnosis confirmed by an epileptologist (MD, LV, JC) (see below); (2) spontaneous and recurrent interictal memory complaints, including autobiographical memory complaint -related to personal events, with poor sensitivity to cueing, and confirmed by a family member -to capture specific rather than vague or attentional complaints. The assessment of this complaint was based on the clinical interview performed by the MD in charge of the patient; (3) absence of objective memory impairment after standard neuropsychological assessment (score considered normal, i.e., within 2 standard deviations of age-matched norms to the FCSRT 9 at 20-minute delayed free and cued recall); (4) MMSE score >25.

Patients were recruited from the epilepsy unit and the cognitive neurology departments of Toulouse University Hospital. All participants shared common features with a consistent diagnosis after several years of follow-up: epileptic seizures suggestive of TLE and recurrent spontaneous autobiographical memory complaints throughout follow-up. If epilepsy was the reason why most patients were referred to the epilepsy unit, TEA was initially diagnosed for some of the five patients referred to the cognitive department. However, this diagnosis was revised during evolution because follow-up demonstrated that they could not be limited to the strict definition of TEA [START_REF] Felician | Transient epileptic amnesia: Update on a slowly emerging epileptic syndrome[END_REF][START_REF] Zeman | Transient epileptic amnesia[END_REF] and these patients were managed like any other patient with TLE afterward.

Patients were matched (for age, gender, hand laterality, and socio-cultural level) with healthy control subjects recruited on a voluntary basis. Control subjects had no chronic diseases and no cognitive complaints. All participants underwent the same neuropsychological evaluation.

Temporal lobe epilepsy diagnosis

TLE diagnosis associated the repetition of clinically stereotyped seizures whose semiology was highly suggestive of a temporal lobe origin [i.e., repeated seizures including one or several initial symptoms such as experiential phenomena (transitory mental states, sensory and memory illusions such as déjà-vu, reminiscences or dreamy-state)], oral automatisms (e.g., swallowing, chewing), epigastric feelings, fear, transient amnesia, partial impairment of memory, loss of contact, language disorders or verbal automatisms (such as repetition of phrases or understandable words, onomatopoeia, humming), [START_REF] Blair | Temporal Lobe Epilepsy Semiology[END_REF] with epileptic activity (EEG abnormalities) on at least one scalp EEG recording suggesting a temporal lobe origin (seizure(s) and/or interictal epileptic discharges and/or focal sharp theta slowing, located over one or both temporal lobes). Each patient underwent a 1.5 or 3 Tesla brain MRI for etiological diagnosis, including at least 3DT1, T2, FLAIR, and spin echo T2 sequences.

Each patient also had several hours of scalp EEG recordings during wake and sleep periods throughout follow-up (except 3 patients, who only had several scalp EEGs awake). When no seizure was recorded on EEG data, the laterality of the hypothetical onset of seizures was based on congruent seizure semiology, location of MRI lesion, and epileptic activities.

Memory complaint rating

The magnitude of the memory complaint was assessed using the reduced (20 questions out of 64) version of the QAM (memory self-evaluation questionnaire). [START_REF] Van Der Linden | Le QAM: questionnaire d'auto-évaluation de la mémoire[END_REF] This questionnaire concerns places, persons, and facts of personal life. It had been validated previously as reliable for testing autobiographical memory, rather than measuring some aspects of attention that might interfere with the memory complaint. We selected the most relevant questions to specifically assess the status of anterograde memory and shorten the length of the clinical assessment.

Initial and three-week neuropsychological assessment

A standard neuropsychological evaluation was performed during two sessions of equal length, separated by a 3-week interval (Table 1, details of the standard tests presented in the Results section). Among other tests, the standard French version of the FCSRT 9 , a verbal memory test consisting of learning 16 words, was administered during the first neuropsychological meeting and only participants with normal scores were included in the full study and tested 3 weeks later (Figure 1). The FCSRT is an explicit verbal memory test consisting of a first encoding stage where 4 sets of 4 words are learned and then recalled immediately. It is then followed by three consecutive stages of free and cued recall during which subjects have to learn the 16 words; the target words are provided if subjects do not recall them. A delayed stage of free and cued recall is performed after 20 minutes.

Psychiatric scales were also proposed to all subjects to assess the levels of mood disturbance (Beck depression inventory), anxiety (State-Trait Anxiety Inventory STAI Y-A), and motivation (Starkstein motivation scale), which could bias neuropsychological performances. [START_REF] Starkstein | Apathy and Withdrawal[END_REF] Long-term memory assessment at 3 weeks Both the free and cued recall parts of the FCSRT were administered by surprise again after three weeks (i.e., the subjects were not informed during the first meeting that they would be retested later on FCSRT words). As participants had normal performances on the FCSRT at the initial assessment, and as this test consists of three sequences of learning and recalling a list of words, this test is over-rehearsed and cannot be considered ecological. Learning is not incidental and does not allow assessment of all the components of episodic memory ("what", where", "when" and sense of agency). [START_REF] Tulving | Episodic Memory: From Mind to Brain[END_REF] Autobiographical memory is multisensory, usually learned incidentally and, in its episodic form, not repeated. Therefore, we designed a more naturalistic test, Epireal, which we expected would be more sensitive. The general idea of Epireal is to incidentally introduce eight standardized real-life mini-events during the neuropsychological assessment (for example, the subject is asked to give the examiner a green binder located on a chair behind him), and to test three weeks later if subjects remembered these events (illustration of minievents in Figure 1; details in eFigure 1 & eTable 1). The eight mini-events were chosen according to the following constraints: events usable by the largest number of clinicians, not requiring constraints of place, time, or expensive material, and strict control of the encoding conditions, so that all subjects experienced a similar multisensory situation. All subjects experienced the same mini-events in the same order. Subjects were not informed that they would subsequently be questioned on these mini-events. To facilitate the whole procedure, it was simply explained that the neuropsychological tests would be administered in two sessions separated by three weeks. Recall of these mini-events was not tested during the first neuropsychological assessment.

During the second neuropsychological assessment, three weeks later, participants were interviewed on the mini-events that had happened and asked to recall them as precisely as possible, as if reliving the moment. This explicit instruction implies a conscious recollection of the memory and a mental re-experience of the event, key components of episodic memory retrieval. [START_REF] Tulving | Episodic Memory: From Mind to Brain[END_REF] Different components of memory were assessed. 1) Sense of agency during retrieval, related to feelings of action, causality, and self-consciousness, i.e., if the participant thinks he/she was an actor or a spectator of the mini-event [START_REF] Tulving | Episodic Memory: From Mind to Brain[END_REF][START_REF] Metcalfe | Autonoetic Metacognition[END_REF] (note that in this study, this was assessed objectively and not subjectively). A response "actor" or "spectator" was considered correct (agency performances) if the subject was indeed an actor (e.g., he himself took the binder) or spectator of the event (e.g., the phone is ringing, the patient does not act on it). 2) "where" context (e.g., on the chair behind the patient). 3) "when" context (e.g., at which moment of the initial evaluation).

A free recall phase was first performed, followed by a cued one. Retrieval of the eight mini-events was rated on 39 [content (what) = 22 max., spatial context (where) = 8 max., temporal features (when) = 9 max.] We added free and cued recall scores to obtain a total score for each memory test.

Statistical analyses

Performances on the different cognitive tests were analyzed by repeated-measures multivariate analysis of variance (MANOVA) with factors of group (patients and controls) and patients' clinical features within the patient groups (i.e., lesion, no lesion, etc.) across the different cognitive tests. A p-value <0.05 was considered significant. We calculated effect size between groups using Cohen's d (effect size was considered weak between 0.2 and 0.5, medium between 0.5 and 0.8, and high above 0.8). All statistics, such as MANOVAs and Pearson correlations, were performed using RStudio and the scipy.stats Python library.

Standard Protocol Approvals, Registrations, and Patient Consent

All participants provided written informed consent to take part in this study. The inclusion of patients and use of clinical data in this study was performed in the framework of an ethics authorization by the Toulouse University Hospital ('MR004 n°2020-140').

Data Availability Statement

Anonymized data will be shared by request from any qualified investigator.

Results

Subjects' demographic and clinical features

Forty-seven patients (24 males, 3 left-handed) matched the inclusion criteria: 42 patients were recruited from the epilepsy unit and 5 from the cognitive neurology departments of Toulouse University Hospital. Thirty-five matched healthy control subjects (23 males, 3 left-handed) were recruited. Main demographic characteristics did not differ significantly between patients and controls (Table 1 1). Fourteen (29.8%) patients matched the International League Against Epilepsy definition for pharmacoresistance. [START_REF] Kwan | Definition of drug resistant epilepsy: Consensus proposal by the ad hoc Task Force of the ILAE Commission on Therapeutic Strategies[END_REF] Mean number of antiseizure medications per patient was 1.54 +/-0.56

(Table 1). The standard neuropsychological and psychiatric evaluation of patients and control subjects is presented in Table 2.

Memory complaint and standard memory evaluation (initial evaluation)

Memory complaint differed significantly between patients and controls as expected (QAM test; F(1, 79)=39.7, p<0.001), (Figure 3A and Table 1). Because it was an inclusion criterion, performance on the verbal test FCSRT did not differ between patients and controls, either for total (free + cued) immediate recall scores (F(1, 79)=0.1, p>0.05) or for total delayed (20 minutes) recall scores (F(1, 79)=0.6; p>0.05) (Figure 3B, maximum performance possible on the FCSRT = 16). Of note, the performance of the patients was slightly lower than that of controls (F(1, 79)=4.3, p=0.039) on the delayed free recall (20 minutes). The patients also repeated significantly more words they had already recalled (F(1, 79)=10.5, p=0.001).

However, patients' individual scores remained within normal range (>-2 SD from the mean of age-matched norms). The learning curves of the two groups superimpose for all four stages of recall, indicating that learning is very similar between the two groups at standard delays (eFigure 2).

Very long-term memory evaluation (assessment at three weeks)

After three weeks, FCSRT scores were significantly lower in patients than in controls, both for free (F(1, 79)=25.2, p<0.001) and total recall (F(1, 79)=27.5, p<0.001) (Table 1, Figure 3C). Performance on the Epireal test was likewise significantly lower in patients than in controls, both for free (F(1, 79)=39.6, p<0.001) and total recall (F(1, 79)=29.0, p<0.001).

There was no significant correlation between memory complaint (QAM scores) and FCSRT (r=0.01, p=0.37) or Epireal total scores (r=-0.24, p=0.09). Interestingly, there was no significant correlation between the FCSRT and Epireal total recall scores, either (r=0.00, p=0.99).

We calculated the proportion of patients showing impairment on the two memory tests using a cut-off below the 5 4). There was no difference in delayed free and total recall scores in the Epireal or FCSRT after 3 weeks according to the MRI profiles (all p > 0.25).

Considering detailed scores on Epireal, retrieval scores of "where" contextual information, "when," and content were all significantly lower in patients than in controls (Table 2). Agency performances were also significantly lower in patients than in controls (spectator: (F(1, 79)=23.8, p<0.001), actor: (F(1, 79)=13.35, p<0.001)).

No influence of lesion type on memory complaint and objective memory deficits

Surprisingly, memory complaint was not significantly different between patients with or without a lesion. After three weeks, free and total recall scores on the Epireal and FCSRT were likewise not significantly different between patients with and without a lesion.

Moreover, it did not differ significantly according to the laterality of the seizure origin.

Within-patient group analyses are provided in eTable 3.

Relation with the severity of epilepsy and psychiatric scales

Memory complaint or recall on the FCSRT or Epireal did not depend on the duration of epilepsy, or pharmacoresistance, or the number of drugs taken (eTable 3 Likewise, no significant correlation was found between the QAM and either the Beck depression inventory (p=0.53) or the STAI (p = 0.06). However, a significant correlation between the QAM and the motivation scale (r=0.40, p=0.005) was found.

We also performed complementary analyses to assess whether the group of patients who did not show an objective impairment at three weeks also showed a specific neuropsychological or lesional pattern. We did not however, observe any statistical difference between this subgroup of patients and the other patients.

Discussion

About 75% of a broad population of patients with TLE with initial subjective memory complaint were found to have objective memory impairment after three weeks, whether they had a brain lesion or not and regardless of the type of lesion and response to antiseizure medication.

The majority of TLE patients showed significant impairment after 3 weeks, regardless of the type of memoranda (list of words or real-life events) and the retrieval modality (free or cued), despite showing no impairment over a standard delay of 20 min. Such a pattern suggests normal learning and retention of information over relatively brief delays, but accelerated long-term forgetting in this TLE population with initial subjective complaint. [START_REF] Muhlert | Accelerated forgetting of reallife events in Transient Epileptic Amnesia[END_REF][START_REF] Hoefeijzers | Accelerated long-term forgetting in transient epileptic amnesia: An acquisition or consolidation deficit?[END_REF][START_REF] Elliott | Measuring forgetting: A critical review of accelerated long-term forgetting studies[END_REF] Even cued recall was impaired after three weeks, suggesting genuine memory impairment that could not simply be explained by effortful or strategic difficulties. [START_REF] Dudai | The Neurobiology of Consolidations, Or, How Stable is the Engram?[END_REF][START_REF] Mckenzie | Consolidation and Reconsolidation: Two Lives of Memories? Neuron[END_REF] Therefore, these results are consistent with a complaint dominated by anterograde very long-term memory difficulties and provide new evidence that initial "subjective" memory impairment should not be too rapidly dismissed and instead should be taken very seriously.

Such an observation may have a significant impact on the management of TLE patients. Most of them are first referred to epilepsy units for recurrent seizures, not for memory disorders, while they also complain about their long-term memory. Clinicians are trained first and foremost to analyze symptoms to make an accurate diagnosis as fast as possible. In this process, the complaints expressed by patients play a critical role because they help practitioners to know what symptoms to look for or to verify whether the complaint matches the symptoms, suggesting that they have correctly pinpointed the disease. Complaints in epilepsy -especially when dealing with subjective symptoms -have, however, a particular status because of the important proportion of psychogenic forms of seizures. Psychogenic non-epileptic seizures represent about 30% of cases in epilepsy centers [START_REF] Abubakr | Psychogenic seizures: Clinical features and psychological analysis[END_REF] and combine heterogeneous subjective phenomena. [START_REF] Reuber | Nonepileptic seizures -subjective phenomena[END_REF] This may lead to a certain skepticism regarding complaints that cannot be confirmed by objective assessment.

One special type of subjective memory complaint has, nevertheless, attracted attention recently. Some patients have specific complaints about forgetting full episodes or details of events of their life, specifically concerning autobiographical information. [START_REF] Muhlert | Accelerated forgetting of reallife events in Transient Epileptic Amnesia[END_REF][START_REF] Voltzenlogel | Remote memory in temporal lobe epilepsy[END_REF] These patients usually have a normal memory evaluation when assessed in a standard manner, i.e., 20 to 60 minutes after encoding the memoranda. Their complaint was therefore initially considered subjective. It is only after special procedures were designed, allowing memory assessment after longer delays of 1 to 8 weeks, that it was observed that some of these patients had objective memory difficulties in the form of rapid forgetting or consolidation difficulties (accelerated long-term forgetting). [START_REF] Butler | The syndrome of transient epileptic amnesia[END_REF][START_REF] Tramoni | Long-term consolidation of declarative memory: Insight from temporal lobe epilepsy[END_REF][START_REF] Blake | Accelerated forgetting in patients with epilepsy: Evidence for an impairment in memory consolidation[END_REF] A high prevalence of accelerated long-term forgetting and autobiographical amnesia is especially noticed in TEA, [START_REF] Felician | Transient epileptic amnesia: Update on a slowly emerging epileptic syndrome[END_REF][START_REF] Zeman | Transient epileptic amnesia[END_REF] although controversies exist regarding the homogeneity of these patients and the mechanisms behind this rapid forgetting.

However, as TEA becomes better known, very long-term delay memory assessment (>1 week) has so far usually been proposed to patients with both ictal amnesia at the forefront of clinical phenotype and interictal complaints of autobiographical memory. In these cases, ictal and interictal memory disorders are the key symptoms guiding referral in consultation.

Therefore, one question remains unanswered in this context. It remains unclear whether or not other epileptic patients, with both subjective memory complaints not particularly suggestive of TEA and an ictal semiology encompassing a series of non-memory symptoms, also show objective very long-term memory impairment. By demonstrating objective accelerated longterm forgetting in patients after 3 weeks belonging to the wider TLE spectrum, the results of our study should lead to rethinking the nosology of TLE syndromes associated with memory disorders, in particular to discussing the relevance of TEA as a syndrome on its own. This study offers additional evidence for widespread, very long-term memory difficulties in epilepsy, as previously shown in subjective complaints. [START_REF] Blake | Accelerated forgetting in patients with epilepsy: Evidence for an impairment in memory consolidation[END_REF] However, our results also shed light on the structural basis of accelerated long-term forgetting. Unlike most previous reports on TEA [START_REF] Felician | Transient epileptic amnesia: Update on a slowly emerging epileptic syndrome[END_REF][START_REF] Zeman | Transient epileptic amnesia[END_REF] , we selected a wide spectrum of TLE patients, in which memory complaint was the main common point. Otherwise, patient etiologies and lesions were highly heterogeneous. Importantly, these difficulties were also evidenced when the MRI was normal and did not vary depending on the type of lesion (hippocampal sclerosis, amygdala enlargement, or extensive temporal lesion). This is an important piece of information,

suggesting that the same level of attention must be paid to a memory complaint regardless of the epileptic syndrome, and associated with a lesion or not. It is necessary to go further than data suggesting that a hippocampal lesion in focal epilepsies is the main predictor of accelerated long-term forgetting, but which do not take into account the patient's complaint and its autobiographical components. [START_REF] Miller | Accelerated Long Term Forgetting in patients with focal seizures: Incidence rate and contributing factors[END_REF] Consequently, verifying long-term (a delay exceeding 3 weeks in the present study) memory must not be limited to TEA but should be proposed to a broad epileptic population with TLE, including those with no visible lesion on brain imagery or in epileptic contexts considered more benign.

Memory complaint was originally and has largely been described in the aging population, as a symptom that could precede mild cognitive impairment [START_REF] Reisberg | The pre-mild cognitive impairment, subjective cognitive impairment stage of Alzheimer's disease[END_REF] and has been related

to subjective self-perceived cognitive decline among apparently cognitively normal individuals. [START_REF] Jessen | A conceptual framework for research on subjective cognitive decline in preclinical Alzheimer's disease[END_REF] It is associated with an increased risk of Alzheimer's disease. [START_REF] Van Harten | Subjective cognitive decline and risk of MCI: The Mayo Clinic Study of Aging[END_REF] Cortical atrophy, 32 white matter degeneration [START_REF] Li | Diffusion Tensor Imaging Study in the Detection of White Matter Degeneration in Subjective Cognitive Decline[END_REF] , and altered connectivity in resting-state networks [START_REF] Li | Aberrant functional connectivity network in subjective memory complaint individuals relates to pathological biomarkers[END_REF] have been observed in patients with memory complaint. In these cases, memory complaint may reflect an early symptom of amyloid β-related pathology. [START_REF] Verfaillie | Amyloid-β Load Is Related to Worries , but Not to Severity of Cognitive Complaints in Individuals With Subjective Cognitive Decline : The SCIENCe Project[END_REF] In parallel, recent studies suggest that accelerated long-term forgetting might be a sensitive marker of very early Alzheimer's disease. [START_REF] Weston | Accelerated long-term forgetting in presymptomatic autosomal dominant Alzheimer's disease: a cross-sectional study[END_REF] In epileptic patients, such links between memory complaint and neural tissue or connectivity damages remain to be demonstrated. Preeminent hypotheses to explain memory complaint in the epileptic population have been:

(1) influence of depressive mood, psychological distress, and disturbance of attentional functions, [START_REF] Grewe | Subjective memory complaints in patients with epilepsy : The role of depression , psychological distress , and attentional functions[END_REF] (2) interference of medication on memory processes, 38 and (3) role of interictal epileptic discharges, especially during sleep. [START_REF] Lambert | Accelerated long-term forgetting in focal epilepsy : Do interictal spikes during sleep matter ?[END_REF][START_REF] Gelinas | Interictal epileptiform discharges induce hippocampal-cortical coupling in temporal lobe epilepsy[END_REF] The first and second hypotheses lack evidence or are supported by inconsistent or scarce results. [START_REF] Tramoni-Negre | Long-term memory deficits in temporal lobe epilepsy[END_REF] Our results do not corroborate these two hypotheses. There was no correlation with self-questionnaires assessing motivation, depression, or anxiety, which is in agreement with previous studies that found no correlation between the Hospital Anxiety and Depression Scale and very long-term memory performance. [START_REF] Butler | The syndrome of transient epileptic amnesia[END_REF] We also did not notice any difference due to the number of antiseizure medications. In addition, only one patient used to take potential amnestic drugs. The impact of multiple antiseizure medications has been suggested in TLE patients for the onset of accelerated long-term forgetting. [START_REF] Cassel | Forgetting in temporal lobe epilepsy: When does it become accelerated? Cortex[END_REF] However, this has not been observed in other TLE cohorts. [START_REF] Muhlert | Accelerated long-term forgetting in temporal lobe but not idiopathic generalised epilepsy[END_REF] The hypothesis of the influence of medication is even more questionable when memory complaint often precedes its introduction.

Although our results are insufficient to speak for the third hypothesis (i.e., role of interictal epileptic discharges), they suggest specific memory consolidation impairment and not a bias of memory tests due to psychiatric symptoms or other psychotropic drugs known to influence cognitive scores. Future works should combine these memory tests with electrophysiological recordings during wake and sleep to determine the influence of interictal epileptic discharges on memory complaint and consolidation processes. Indeed, one of the major observations of our work is the absence of significant differences between patients with or without a lesion or among lesion types, regardless of the response to antiseizure medication and the frequency of seizures. With the caveat that an underestimation of the frequency of seizures and asymptomatic seizures 39 cannot be excluded, we can hypothesize that alterations of connectivity in a widespread long-term memory network (overlapping core medial and lateral temporal nodes) related to epileptic abnormalities, rather than lesions, may impact consolidation processes. Such a hypothesis would match several recent observations: reduced resting state functional connectivity correlated with accelerated long-term forgetting, [START_REF] Audrain | Cognitive and functional correlates of accelerated longterm forgetting in temporal lobe epilepsy[END_REF] consolidation impairment correlated with activation of interictal hippocampal epileptic discharges during sleep in TLE [START_REF] Lambert | Accelerated long-term forgetting in focal epilepsy : Do interictal spikes during sleep matter ?[END_REF] and with a pathological coupling of cortical spindles with hippocampal interictal epileptic discharges in animals. [START_REF] Gelinas | Interictal epileptiform discharges induce hippocampal-cortical coupling in temporal lobe epilepsy[END_REF] The requirement for two meetings at three-week intervals initially appears timeconsuming and difficult to schedule. However, the possibility of interleaving an ecological task as in Epireal and the option to divide the assessment into two, counterbalances this apparent limitation. The evaluation is usually exhaustive, at least in a substantial portion of epileptic patients. [START_REF] Brissart | French neuropsychological procedure consensus in epilepsy surgery[END_REF] Therefore, the global duration of the assessment is not significantly longer with tests like Epireal.

In this study, we also introduced a new test, Epireal, on the grounds that it was more ecological (i.e., relied on more sensory modalities and had a clearer episodic structure and personal relevance than usual word lists) and could provide a richer assessment of autobiographical episodic memory. The effect size was higher for Epireal than for the word list. It also detected memory deficits in more patients. Interestingly, it also clearly revealed the episodic nature of the long-term memory deficit in that both the "where" and "when" components were impaired, as well as the point of view (actor vs. spectator) of the patients when they recalled the Epireal episodes. Such a test also reveals that memory difficulties are not limited to the verbal modality. It is also particularly interesting to note that performance on the Epireal test did not correlate at all with the FCSRT, suggesting that it captures different aspects of memory. It is important to note that impaired autobiographical episodic memory has already been largely documented in patients with TLE, though regarding retrograde memory [START_REF] Voltzenlogel | Remote memory in temporal lobe epilepsy[END_REF][START_REF] Lemesle | Accelerated long-term forgetting and autobiographical memory disorders in temporal lobe epilepsy: One entity or two?[END_REF][START_REF] Butler | Recent insights into the impairment of memory in epilepsy: Transient epileptic amnesia, accelerated long-term forgetting and remote memory impairment[END_REF] . In contrast, Epireal assesses the ability to form new long-term memories, i.e., anterograde episodic memory, which is virtually never done as part of the neuropsychological assessment because of the lack of adequate tools (see, however, [START_REF] Tramoni | Long-term consolidation of declarative memory: Insight from temporal lobe epilepsy[END_REF][START_REF] Helmstaedter | Ecological Validity of List-Learning Tests and Self-Reported Memory in Healthy Individuals and Those with Temporal Lobe Epilepsy[END_REF][START_REF] Hoefeijzers | Capturing real-life forgetting in transient epileptic amnesia via an incidental memory test[END_REF][START_REF] Ricci | Disruption of learning and long-term retention of prose passages in patients with focal epilepsy[END_REF] Intriguingly, we failed to identify objective memory deficits in 23 % of patients. We

were not able to find a specific neuropsychological or lesional factor that would make these patients specific compared to the rest of the group. Future work should aim at clarifying the origin of the complaint of these patients.

Pragmatically, however, combining this new ecological tool with the classical FCSRT allows objective accelerated long-term forgetting to be revealed in 27.7% more epileptic patients with memory complaint. Overall, about 75% of the patients were impaired on one or both tests. Thus, the addition of a test like Epireal is not a simple binary alternative within the available neuropsychological arsenal, but a complementary tool with the ability to screen and detect objective long-term memory consolidation difficulties in more patients.

Conclusion

The results of this study highlight that memory difficulties in epilepsy are very likely to be more heterogeneous than expected. Overall, qualifying a memory complaint as "subjective" should be done cautiously, or even avoided, as it may lead to an inappropriate diagnosis, insufficient therapeutic evaluation, or stigmatization. Generalizing long-term detection of memory disorders may be a goal easily achievable using a two-stage neuropsychological assessment and appropriate tools such as the ones used in this study.

Further work should focus on connectivity alteration of long-term memory deficits in conjunction with wake and sleep EEG for interictal analyses linked to neuropsychological assessment. The two modes of recall (free and cued) allow distinguishing between disorders of storage and retrieval processes.

Supplementary material legend eFigure 1:

Details of the mini-events and Epireal procedure.

During the second meeting after 3 weeks, the participant waits in the same waiting room as before meeting 1. No spatial or temporal clue about meeting 1 is given to the participant during meeting 2. None of the objects used during meeting 1 remain during meeting 2 to avoid influencing recall. The examiner asks the participant to recall every detail that he/she can of meeting 1 (content, spatial and temporal context, order of events, agency). This free recall phase is subsequently completed by cued recall if the participant failed to retrieve part or all of an event.

eFigure 2:

Line graphs for the free recall and total (free+delayed) recall on the FCSRT for patients and controls.

The curves of the two groups superimpose for all four stages of recall, indicating that the learning curves of the two groups are very similar at standard delays.

eTable 1:

Example of scoring a mini-event.

Example of event 5: During his/her absence, the examiner makes a phone call so that a phone rings twice in the office (each time 4 rings, 1-minute interval between them). The examiner has to count 1 point for each right answer, for free recall, cued recall, and recognition. Please note that the "Recognition score" was not considered in the results presented in this study, to allow a strict comparison between Epireal and FCSRT.

Figure 1 :

 1 Figure 1:

Figure 2 :

 2 Figure 2:

Figure 3 :

 3 Figure 3:

Figure 4 :

 4 Figure 4:

eTable 2 : 3 :

 23 Clinical epileptic features and details of patients. Patients are sorted according to memory test scores. Test(s) with deficits after 3 weeks: None FCSRT only Epireal only FCSRT + Epireal AE: Enlargement of the amygdala; CBZ: Carbamazepine, ESL: Eslicarbazepine, GBT: Gabapentin, LMT: Lamotrigine, LVT: Levetiracetam, OXC: Oxcarbazepine, VPA: Sodium valproate, ZNS: Zonisamide; B: Bilateral; HS: Hippocampal sclerosis; IEDs: Interictal epileptic discharges; STS: Sharp transient and slow activities; L: Left; R: Right; U: Uncertain; yr.: years eTable Memory complaint rating and memory performances at 3 weeks, according to epileptic clinical features. Numbers in parentheses indicate the number of patients included in the analyses. * DF=1, 45 ** DF=3, 43 ***DF=2, 44. eReferences: e1. de Wall C, Wilson BA, Baddeley AD. The Extended Rivermead Behavioural Memory Test: A Measure of Everyday Memory Performance in Normal Adults. Memory. 1994;2:149-166.

  ). Compared to other ecological and multidimensional tests, like the Extended Rivermead behavioural memory test or tests using the concept of mini-events that have influenced the creation of Epireal, e1 Epireal is embedded incidentally in the course of neuropsychological assessment. It also allows analyses of different components of the memory that can participate in the deficit such as content, sense of agency, or what/where context. In this sense, a test like Epireal, which was well tolerated by the patients, may be a useful addition to the standard neuropsychological workup.

Table 1 :

 1 Control subjects' and patients' clinical and demographic characteristics.

	Control subjects' and patients' clinical and demographic characteristics
		Patients (n=47)	Control subjects (n=35)	P
	Age (year, mean, SD)	46.6 +/-16	48.9 +/-15.2		0.51
	Gender	24M	23M		0.63
	Level of education (years,	13.06 (+/-3.3)	13.37 (+/-2.3)	0.64
	mean, SD)
	Handedness	3L	3L		0.71
	Patient's clinical profile
	Location of seizure origin Unilateral		10R, 14L
		Bilateral		3
		Uncertain		19
	Duration of epilepsy*	≥11 yr		1
	(no. patients)	≥6-10 yr		15
	[mean (sd): 10.8 (10.5) yr]	≥1-5 yr		16
	Frequency of seizures*	<1/yr		18
	(no. patients)	≥1/yr		17
		≥1/m		10
		≥1/w		1
		1/d		0
	Lesion type	No lesion		12
	(no. patients)	Hippocampal sclerosis		12
		Amygdala enlargement		12
		Extensive temporal lesion	11
				(autoimmune encephalitis sequelae (3);
				herpetic encephalitis sequelae (1);
				cavernoma (3); arteriovenous
				malformation (1); astrocytoma (1); cortical
				abnormality with meningoencephaloceles
				(1); trauma sequelae (1))
	Medical treatment	None		3
	(no. patients)	1 antiseizure medication	27
		2 antiseizure medications	15
		3 antiseizure medications	2
	M: Male; L: left; R: right; SD: standard deviation. *Details per patient are available in
	Supplementary Material eTable 3 and eTable 3. The frequency of seizures was self-estimated
	by patients.

Table 2 :

 2 Memory complaint, memory scores, standard neuropsychological tests, psychiatric scales in patients and control subjects. The cued recall test is only for words that were not initially recalled in the free recall trial.

	Test (maximum score)	Patients' mean score (SD)	Control subjects' mean score (SD)	P	Cohen's d
	Subjective memory complaint
	QAM (6)	3.1 (0.6)	2.3 (0.5)	<0.001**	1.17
	Memory tests -Meeting 1 ϕ
	FCSRT delayed free recall (16)	12.3 (2.1)	13.2 (1.5)	0.039 *	0.46
	FCSRT delayed free + cued recall 9 (16)	15.8 (0.5)	15.8 (0.3)	0.42	-
	Memory tests -Meeting 2
	FCSRT free recall (16)	4.2 (3.0)	7.6 (3.3)	<0.001**	0.94
	FCSRT total recall (16)	9.1 (3.6)	12.7 (2.3)	<0.001**	0.99
	Epireal free recall (39)	7.0 (3.1)	11.8 (4.1)	<0.001**	1.11
	Epireal total recall (39)	21.0 (4.5)	26.9 (3.3)	<0.001**	1.18
	Epireal contextualization
	-"where" (8)	5.4 (1.6)	6.6 (1.1)	<0.001**	0.82
	-"when" (9)	6.5 (1.8)	7.7 (1)	<0.001**	0.79
	Epireal content details -"what" (22)	16.9 (2.8)	19.0 (1.9)	<0.001**	0.74
	Epireal retrieval agency	4.2 (1.9)	5.6 (1.3)	<0.001**	0.74
	-spectator (8)
	-actor (31)	24.5 (4)	27.9 (2.2)	<0.001**	0.89
	Standard neuropsychological tests
	TMT-B § (seconds)	76.9 (34.2)	84.2 (52.9)	0.45	-
	WAIS digit symbol (133)	67.7 (17.1)	74.3 (16.4)	0.03*	0.37
	Fluency letter	22.1 (6.8)	26 (7.6)	0.02*	0.52
	Fluency animals	28.2 (7.7)	31.6 (7.3)	0.02*	0.43
	Confrontation naming	39.5 (0.8)	39.4 (1.5)	0.55	-
	Psychiatric scales
	Beck depression inventory (39)	5.8 (4.1)	1.6 (1.9)	<0.001**	1.05
	STAI (80)	37 (9.5)	29.4 (7.5)	<0.001**	0.79
	Starkstein scale (42)	11.4 (5)	9.5 (3.5)	0.03*	0.41

ϕ

Ethical publication statement

We confirm that we have read the Journal's position on issues involved in ethical publication and affirm that this report is consistent with those guidelines.


Quentin Cassar

Samuel Caravera

Gaëtan Macgrogan

Thomas Bücher

Philipp Hillger

Ullrich Pfeiffer

Thomas Zimmer

Jean-Paul Guillet

Patrick Mounaix
email: patrick.mounaix@u-bordeaux.fr

Ga Ëtan Macgrogan

Thomas B Ücher

Terahertz refractive index-based morphological dilation for breast carcinoma delineation

teaching and research institutions in France or abroad, or from public or private research centers.

Introduction

Terahertz imaging and spectroscopy have rapidly spread to different application areas thanks to the continued development of efficient emitters and detectors between 0.1 and 7-THz [START_REF] Dhillon | The 2017 terahertz science and technology roadmap[END_REF] . The biomedical field is one domain of study that could benefit from terahertz wave properties [START_REF] Pickwell | Biomedical applications of terahertz technology[END_REF][START_REF] Romanenko | The interaction between electromagnetic fields at megahertz, gigahertz and terahertz frequencies with cells, tissues and organisms: risks and potential[END_REF] . Radiations at terahertz frequencies have been shown to be non-ionizing and non-hazardous for biological tissues at the power commonly employed to inspect the super-cellular level [START_REF] Il'ina | State-of-the-art of studies of the effect of terahertz radiation on living biological systems[END_REF] . Besides, terahertz radiations are notably sensitive to the presence of polar molecules such as the most abundant component of the body: water [START_REF] Møller | Terahertz reflection spectroscopy of debye relaxation in polar liquids[END_REF] . Hence, different medical topics have been assessed with terahertz imaging and spectroscopy to look for alternative and complementary methods to the existing ones. These investigations cover a broad range of possible surgical and clinical applications [START_REF] Sy | Terahertz spectroscopy of liver cirrhosis: investigating the origin of contrast[END_REF][START_REF] Arbab | Terahertz spectroscopy for the assessment of burn injuries in vivo[END_REF][START_REF] Taylor | Thz medical imaging: in vivo hydration sensing[END_REF] . Among them, cancer diagnosis remains the most widely investigated topic throughout the literature, covering blood [START_REF] Jeong | Characterization of blood using terahertz waves[END_REF][START_REF] Reid | Terahertz time-domain spectroscopy of human blood[END_REF] , brain [START_REF] Oh | Study of freshly excised brain tissues using terahertz imaging[END_REF][START_REF] Meng | Terahertz pulsed spectroscopy of paraffin-embedded brain glioma[END_REF][START_REF] Yamaguchi | Brain tumor imaging of rat fresh tissue using terahertz spectroscopy[END_REF] , colorectal [START_REF] Reid | Terahertz pulsed imaging of freshly excised human colonic tissues[END_REF][START_REF] Eadie | Optimizing multi-dimensional terahertz imaging analysis for colon cancer diagnosis[END_REF] , gastric [START_REF] Hou | Terahertz spectroscopic investigation of human gastric normal and tumor tissues[END_REF][START_REF] Ji | Feasibility of terahertz reflectometry for discrimination of human early gastric cancers[END_REF] , liver [START_REF] Sy | Terahertz spectroscopy of liver cirrhosis: investigating the origin of contrast[END_REF] , lung [START_REF] Brun | Terahertz imaging applied to cancer diagnosis[END_REF] , oral [START_REF] Sim | Terahertz imaging of excised oral cancer at frozen temperature[END_REF] , skin [START_REF] Woodward | Terahertz pulse imaging in reflection geometry of human skin cancer and skin tissue[END_REF][START_REF] Woodward | Terahertz pulsed imaging of skin cancer in the time and frequency domain[END_REF] and breast cancer [START_REF] Ashworth | Terahertz pulsed spectroscopy of freshly excised human breast cancer[END_REF][START_REF] Chavez | Assessment of terahertz imaging for excised breast cancer tumors with image morphing[END_REF][START_REF] Cassar | Pilot study of freshly excised breast tissue response in the 300-600 ghz range[END_REF][START_REF] Chavez | Breast cancer detection with low-dimensional ordered orthogonal projection in terahertz imaging[END_REF][START_REF] Okada | Terahertz near-field microscopy of ductal carcinoma in situ (dcis) of the breast[END_REF] .

Investigations, conducted on breast cancer, mainly aim to develop supporting procedures for breast-conservative surgeries through breast tumour margin delineation. The success of breast-conserving surgeries is dictated by the accuracy of delineating the concentric margins of excised breast volumes. Although there is no clear description of what ideal margins are, it is recommended that no cancer cells remain adjacent to any inked edge/surface of the specimen [START_REF] Buchholz | Margins for breast-conserving surgery with whole-breast irradiation in stage i and ii invasive breast cancer: American society of clinical oncology endorsement of the society of surgical oncology/american society for radiation oncology consensus guideline[END_REF] . Conserving surgeries are usually followed by postoperative radiation management to eradicate microscopic remains of disease [START_REF] Fajdic | Criteria and procedures for breast conserving surgery[END_REF] . Margin cleanliness is assessed via biopsy examinations during which excised volumes are subsequently fixed into formalin solution, embedded into paraffin, sliced in micrometric sections and immersed into different alcohol and biological stain baths. Usually, hematoxylin and eosin stains are used. The reason for that is that hematoxylin stains cell nuclei blue and eosin stains both the cytoplasm and the extracellular matrix pink. The stain draws the global layout of a tissue structure so that a pathologist judges the cleanliness of the margin [START_REF] Alturkistani | Histological stains: a literature review and case study[END_REF] . Overall, two extreme cases of margin delineation can be observed: (i). positive margins -malignant cells are located at the edge of the excised volume; (ii). negative margins -an absence of tumor cells at the edge or the distance of abnormal cells from the edge is at least more than 1-mm. Following histopathologic inspection, up to 20% of excised breast samples are reported to exhibit positive margins [START_REF] Jacobs | Positive margins: the challenge continues for breast surgeons[END_REF] . Reasons behind tumor edge delineation failure are often presence of in situ carcinoma at close proximity to the surgical margin, discontinuous tumor spread from the original surgery site, or inappropriate presurgical tumor localization and inappropriate excision during surgery [START_REF] Landercasper | Reasons for re-excision after lumpectomy for breast cancer: insight from the american society of breast surgeons mastery sm database[END_REF] . A positive margin inevitably leads to a second surgery to favor low recurrence risk and to attain more widely clear surgical margins. In return, a second surgery concomitantly increases the morbidity rate. So far, different research teams worldwide have reported the ability of terahertz imaging and spectroscopy to discriminate 1 between healthy and malignant breast tissues. These studies were primarily conducted on formalin-fixed and paraffin-embedded breast tissues [START_REF] Hassan | Terahertz imaging for margin assessment of breast cancer tumors[END_REF][START_REF] Bowman | Terahertz imaging of excised breast tumor tissue on paraffin sections[END_REF][START_REF] Cerica | Terahertz pulsed imaging of paraffin-embedded human breast cancer tissue[END_REF] . Such investigations opened the route for clinical studies on freshly excised breast volumes [START_REF] Brun | Terahertz imaging applied to cancer diagnosis[END_REF][START_REF] Ashworth | Terahertz pulsed spectroscopy of freshly excised human breast cancer[END_REF][START_REF] Cassar | Pilot study of freshly excised breast tissue response in the 300-600 ghz range[END_REF] . The capabilities of terahertz radiation demarcation between normal and abnormal tissue regions were originally attributed to free-water content. Indeed, free-water molecules have been proven to present a specific permittivity step around 900-GHz [START_REF] Møller | Terahertz reflection spectroscopy of debye relaxation in polar liquids[END_REF] .

Moreover cancer tissues are known to exhibit a greater free-water content than normal tissues [START_REF] Mcintyre | Cell hydration as the primary factor in carcinogenesis: a unifying concept[END_REF] . However, further studies have suggested that the origin of contrast could not be solely attributed to water. That is because specific dielectric features exhibited by breast tissues, in the low terahertz frequency band, were not observed in water dielectric profile [START_REF] Cassar | Terahertz Radiations for Breast Tumour Recognition[END_REF] . Hence, it has been suggested that, specific functional groups play a potential role [START_REF] Ashworth | Terahertz pulsed spectroscopy of freshly excised human breast cancer[END_REF] . Globally, the refractive index of breast cancer tissues has been shown to be higher than the one observed for normal tissues over the terahertz band. On the contrary, the related absorption coefficient was reported as unsatisfactory parameter for demarcation [START_REF] Cassar | Terahertz Radiations for Breast Tumour Recognition[END_REF][START_REF] Fitzgerald | Terahertz pulsed imaging of human breast tumors[END_REF] . Additionally, the contrast level between healthy and malignant tissues depends on cancer cell density. In fact, while the resolution of any light-based imager remains dictated by the diffraction limit, two objects separated by a distance less than the wavelength cannot be distinguished. For instance, the spatial resolution of a far-field imaging system operating at 1-THz will be limited to 0.3-mm. Hence, the respective response to the external terahertz radiation stimuli of two biological entities, separated by a distance smaller than 0.3-mm, will have to be averaged. Considering the typical diameter of the eukaryotic cell is at the order of tens of microns, it can be concluded that, such a terahertz imager cannot manage to resolve entities at the cellular level. It has, however, been demonstrated that the use of computational imaging system operating in a total internal reflection geometry could resolve features with a sub-wavelength lateral resolution. [START_REF] Barr | Super-resolution imaging for sub-ir frequencies based on total internal reflection[END_REF] While it can be expected that high densities of cancer cells will lead to a well-defined demarcation, the dielectric response of isolated abnormal groups may be blurred by the healthy surrounding and ultimately leading to recognition analysis failure. Although the diffraction limit of resolution may complicate recognition in areas sparsely populated by cancer cells [START_REF] Hillger | A 128-pixel system-on-a-chip for real-time super-resolution terahertz near-field imaging[END_REF] , it also raises delicate questions on the exact frontier between two well localized normal and abnormal regions. Indeed, rather than depicting a sharp contrast between areas, the obtained cliché may inevitably exhibit a smooth gradient from one to another area which is a result of class-overlapping. That is particularly limiting when it comes to providing a pixel-by-pixel diagnosis based on the information collected.

The present work proposes a new approach for the clinical classification of breast tissue pixels that overcomes the limitations aforementioned. The method is based on the extraction of the terahertz refractive index map of freshly excised samples followed by morphological dilation. A high value of the refractive index has been reported as a reliable measure of the presence of cancer within a tissue [START_REF] Ashworth | Terahertz pulsed spectroscopy of freshly excised human breast cancer[END_REF][START_REF] Cassar | Pilot study of freshly excised breast tissue response in the 300-600 ghz range[END_REF] . Morphological dilation is a part of set-theory [START_REF] Jech | Set theory[END_REF] and is commonly employed to images having characteristics of ambiguity and vagueness [START_REF] Meyer | Morphological segmentation[END_REF] . It consists of expanding a given shape contained in the input image. In biology, morphological processing was notably employed for counting blood cells during blood smear test [START_REF] Tulsani | Segmentation using morphological watershed transformation for counting blood cells[END_REF] , to isolate female gametocyte [START_REF] Caponetti | Fuzzy mathematical morphology for biological image segmentation[END_REF] or for skin cancer segmentation [START_REF] Lee | Skin cancer extraction with optimum fuzzy thresholding technique[END_REF] .

Operating dilation from regions exhibiting a higher refractive index should allow bypassing class-overlapping limitations. Such a process is referred to as terahertz refractive index-based morphological dilation and operates as follows: (i). the refractive index map of a freshly excised breast tissue is extracted through a specific objective function minimization; (ii). a refractive index threshold is defined such that pixels exhibiting a refractive index higher than the threshold are classified as malignant while others are classified as benign; (iii). morphological dilation is used to spread the malignant zones to the neighborhood.

To conduct these investigations, different freshly excised breast tissues have been scanned in reflection geometry by means of a terahertz spectrometer. The refractive index maps have been extracted. Different refractive index thresholds and dilation shapes have been tested. The related pixel classifications have been compared to those provided by a pathologist. Finally, the sensitivity and specificity of each combination of threshold -dilation shape have been derived.

The paper is organized as follows: Section 2 describes the experimental framework to acquire raw terahertz images of the freshly excised breast tissues. Section 3 describes the mathematical background to extract the refractive index map. Section 4 defines the morphological dilation and the respective dilation shapes employed in the study. Section 5 describes the registration of obtained images with respect to the pathological cliché. Section 6 details the evaluation of compliance between the classifications provided respectively by the pathologist and the reported strategy. Section 7 presents the results for different samples. Finally, Section 8 presents the conclusions.

Experimental Framework

The experimental protocol was assessed and approved by the ethics committee of the Bergonié Institute. Human tissue analysis have been conducted in view of the fundamental ethical principles as stipulated in the Helsinki declaration and its later revisions. Written informed consent from each patient undergoing breast surgery was collected, stipulating their agreement regarding the use of their tissues for research purposes.

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Breast Tissue Samples

Following surgery, breast excisions were cut into slices of a few millimeters and kept into physiological serum before measurement to ensure the moisture content and delay the necrosis. A maximum of one hour elapsed between the end of surgery and the terahertz acquisition starting time. Once measurement was complete, excised tissue samples were placed in formalin-buffered solution. This process enabled the further histology routine to compare the diagnoses provided by the reported method and the pathologist. Biological samples analyzed using the method about to be reported were obtained from three different patients. One sample was excised from each of these patients.

Measurement Setup

Time-domain terahertz pulsed images were acquired with a TPS3000 spectrometer (TeraView Ltd, Cambridge, UK) operating in reflection geometry. In such systems, terahertz pulses are generated from the activation of a GaAs photoswitch. A photoswitch consists of a discontinuous metallic antenna patterned onto a photoconductive layer. Ultra-fast near-infrared pulses with an energy greater than the semiconductor band gap are focused onto the gap between the two electrodes forming the photoswitch.

The incident pump laser thus propagates within the photoconductive layer and generates electron-hole pairs due to absorption.

Those photocarriers are then accelerated within the electric field of the biased antenna. The acceleration of these charges produces a transient current that drives the metallic antenna and is eventually emitted as a broadband terahertz pulse. The bandwidth directly depends on the lifetime of the carriers before recombination. The carrier lifetime in the GaAs crystal is in the subpicosecond scale, hence enabling pulses with a bandwidth ranging from 200-GHz to 2-THz.

The schematic of the experimental set-up is given in Figure 1. The route of the terahertz pulses is governed by two planar mirrors and a knife-edge right-angle prism mirror (KERAPM). The terahertz pulses are focused on the tissue sample supported by a 2-mm thick non-birefractive C-cut sapphire substrate (see Supplementary Information, Supplementary Fig. 1.) via a polytetrafluoroethylene (PTFE) lens. The maximum incident angle of the terahertz pulses is 10 • . Both the reflections at the air-sapphire and sapphire-tissue interfaces are then focused onto a photoconductive antenna detector. The detector is sourced from the same ultra-fast near-infrared pulses used for terahertz wave generation with a beam splitter. The pulses are, however, delayed in time with a mechanical delay line. The periodic variation of the delay line length allows a time gated detection of terahertz pulses reflected by the object. In order to reduce the natural absorption of terahertz pulses by water vapor molecules, the terahertz route is confined within nitrogen chamber.

Refractive Index Map

To extract the refractive index from a raw frequency image, a reference electric field has to be recorded. The reference electric field E r (ω) refers to the electric field generated by the acquisition system. The reference measurement records the electric field of the reflection from a metal plate that is located where the sapphire substrate sample holder is aimed to be positioned for tissue imaging. From the reference electric field E r (ω), the experimental transfer function T s (ω), which is a measure of the disturbance experienced by the incident field as a result of the interaction with the sample, can be calculated:

T s (ω) = E s (ω) E r (ω) , (1)
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with E s (ω) the sample frequency-dependent electric field. The shape of transfer function T s (ω) is a function of the refractive index n(ω) and the extinction coefficient κ(ω) of the sample under inspection. E s (ω) depends on the Fresnel's coefficients in transmission T (ω) and in reflection R(ω), and on propagation coefficients P(ω, d):

E s (ω) ∝ T air-sapphire (ω) × R sapphire-tissue (ω) × T sapphire-air (ω) × P 2 sapphire (ω, d), (2)
with d being the thickness of the sapphire substrate. The Fresnel's coefficients T (ω) and R(ω), as well as propagation terms P(ω, d) relate to the refractive index n(ω) and the extinction coefficient κ(ω) through:

T a-b (ω) = 2 na na + nb , (3a) R a-b (ω) = na -nb na + nb , (3b)
P a (ω, d) = e -j ωd c na , (3c)
where a and b are the indices of the respective medium, n is the complex refractive index defined as n = n(ω)jκ(ω) and c is the light velocity in vacuum. Although the extinction coefficient κ(ω) is involved in the calculation of the transfer function T s (ω), no significant differences have been reported in the literature between normal and abnormal tissue extinction [START_REF] Ashworth | Terahertz pulsed spectroscopy of freshly excised human breast cancer[END_REF][START_REF] Cassar | Terahertz Radiations for Breast Tumour Recognition[END_REF] .

Hence, solely the refractive index is further considered as a possible intrinsic parameter for demarcation.

Map Extraction

The extraction of the complex refractive index n(ω) at each pixel from the experimental transfer function T s (ω) can be performed by solving an inverse electromagnetic problem. Inverse electromagnetic problems usually minimize a specific convex objective function. This function denotes the discrepancies between the experimental waveform E s (ω) and the waveforms

E c
x (ω) successively computed from a set of candidate parameters, where the x-index refers to the x th -candidate tested. The candidate waveforms E c x (ω) are computed as stipulated in [START_REF] Cassar | Iterative tree algorithm to evaluate terahertz signal contribution of specific optical paths within multilayered materials[END_REF] . The corresponding transfer functions T c x (ω) are calculated in the same way as described by (1). The measures of discrepancies δ M x (ω) between the experimental transfer function T s (ω) and the computed transfer functions T c x (ω) are defined as:

δ M x (ω) = ln( |T s (ω)| |T c x (ω)| ). (4)
The natural logarithmic ratio is favored here instead of standard difference as it is more penalizing. Finally, the objective function χ(ω) to be minimized is defined as:

χ(ω) = δ M(ω) × δ M(ω). (5)
The minimization of the transfer function is subject to the following set of candidate parameters:

min n(ω),κ(ω) χ(ω), subject to n ∈ [1.5; 3], with ∆n = 1.10 -2 , κ ∈ [0; 1], with ∆κ = 1.10 -3 . (6)
It was stated before that the sample is maintained by the sapphire substrate. Instead of extracting the properties of the sapphire substrate for each pixel, the properties were extracted upstream, in absence of a sample, and following the same minimization process. The sapphire properties are provided in Supplementary Information, see Supplementary Fig. 2. Finally, applying the above process to each electric field stored in each pixel of the sample image allows to construct the refractive index map.

Once the refractive index map is obtained, it is converted to a binary map that shows areas that are considered malignant or benign. To do so, a threshold among the refractive index vector has to be set. Depending on the defined value for the threshold, one may progressively increase or decrease the extent of areas classified as malignant, since pixels with a refractive index higher than the threshold are classified as cancerous. A schematic of the process is given in Figure 2.

Operating Frequency

Although the refractive index is often referred to as optical constant, its profile varies as a function of the frequency. Previous studies have reported the terahertz frequency dependent refractive index values of abnormal and normal breast tissues [START_REF] Fitzgerald | Terahertz pulsed imaging of human breast tumors[END_REF] . Overall, the global difference between these values was shown to be the highest between 300-GHz and 700-GHz, roughly. Hence, rather than investigating the entire band, the classification was operated at 550-GHz, as a good trade-off between signal-to-noise ratio (SNR) and higher frequency spatial resolution [START_REF] Pfeiffer | Ex vivo breast tumor identification: Advances toward a silicon-based terahertz near-field imaging sensor[END_REF] . However, naively classifying pixels via the refractive index exhibited at 550-GHz may hardly be relevant. In particular, the refractive index extracted at the edges of malignant regions with low density may present values close to the ones of healthy tissues. Therefore, morphological dilation is introduced to overcome this limitation.

Morphological Dilation

Prior to dilation, the refractive index map is converted to a binary image as it was described in the previous section. The dilation can therefore be referred to as binary dilation. The dilation consists of a shift-invariant addition, denoted "⊕", within the meaning of Minkoswki [START_REF] Najman | Mathematical morphology: from theory to applications[END_REF] . Mathematically, let's define P as an ensemble that contains the pixels (x, y) of the tissue imaged. The binary dilation ∂ Λ (P) of P by a shape Λ ∈ Z 2 -also referred to as a structuring element, is given by:

∂ Λ (P) = P ⊕ Λ = {x + λ , y + λ |λ ∈ Λ} , (7)
where λ ∈ Λ produces the translation from P to ∂ Λ (P). Supposing the matrix P and the structuring element Λ as represented in Figure 3, the matrix ∂ Λ (P) is obtained by superimposing the center of Λ aligned with each pixel in P that has a value of 1. Therefore, depending on the classifier considered, a pixel may be attributed to the malignant group if at least one of the component λ of the structuring element Λ n -where n ∈ N * -reports a pixel whose refractive index is higher than the defined refractive index threshold. Alternatively, the structuring elements can be seen as the area of influence of a cancerous pixel.

Consequently pixels with a refractive index lower than the threshold but situated in such an area of influence, are turned into malignant pixels. It is however important to note that the process is constrained to a unique dilation and therefore, newly classified malignant pixels cannot, in turn, exercise a zone of influence.

In order to carry out the dilation and the registration steps that follow, it is essential to preserve the morphology of the imaged sample. To do this, the dilation procedure must be carried out with respect to the initial contour of the sample generated from a standard contouring algorithm, thus preventing the appearance of cancerous pixels outside the original surface of the sample. A schematic of the dilation process operated on a binary refractive index map is given in Figure 5.

Image Registration

The classification images provided by the reported method and the ones given by the pathologist do not share the same coordinate system. Image registration is the process of migrating different images into one common coordinate system [START_REF] Goshtasby | 2-D and 3-D image registration: for medical, remote sensing, and industrial applications[END_REF] .

Therefore, image registration is necessary to enable the comparison between the data sets. Effectively, the spatial resolution of the optical microscope used to acquire pathology clichés is far greater than the one of the employed terahertz imager.

Additionally, the orientation of the tissue sample in the terahertz image and in the clinical image are expected to be different, as they are not acquired with the same angle. A simple pixel-by-pixel comparison is therefore not possible as it stands. Prior to comparison, images have to be resized and reorientated. The registration process is feature-based and solely involves image contours to avoid unintentional human bias. The different steps that are followed to register the images with respect to each other are hereafter described.

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Contouring

Contour lines, also called isolines, can be calculated by interpolating the value of the scalar field found at each pointel of each pixel. An infinite number of isolines can however be delineated. The choice of the contour to define the spatial extent of the sample in the image remains therefore subjective. For each sample, the isoline that suited the visualized tissue area best was determined by carefully comparing the terahertz image and the different contour levels.

Resizing

As the resolution of the images is different, it is necessary to resize the histology pictures. To do so, a bicubic interpolation is operated onto pathology images. Contrary to the previous interpolation, where it is based on the four nearest pixels, bicubic interpolation takes into account a neighborhood of sixteen pixels. Therefore, bicubic interpolation provides a smoother histology slide than simple bilinear interpolation.

Reorientation

First, the contour of the terahertz image is manually and progressively twisted to bring it closer to the twist angle of the pathology contour. Once the orientations approximately match, the pathology contour is iteratively rotated to establish the correlation between the two contour matrices at each step. Basically, it consists in determining the Pearson's correlation coefficients [START_REF] Kaur | Image recognition using coefficient of correlation and structural similarity index in uncontrolled environment[END_REF] . The rotation angle providing the highest positive correlation is selected and the terahertz image is correspondingly rotated. The flow chart of these three pre-treatments, namely contouring, resizing and reorientation for image registration is provided in Figure 6.

Image Discrepancies Issues

Although one can resize and reorientate the two images with respect to each other, the pathology cliché and the terahertz image may not perfectly depict the same information. First, while terahertz imaging is performed directly on freshly excised tissues, the pathology diagnosis is established after the histology routine. Moreover, to obtain the pathology image, the excised tissue is first fixed in neutral buffered formalin, then dehydrated in subsequent alcohol baths with increasing concentrations, then cleared in a solvent before being infiltrated and finally embedded in paraffin wax. At this stage, the processed tissue is encased in a paraffin block that can be sliced in sections of a few microns thickness to be deposited on glass slides. These tissue sections are deparaffinized, rehydrated and subsequently stained with hematoxylin and eosin dyes. Finally, they are dehydrated in alcohol and cleared in a solvent before being mounted with a coverslip. The embedding, the sectioning and the desiccation alter the global structure of the tissues. These alterations are collectively referred as artefacts [START_REF] Aresta | Grand challenge on breast cancer histology images[END_REF] . Artefacts include loss of tissue area and details, folds and wrinkles or cracks and holes. These alterations may result in misinterpretation as they are modifying the morphological structure of tissues. Alternatively, these artefacts may drastically limit the evaluation of the terahertz classification compliance (see Supplementary Information Supplementary Fig. 3, for an example based on one of the tissue reported by the present work). However, histological slides remain the only available reference picture that allows one to examine the performances of classifier under-test. Overall, there are two ways to deal with such issues: (i). correcting the histology slides at risk of adding artificial information; (ii). comparing directly the terahertz image with the raw pathology image at risk of underestimating the efficiency of the method. The first way would require to morph the pathology image to correspond to the terahertz picture. Some procedures to do so were reported in the literature [START_REF] Pichat | A survey of methods for 3d histology reconstruction[END_REF] . However, these methods

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are cumbersome and the evaluation of the histological cliché reconstruction is often complicated since no perfect reference pathology image exists. As terahertz imaging remains a new technology for breast carcinoma delineation, the second approach was favored -at risk of underestimating the efficiency of the classifiers.

Diagnosis Compliance

Following the histology routine, pathology images are colored in different shades of blue and pink. The pathologist draws the contour of malignant areas based on his/her expertise. From the interpretation of the pathologist, the images were binarized and each pixel was classified either as benign or as malignant [START_REF] Peter | Development and testing of a single frequency terahertz imaging system for breast cancer detection[END_REF] .

Once both diagnosis images exhibit binary information, have the same size and orientation, the compliance between them can be evaluated. In case of discrepancies, the pathologist classification prevails over terahertz delineation. The present section describes how the ability of classifiers was evaluated with respect to the pathologist one.

Performance of the Classification Test

As each diagnosis presents a binary information, four different cases can be distinguished: i. True negative: both methods classify a pixel as benign;

ii. True positive: both methods classify a pixel as malignant;

iii. False positive: the terahertz method stands for a malignant pixel while histology stipulates a benign pixel; iv. False negative: the terahertz method stands for a benign pixel while histology stipulates a malignant pixel;

Hence, for each refractive index threshold associated with a specific classifier, one can fill the corresponding confusion matrices that highlight the classification procedure performances. In such error matrices, the rows represent the instances in the terahertz class, here the predicted class, while columns represent the actual diagnosis provided by histology examination [START_REF] Powers | Evaluation: from precision, recall and f-measure to roc, informedness, markedness and correlation[END_REF] .

From these matrices, the effectiveness of the classification method is assessed by creating the receiver operatic characteristic (ROC) curve [START_REF] Rizk | Deep belief networks and cortical algorithms: A comparative study for supervised classification[END_REF] for each classifier. The ROC curve represents the ability of the classifier to provide the correct diagnosis as the refractive index threshold varies. The ROC curve is obtained by plotting the true positive rate (TPR) as a function of the false positive rate (FPR). The TPR is defined as the number of true positives divided by all pixels classified by the pathologist as positives: true positives and false negatives. The FPR is defined as the number of false negatives divided by all pixels classified by the pathologist as negatives: false positives and true negatives. It can also be thought as a plot of the sensitivity -that is equivalent to the TPR defined in equation ( 8), against the probability of false-alarm -that can be calculated as (1specificity) and defined in equation ( 9) [START_REF] Tharwat | Classification assessment methods[END_REF] . These measures of performances are favored as they are not sensitive to changes in data distributions, compared to accuracy and to error rate. Hence, both metrics can be used with imbalanced data [START_REF] García | Theoretical analysis of a performance measure for imbalanced data[END_REF] .

True Positive Rate = Sensitivity = True Positives True Positives + False Negatives ,

False Positive Rate = 1 -Specificity = False Positives False Positives + True Negatives .

To complement these measures, the area under each ROC curve (AUC) is calculated as it relies on the performance of score classifiers for all possible classification thresholds [START_REF] Fawcett | An introduction to roc analysis[END_REF] .

Finally, the best discrimination thresholds are selected as the ones that provide the highest sensitivity while preserving the healthy tissue area from false diagnosis, i.e. specificity. It is noted that the aforementioned classification procedure is studied for the specific case of breast conserving surgery. Hence, it is essential to preserve the healthy area while removing the malignant zones. Ultimately, the best classifiers are selected as the ones that provide the highest measure of T PR -FPR, since higher values of this function indicates more accurate results.

Results

In this section, the classifiers are employed to evaluate their effectiveness on three freshly excised breast tissues. Two of these samples were diagnosed as invasive ductal carcinoma (IDC) and one was identified as an invasive lobular carcinoma (ILC).

These samples are referred to as test sample TS#1, TS#2 and TS#3. (iii). Raw terahertz image at 550-GHz; (iv). Refractive index map at 550-GHz.

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TS#1

TS#1 is an invasive ductal carcinoma. The pathology image with some enlightened pathology areas, the pathology mask, the raw terahertz image obtained at 550-GHz and the correlated refractive index map are presented in Figure 7.

It can be observed that the raw terahertz image as well as the refractive index map exhibits specific features that correspond to the pathology image. Regions depicted in Figure 7.a. and Figure 7.b. correspond to fibrous tissues that are included in an adipose matrix. Such regions are therefore expected to globally give rise to a lower refractive index than the one classified as malignant as depicted in Figure 7.c. and Figure 7.d. Although such a refractive index seems overall lower than the refractive index of the tumour, it remains relatively close to it. Therefore, classifying only on the basis of the refractive index would certainly prove to be inefficient. The sensitivity and the specificity of each structuring element classifier for varying refractive index threshold were calculated for TS#1. The corresponding ROC curves and T PR -FPR functions are given in Figure 8.

Each Λ n -dependent ROC curve is located to the left of the T PR = FPR line in Figure 8, proving that the fraction of true positives is greater than the proportion of false positives. It is clear that the use of the refractive index alone as a classifier (Λ 0 ) is shown to be less efficient than associating the refractive index with a classifier. Such a statement is not surprising as the classification does not consider the neighborhood. While on ROC graphics, depicted in Figure 8, it does not seem that obvious which classifier among Λ 1 , Λ 2 and Λ 3 performs well, the T PR -FPR visualization indicates that the structuring element Λ 3 in association with a high refractive index threshold by about 2.6 is the most efficient rule of classification. The association provides a classification with a sensitivity by around 80% and a specificity of 82%. What is more, the wider the structuring element, the higher the refractive index has to be set for good performances. Effectively, starting with a high refractive index makes it possible to identify, in a first instance, tissue areas densely populated with cancer cells, while a broad structuring element makes it possible to efficiently spread the identification over a wide zone.

The corresponding AUC for each ROC curve, the T PR -FPR value, the sensitivity and the specificity for the first two best refractive index thresholds are given in Table 1 (see Supplementary Information, Supplementary Table 1. for the complete list of performances). While Λ 1 and Λ 2 are less efficient than Λ 3 for both sensitivity and specificity, the Λ 0 classifier provides a slightly greater sensitivity for a threshold of 2.1, by about 83%. However, the gain of 4% in sensitivity with respect to Λ 3 costs concomitantly 20% in method specificity. Reasonably, this gain is not worth it, considering such a drastic decrease in classification specificity. Alternatively, if one wants to increase the sensitivity while maintaining specificity at a reasonable level, second best thresholds may offer a promising substitute. On using the second best threshold provided by Λ 3 of 2.5, an increase of 7% in sensitivity conjointly leads to a decrease by about 12% in specificity. By doing so, one reaches a sensitivity of 86%.

The superimposition of the classification images from the reported method and the clinical one, corresponding to the performances listed in Table 1 are given in Figure 9. TS#2 sample is an invasive ductal carcinoma from which a 67 years old woman was suffering. The initial tumor site was found to be roughly 100 mm 2 . On Figure 10, the pathology image with some enlightened pathology areas, the pathology mask, the terahertz image at 550-GHz, and the refractive index map are shown. The pathology image as well as the pathology mask exhibit the presence of a hole, where no tissue is found. The lack of tissue in the middle of the section is not natural and enlightens the issues, that have been previously reported towards pathology images. Hence, this specific region is not considered for performance evaluation. 12/18

The most effective classifiers towards conserving classification are Λ 2 and Λ 3 , both for a threshold set at 2.1. While the combination of such a threshold with Λ 2 provides a sensitivity of 67% and a specificity of 70%, the same threshold operating with Λ 3 gives rise to a sensitivity by about 78% and a specificity of 57%. Hence, tuning the structuring element geometry would offer an interesting trade-off between specificity and sensitivity. The respective performances of each classifier applied to TS#2 are listed in Table 2 (see Supplementary Information, Supplementary Table 1. for the complete list of performances). The classification maps involving each classifier and their respective best performing thresholds are exposed in Figure 12.

These images show the improvement in classification with the use of morphological dilatation. Moreover, they highlight the difficulties of good prediction at the outer margins. Low performance at the outer margins may come from the non-conformity of the information in these areas between the terahertz image and the histology picture. The most convincing hypothesis for this non-conformity is the tissue deformation imposed by the histological routine.

TS#3

In contrast to the two previous samples, the TS3 sample was taken from an 83 years old patient with an invasive lobular carcinoma. On Figure 13, the pathology image with some enlightened pathology areas, the pathology mask, the terahertz image at 550-GHz, and the refractive index map are shown.

The ROC curves plotted in Figure 14 The AUC values and the performances for each classifier are given in Table 3 (see Supplementary Information, Supplementary Table 1. for the complete list of performances). Despite the lower efficiency the most accurate classifying strategy remains Λ 3 when associated with a refractive index threshold of 2.3. The T PR -FPR measure is by around 0.28 with a sensitivity of 53% and a specificity of 76%. As already indicated these performances are below the ones reached for other study cases.

Λ 2 classifier offers a greater specificity of 85% but simultaneously concedes 11% upon sensitivity, thus falling below the critical threshold of half the number of malignant pixels correctly classified. The weak density of cancer cells within a lobular carcinoma slice may lead one to opt for Λ 0 classifier operating in association with a low refractive index threshold to maximize

Figure 1 .

 1 Figure 1. Schematic of the acquisition system.

4 / 18 Figure 2 .

 4182 Figure 2. Thresholding principle applied to the refractive index map. a: Schematic refractive index map; b: Binary refractive index map with a threshold set at 2.4; c: Binary refractive index map with a threshold set at 2.1; d: Binary refractive index map with a threshold set at 1.8;

Figure 3 ./ 18 Figure 4 .

 3184 Figure 3. Morphological dilation operated with a cross structuring element Λ on the matrix P.

Figure 5 .

 5 Figure 5. Schematic of a morphological dilation applied to a binary refractive index map over a tissue sample. a: Binary refractive index map with a threshold set at 1.8; b: Morphological dilation applied to the binary refractive index map with an arbitrary classifier Λ n .

Figure 6 .

 6 Figure 6. Flow chart of the registration procedure for predicted diagnosis evaluation.

Figure 7 .

 7 Figure 7. Sample TS#1. (i). Pathology image and correlated view of the respective zones a, b, c and d; (ii). Pathology mask; (iii). Raw terahertz image at 550-GHz; (iv). Refractive index map at 550-GHz.

Figure 8 .

 8 Figure 8. Left: receiver operating characteristic for the different classification methods, at 550-GHz applied to TS#1. The black line stands for T PR = FPR. Right: Refractive index threshold as a function of the T PR -FPR measure for the different classifiers.

Figure 9 .

 9 Figure 9. TS#1 tissue sample classification maps at 550-GHz for Λ 0 , Λ 1 , Λ 2 , Λ 3 and their respective first two best thresholds. "Not applicable" refers to regions where the binary pathology classification and the binary terahertz classification image do not match spatially. The values listed in each box are respectively standing for the refractive index threshold, the true positive rate and the false positive rate.

Figure 10 .Figure 11 .

 1011 Figure 10. Sample TS#2. (i). Pathology image and correlated view of the respective zones a, b, c and d; (ii). Pathology mask; (iii). Raw terahertz image at 550-GHz; (iv). Refractive index map at 550-GHz.

Figure 12 .

 12 Figure 12. TS#2 tissue sample classification maps at 550-GHz for Λ 0 , Λ 1 , Λ 2 , Λ 3 and their respective first two best thresholds. "Not applicable" refers to regions where the binary pathology classification and the binary terahertz classification image do not match spatially. The values listed in each box are respectively standing for the refractive index threshold, the true positive rate and the false positive rate.

18 Figure 13 .Figure 14 .

 181314 Figure 13. Sample TS#3. (i). Pathology image and correlated view of the respective zones a, b, c and d; (ii). Pathology mask; (iii). Raw terahertz image at 550-GHz; (iv). Refractive index map at 550-GHz.

Table 1 .

 1 Statistical measure of the performance of the classifiers and AUC. The sensitivity and specificity obtained for the best performing classifier -refractive index threshold association is given in bold.

	Classifier	Λ 0		Λ 1		Λ 2		Λ 3
	AUC	0.7804	0.8149	0.8285	0.8360
	RI-Threshold	2.1	2.2	2.4	2.3	2.5	2.4	2.6	2.5
	TPR -FPR	0.4540 0.4181 0.5227 0.4829 0.5759 0.5093 0.6068 0.5433
	Sensitivity-%	83	62	72	84	76	86	79	86
	Specificity-%	62	79	81	65	81	65	82	69
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Table 2 .

 2 Statistical measure of the performance of the classifiers and AUC. The sensitivity and specificity obtained for the best performing classifier -refractive index threshold association is given in bold.

	Classifier	Λ 0		Λ 1		Λ 2		Λ 3
	AUC	0.6976	0.7307	0.7264	0.7127
	RI-Threshold	1.9	1.8	2.1	2.0	2.1	2.2	2.1	2.2
	TPR -FPR	0.3013 0.3006 0.3395 0.3307 0.3697 0.3113 0.3480 0.3295
	Sensitivity-%	62	76	54	69	67	51	78	62
	Specificity-%	68	54	80	64	70	80	57	71

Acknowledgements

The authors acknowledge the German Research Foundation for funding this work as a part of the Priority Program ESSENCE (SPP 1857). The authors gratefully acknowledge partial financial support for this work from the French Nouvelle-Aquitaine Region. The authors would like to acknowledge Jean-Baptiste Perraud and Dominika Warmowska for fruitful discussions.

the sensitivity, despite a concomitant loss in specificity. The corresponding classification images for TS#3 for each classifier and the correlated best refractive index threshold are demonstrated in Figure 15. The global classification clearly suffers from the spatial discrepancies between the fresh state tissue and the histological state. Even though such differences are expected to be the main roots behind classification accuracy weakness, the histological type of TS#3 may also trigger difficulties. It can be assumed that the classification strategy may provide better performances when applied on ductal carcinoma cases than on lobular ones. However, it is noted that the number of samples investigated does not allow to assert such a hypothesis.

Conclusions

In this paper, a new approach to support breast carcinoma margin delineation during surgeries with terahertz radiations was proposed. The method relies on the acquisition of the excised samples by means of a terahertz time-domain imager followed by a segmentation based on the extracted refractive index map at 550-GHz and its morphological dilation. Morphological dilation was introduced to overcome the weakness of the refractive index alone as a classifier in tissue regions sparsely populated with cancer cells. Dilation was used to construct a zone of influence of pixels. Hence, tissue areas close to regions identified as malignant were succesfully classified as cancerous despite a refractive index suggesting benign zones.

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The performances of the classifications were assessed for three different samples. Overall, the association of a high refractive index threshold with a wide dilation has shown to be the most appropriate combination to maintain both method sensitivity and specificity at decent levels for invasive ductal carcinoma. The best performances of the methods have been reported to stand by about 80% in sensitivity and 82% in specificity. On the contrary, the same methodology applied onto an invasive lobular carcinoma showed lower performances. Various hypothesis were drawn to determine the roots for classification failure. While lobular carcinoma are globally less populated by cancer cells than the ductal histology type, pathology image alterations may also have contribute by rendering the diagnosis evaluation tedious.

The recognition performances of malignant areas could be improved. Indeed, the terahertz classification has localized false negatives surrounded by true positives. Therefore, implementing an additional and simple processing that classifies as malignant, benign-predicted pixels that are encircled by cancerous ones would enhance the classification accuracy.

Although investigations on higher rank classifier, i.e. for Λ n with n > 3, have not been conducted, a more efficient structuring element could be found. Nevertheless, a high rank for a structuring element is accompanied by an equally high refractive index threshold. Thus, a reasonable assumption would be that the refractive index suitable for the use of these higher-ranked classifiers lies beyond the optical properties of biological tissues.

This preliminary investigation towards terahertz refractive index-based morphological dilation may open the routes to refine strategies to improve the accuracy with which breast tumour margins are delineated. However, the field still stands in its early stages and suffers challenges due to pathology reference image alterations that complicate classification correctness assessment. Additionally, performance comparison with other classification algorithms are yet to be investigated and will be needed to pursue with the proposed methodology. Finally, and in authors's opinion, the applicability of terahertz waves for breast carcinoma margin demarcation still requires further studies to evaluate its feasibility in the clinical environment.

Methods

Numerical procedures were conducted with in-house software, written with the MatLab development framework. The software follows mathematical procedures described in this paper and our preceding works.

Author contributions statement

Additional information

Competing interests: the authors declare no conflict of interests.