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Research report
Fronto-limbic dysfunction in borderline personality disorder: A 18F-FDGpositron emission tomography study
José Salavert a,b,⁎, Miquel Gasol a, Eduard Vieta c,⁎, Ana Cervantes a,Carlos Trampal d, Juan Domingo Gispert d,e
a Borderline Personality Disorder Institute, Psychiatry Department, Capio Hospital General de Catalunya, Sant Cugat del Vallès, Barcelona, Spainb Psychiatry Department, Hospital San Rafael, H Univ Vall d'Hebron, Barcelona, Spainc Bipolar Disorders Program, Hospital Clinic, University of Barcelona, IDIBAPS, CIBERSAM, Barcelona, Spaind Institute of Advanced Technology, Barcelona Biomedical Research Park, Spaine Networking Biomedical Research Center in Bioengineering, Biomaterials and Nanomedicine (CIBER-BBN), Spain
a r t i c l e i n f o
⁎ Corresponding authors. Vieta is to be contactedProgram, Clinical Institute of Neuroscience, UniversBarcelona, CIBERSAM, Villarroel, 170, 08036-Barcelon2275401; fax: +34 932275795. Salavert, PsychiatrySan Rafael, Hosp Univ Vall d'Hebron, Psg. Vall d'HeBarcelona, Spain. Tel.: +34 93 2112508; fax: +34 93
Article history:Received 24 October 2010Received in revised form 8 January 2011Accepted 8 January 2011Available online 26 January 2011
Introduction: Several functional neuroimaging studies have demonstrated abnormalities infronto-limbic pathways when comparing borderline personality disorder (BPD) patients withcontrols. The present study aimed to evaluate regional cerebral metabolism in euthymic BPDpatients with similarmeasured impulsivity levels bymeans of 18F-FDG PET during resting stateand to compare them against a control group.Methods: The present study evaluates regional cerebral metabolism in 8 euthymic BPD patientswith 18F-FDG PET during resting state as compared to 8 controls with similar socio-geographiccharacteristics.Results: BPD patients presented a marked hypo-metabolism in frontal lobe and showed hyper-metabolism in motor cortex (paracentral lobules and post-central cortex), medial and anteriorcingulus, occipital lobe, temporal pole, left superior parietal gyrus and right superior frontalgyrus. No significant differences appeared in basal ganglia or thalamus.Conclusions: Results reveal a dysfunction in patients' frontolimbic network during rest andprovide further evidence for the importance of these regions in relation to BPD symptomatology.
Studies up to the date suggest that Borderline PersonalityDisorder (BPD) has a biological and psychosocial basis.According to neurobiological factors underlying BPD, differ-ent neuroimaging studies have shown specific structural and
functional abnormalities when comparing BPD patients withcontrols.
Structural imaging studies show predominantly smalleramygdala (more frequently in impulsive–aggressive BPDpatients) and hippocampal volumes in adult patients withBPD (Brambilla et al., 2004; Schmahl et al., 2003; Zetzscheet al., 2007). Many studies in Post Traumatic Stress Disorder(PTSD) also report reduced hippocampal volume in thosepatients, but the reduction of amygdalar volume seems todifferentiate BPD patients from those affected by PTSD(Schmahl and Bremner, 2006). A reduced volume of theanterior cingulate cortex (ACC) has been reported as well(Brambilla et al., 2004; Hazlett et al., 2005; Minzenberg et al.,2007; Whittle et al., 2009).
Functional imaging studies' most consistent finding whenstudying brain metabolism at baseline has been of an altered
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metabolic activity (hyper or hypoactivation compared tocontrols) in the frontal region, particularly the medial frontalarea (Broadman areas (BA) 24, 32 and 33) which includespart of the cingulate (ACC; BA 24) and the dorsolateralprefrontal cortex (BA 9, 10 and 46) and ventromedialprefrontal cortex (VMPF) (including medial orbitofrontalcortex (OFC) and subgenual cortex) (De La Fuente et al., 1997;Soloff et al., 2003; Juengling et al., 2003; Lange et al., 2005;Goethals et al., 2005). Furthermore, studies using experi-mental paradigms that employ tasks involving the regulationof emotion by including the presentation of emotionalstimuli, exposure to autobiographical memories or the useof cognitive-emotional Stroop tasks, highlight the importanceof functional disconnection within limbic-frontal circuitryduring emotion regulation (principally negative emotion) inBPD (Donegan et al., 2003; New et al., 2007; Silbersweig et al.,2007; Koenigsberg et al., 2009). These studies point outdifferent cerebral structures responsible for cortico-limbicdysfunction in BPD but basically show orbital frontal cortex(OFC) including ventromedial prefrontal cortex (VMPF) to bedysfunctional (hypoactive) during cognitive-emotional tasks.Moreover BPD patients studied, also exhibit a higheramygdala reactivity under emotionally negative stimulationand different ACC activation patterns under cognitive-emotional tasks when compared to controls (Donegan et al.,2003; Minzenberg et al., 2007; New et al., 2007; Silbersweiget al., 2007; Buchheim et al., 2008; Koenigsberg et al., 2009).All the above mentioned abnormalities seem to take place infronto-limbic pathways, known to be associated with theexpression and control of two of the main behavioraldimensions of BPD: emotional dysregulation and aggressiveimpulsivity (American Psychiatric Association, 2001).
Some of the main caveats of neuroimage studies in BPDup to the date which may lead to different findings of hyperand hypoactivation of the same anatomical areas in thesetype of studies are: 1) small sample sizes; 2) the inclusion ofdifferent subtypes of BPD (predominantly impulsive versuspredominantly anxious, with or without PTSD comorbidity,with or without dissociative or psychotic-like symptoms);3) neurofunctional influence by ongoing pharmacologicaland psychotherapeutic treatments; 4) differences in genderhomogeneity; 5) differences in clinical homogeneity; 6) im-portant methodological differences between studies and theuse of not satisfactory statistical analyses and finally 7) arelative lack of neuroimaging studies in BPD population.
The present study aimed to evaluate regional cerebralmetabolism in euthymic BPD patients with similar measuredlevels of impulsivity by means of 18F-FDG Positron EmissionTomography (PET) during resting state, and to compare themagainst a control group with similar socio-geographiccharacteristics. The study pretends to contribute to existingliterature on brain metabolism in BPD patients under restingconditions since there is no previously published study of thistype in Spanish population. Based on previously exposedfindings, in the present study functional differences in fronto-limbic network between patients and controls were pre-dicted, as the basic neural mechanism responsible fordysregulated emotion in BPD. No specific frontal-limbicregions were hypothesized to be altered but we did expectan effect in prefrontal cortex, anterior cingulate (ACC) andamygdala as regions of interest.
2. Method
2.1. Subjects
A total of 16 participants were included in this study (8BPD outpatients and 8 healthy controls). Patients wereselected from those attending follow-up sessions at theBorderline Personality Disorder Institute in Capio-HospitalGeneral de Catalunya, after being included in the Institute'streatment program and showing: a) positive BPD diagnosisaccording to DIB-R (scaled score ≥8) and SCID-II assessment,b) score ≤15 on the Beck Depression Inventory (BDI);c) score ≤20 on state anxiety of the State-Trait AnxietyInventory (STAI); d) absence of substance abuse in theprevious 2 months as determined by means of weekly urinetoxicology screenings for drugs of abuse; e) absence ofcurrent anorexia; and f) free of psychotropic medication for1 month at the moment of evaluation. Controls wererecruited from volunteer control samples collected by theInstitute of Advanced Technology–Barcelona BiomedicalResearch Park for neuroimage studies. Those included in thehealthy control sample a) reported no current or pastpsychiatric disorder after a complete screening for axis Iand II disorders b) were not currently taking any psychotropicmedication nor c) taking substances of abuse, undertakingone urine toxicology screen for drugs of abuse prior to the PETstudy.
All of the 16 participants were right-handed.
2.2. Procedure
Patients included in this study received a first diagnosis ofBPD when included in a treatment and follow-up program. Atthe moment of their inclusion in the study all patients hadbeen in the follow-up program for at least 1 month. A seconddiagnosis was obtained from an external and experiencedpsychiatrist at the moment of inclusion in the study. First andsecond diagnoses were based on the assessment of BPD usingSCID-II and DIB-R, carried out by two trained independentraters. Interrater reliability for BPD diagnosis was 1.00 usingboth interviews. The inclusion of patients in the study wassubject to BPD diagnostic coincidence. Patients were alsoassessed on their mood and anxiety by means of the BDI andthe STAI (state anxiety score).
Control subjects were screened by means of the MINIInternational Neuropsychiatric Interview (MINI) to rule outaxis I disorders. They were included in the study only if nopast history of, or current psychopathology was detected. Thestudy was carried out in accordance with the current (2004)version of the Declaration of Helsinki. The study protocol wasreviewed by the Capio Hospital General de Catalunya ethicalcommittee and written informed consent of the participantswas obtained after the nature of the procedures had beenfully explained.
2.3. Instruments
BPD diagnosis in the patient group was assessed using theSpanish validated versions of the Structural Clinical InterviewDiagnosis (SCID) II schedule for personality disorders(Gómez-Beneyto et al., 1994) and DIB-R (Barrachina et al.,
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2004). The first one is a validated version of the originalsemistructured interview diagnostic of the 11 possiblepersonality disorders according to DSM-III-R (Williamset al., 1992); and the latter is a validated version of theoriginal semistructured interview made up of 125 items usedto determine the diagnosis and severity of BPD patients(Zanarini et al., 1990).
Patients' emotional state was measured by means of theSpanish versions of the BDI (Conde and Useros, 1975), andthe STAI's state anxiety score (Spielberger et al., 1986). Theformer is a validated version of the original 21-item BDI (Becket al., 1988), and the latter of the original 21-item STAI(Spielberger et al., 1970).
Impulsivity in all patients was assessed using the Spanishversions of the Barratt Impulsivity Scale (BIS-11) (Oquendoet al., 2001b) and the Sensation Seeking Scale— Form V (SSS-FV) (Pérez and Torrubia, 1986).
Finally, patients' trait aggression was measured by meansof the Spanish version of the Buss-Durkee Hostility Inventory(BDHI) (Oquendo et al., 2001a).
Healthy controls were screened using the Spanish versionof the MINI International Neuropsychiatric Interview (MINI)for axis I disorders (Ferrando et al., 1997) and the SalamancaQuestionnaire for Personality Disorders (Pérez Urdániz et al.)for axis II disorders. The first is a widely used short structureddiagnostic interview for DSM-IV and ICD-10 psychiatricdisorders with an administration time of approximately15 min. The second is a screening instrument recentlydeveloped in Spain for the detection of 11 personalitydisorders according to DSM-IV-TR and ICD-10 criteria. Eachdisorder is evaluated with 2 questions with four answerpossibilities (false = 0 points; sometimes true = 1 point;frequently true = 2 points; always true = 3 points). Theestablished cut-off point for each disorder is 2/3. Thisinstrument is available in Spanish in http://www.iqb.es/diccio/t/test_personalidad.pdf.
2.4. Image acquisition
Images were acquired in a PET tomograph (Siemens ECATEXACT HR+) 45 min after the injection of approximately370 MBq of 18F-FDG during 20 min. Participants received noother special instructions, except to try to remain as relaxedas possible. PET study was performed after a fasting period ofover 6 h. Smoking, coffee or psychoactive beverages wereforbidden before the PET study. Prior to the acquisition of theemission scans, a 10-minute transmission scan was per-formed using three retractable line sources of Ge-68. Thetransmission scan was used to correct the degrading artefactsof attenuation and scatter and images were reconstructedwith a filtered back-projection algorithm using a Hann filterwith a cut-off frequency of 4.9 mm. Reconstructed imageshad a resolution of approximately 4.0 mm FWHM, a matrixsize of 128×128×63 and voxel size of 2.57×2.57×2.43 mm.
2.5. Image analysis
To enable voxel-by-voxel comparisons, images were spa-tially normalized using the routines provided with the SPM2software package (www.fil.ion.ucl.ac.uk/spm) and smoothedusing a Gaussian kernel of 12 mmFWHM. Tracer activity values
were proportionally normalized to the global activity of eachPET, thus representing relative metabolic activity.
After images had been pre-processed, two independentanalyses were carried out. First, mean images for each groupwere calculated and subtracted, thus representing relativebetween-groups differences of metabolic activity.
Besides, PET images were statistically analyzed voxel-by-voxel with the SPM2 software package using an intensitythreshold of 0.8, i.e. only voxelswithan intensity level above0.8of the mean level for that scan were included in the statisticalanalysis. Differences between groups were assessed by one-tailed t-tests, without including covariate effects such as age orsex, previously determined as non-significant. Statisticalsignificance threshold was set to uncorrected p-values ofpb0.001 and extent threshold to 10 (i.e., only clusters withmore than 10 voxels are taken into consideration). Survivingvoxels were overlaid on an MR template to improve theanatomical localization of the activations.
2.6. Socio-demographic and clinical variable analyses
Comparisons between groups in socio-demographic vari-ables were computed by means of Student's t-test, Mann-Whitney U-test or chi-square, as appropriate.
3. Results
Patients and controls were not different in mean age(mean=35.5, SD=9.27, range [22–47] for patients, andmean=32, SD=7.86, range [21–46] for controls; t=0.815,pN0.1) and gender distribution (females were 75% in thepatients group and 62.5% in the controls; χ²(1)=0.291,pN0.1) (see Table 1).
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Patients showed a median score of 10.5 (range 7–15) onthe BDI, and of 13,125 (range 10–20) on the STAI state anxietyscore. Patients median score for aggression (BDHI) was 44.6(range 35–57), and fore impulsivity measures of 51.1 (range36–67) on the BIS-11 and 25 (range 10–35) on the SSS-FV.
When comparing the clinical scores in the patient's groupbetween males (n=2) and females (n=6), there were nosignificant differences according to gender in any of the scalesanalysed: BDI (U=3, pN0.1), STAI state anxiety score (U=6,pN0.1), BDHI (U=6, pN0.1), BIS-11(U=3, pN0.1), SSS-FV(U=4, pN0.1).
Looking at metabolic differences between patients andcontrols descriptively as a percentage of global activity (Fig. 1),BPD patients presented a marked hypometabolism in thefrontal lobe, posterior cingulated cortex, precuneus, marginalcortex and middle and inferior temporal areas. Patientsshowed hyper-metabolism in the motor cortex and para-central lobules (superior frontal lobe), cerebellum,medial andanterior cingulus, superior parietal lobe, superior temporalcortex, occipital lobe, temporal pole and amygdala. Nomarkeddifferences appear in the basal ganglia or thalamus. Betweengroup differences presented a symmetrical pattern.
Results of the SPM voxel-by-voxel analysis of the PETimages showed two statistically significant areas of hypome-
Fig. 1. Metabolic differences between patients (BPD) and con
tabolism and five areas of hypermetabolism. These arepresented separately for the hypo- and hyper-metabolicareas in Table 2 and Fig. 2. The labeling of the macroscopicalactivated areas follows the atlas described at Tzourio-Mazoyer et al. (2002). Hypometabolic areas correspond tomiddle frontal right gyrus and middle frontal left gyrus,orbital part. Hypermetabolic areas correspond to left middleoccipital gyrus, right superior frontal gyrus, left cuneus, leftsuperior parietal gyrus and left lingual gyrus.
4. Discussion
Our results reveal that frontal brain regions such as theorbitofrontal cortex (OFC) responsible for emotional execu-tive functioning and dorsolateral prefrontal cortex (DLPFC),principally involved in cognitive executive functioning, showa lower metabolic activity at rest compared to controls in thegroup of BPD patients studied. This is in accordance withresults reported by other groups (De La Fuente et al., 1997;Soloff et al., 2003) and is interesting because these frontalregions are known to be recruited during emotional self-regulation and are related to amygdala's reactivity modula-tion (Kim et al., 2003; Phan et al., 2005; Urry et al., 2006;Schmitz and Johnson, 2007). It is also important to consider
trols (Ctrl) expressed as percentage of global activity.
Table 2Statistically significant (pb0.001) between-group differences for the contrasts (CtrlNBPD and CtrlbBPD). Ctrl=controls; BPD=borderline personality disorder.
Cluster level Voxel level x, y, z (mm)
Cluster # # of Voxels P unc. p-PWE p-FDR T Ze P unc
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that dysfunction of prefrontal cortex, including anteriorcingulus (ACC), seems to be correlated along with hippo-campus, with abnormal functioning of the memory system inBPD patients, with poorer performance in retrieval tasks thancontrols only in relation to traumatic or emotionallysignificant memories (Schmahl et al., 2004; Sala et al., 2009;Mensebach et al., 2009). This supports the impact of earlytraumatic experiences in the developing nervous system andits relation to limitations in memory control in individualswith BPD.
No statistically significant differences were observedbetween groups in amygdala activation taking into accountthat brain metabolism was studied at baseline. New et al.(2009), found that BPD patients with impulsive aggressionincreased relative glucose metabolic rate (rGMR) in OFC andamygdala when provoked, whereas they found decreasedrGMR in anterior, medial, and dorsolateral prefrontal regions.A previous study by the same group (New et al., 2007)deepened in the implication of the amygdala in aggressivebehaviour. Moreover, other authors (Soloff et al., 2003)concluded that decreased glucose uptake in medial orbitalfrontal cortexmight be associatedwith diminished regulationof impulsive behavior in BPD. Under the light of these reports,our finding of decreased FDG uptake in the frontal areas ofBPD patients could be attributed to a higher impulsivebehaviour than controls. However, no noticeable differenceswere found in the amygdala in our sample which wouldindicate that patients were not experiencing aggressivenessduring 18F-FDG uptake, which is consistent with the fact thatall the subjects in the study were asked to relax. This mighthave not been the case should the patients have been exposedto provoking stimuli or asked to recall negative moments intheir life during the uptake period.
The present results revealed increased metabolism inanterior cingulus (ACC) and as reported by Juengling et al.(2003). ACC is another specific frontal brain region engagedin affective-emotional control, primarily regulating autonom-ic and neuroendocrine aspects and pain processes and adysfunction in this region could be related to BPD'scharacteristic affective dysregulation (Schmahl and Bremner,2006) and could also be concordant with pathologicalantinociceptive processes in BPD patients (Juengling et al.,2003). Right superior frontal gyrus has been related withhumour appreciation, affect-laden autobiographical episodic
memory and together with fusiform gyrus involved in facialexpression recognition (Fink et al., 1996; Stuss et al., 1999;Keenan et al., 1999; Shammi and Stuss, 1999).
Interestingly, our finding of increased activation in leftprimary visual processing areas (lingual gyrus, cuneus andmiddle occipital gyrus) is in accordance to Koenigsberg et al.findings (2009) and gives support to this group's proposal ofvisual hyperawereness towards affective stimuli which maybe invisible to others in the case of BPD patients. Hyperme-tabolism observed in left lingual gyrus is specially of interestbecause this region not only plays a role in visual processing,would be involved along with other brain regions in acontinuous matching process between internal representa-tions of the environment and external reality; moreover it hasalso been suggested to be part of a network involved in socialdecision making (Schmidt et al., 2007; Rilling et al., 2008).This could be linked to BPD patient's unstable sense of selfand their patterns of markedly unstable relations.
We didn't replicate the findings of De La Fuente et al.(1997) of decreased metabolism in the basal ganglia andthalamus in agreement with the investigation of Juenglinget al. (2003). Hypometabolism of the basal ganglia reportedby De La Fuente et al. (1997) has been observed in affectivedisorders, anxiety disorders and alcohol use disorders andmay be mediated by BPD's high comorbidity with these Axis Idisorders.
Left superior parietal gyrus including post-central cortexand superior temporal cortex, which showed hyperactivationin BPD patients in the present study, have also been shown toplay a general role in executive functioning along withprefrontal cortex (Collette et al., 2005) and interestingly,increased size of this region has recently been related todissociative symptoms in BPD patients in the presence ofchildhood abuse (Irle et al., 2007).
It is also worth mentioning our finding of hypoactivation inposterior cingulus and precuneus, both structureswith a role inthe ability to attribute mental states to oneself and others andinterpret correctly other people's minds along with medialprefrontal cortex regions (den Ouden et al., 2005); cognitiveability in which BPD patients show difficulties.
Finally, we will point out the finding of BPD patient'shyperactivation in cerebellum. This is interesting because thetraditional belief that this structure is exclusively involved inmotor control has been definitively surpassed. We actually
Fig. 2. Statistically significant areas of hypometabolism (CtrlNBPD) and hypermetabolism (CtrlbBPD) in the SPM voxel-by-voxel analysis of the PET images.Hypometabolic areas: middle frontal right gyrus (Cluster #1) and middle frontal left gyrus, orbital part (Cluster #2). Hypermetabolic areas: left middle occipitalgyrus (Cluster #3), right superior frontal gyrus (Cluster #4), left cuneus (Cluster #5), left superior parietal gyrus (Cluster #6) and left lingual gyrus (Cluster #7).
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know that cerebellum is implied in cognitive functions suchas executive function and language and in affective functionssuch as emotional regulation (Schmahmann and Caplan,2006; Chen and Desmond, 2005; Schmahmann and Sherman,1998).
As hypothesized a dysfunction in the patients frontolimbicnetwork is shown in the present study at baseline conditions(significantly for DLPFC and OFC and tending to significance forACC and amygdala). This provides further evidence for theimportanceof these regions in relation toBPDsymptomatology,reflecting a vulnerability to affective instability and emotiondysregulation in BPDpatients. The significance of otherfindingsdiscussed in the paper remains unclear and more researchis needed in order to clarify a possible relation with BPDpsychopathology.
One of the major caveats of the present paper is therelatively small sample size, since only 8 patients wereincluded in each group. Another limitation is that psycho-pharmacological and psychotherapeutic treatments can insome extent change regional cerebral functioning in differentpsychiatric conditions but studying BPD patients withouttreatment can be extremely difficult and raise ethical issuesdue to these patients natural predisposition to self-harm andto attempt suicide on a frequent basis. In addition, recentneuroimage studies with very small patient samples haveshown changes in relevant neural systems for BPD afterpsychotherapeutic treatment with valid psychological ther-apies for this disorder such as dialectic-behavioral-therapy(DBT) and psychodynamic psychotherapy (Schnell andHerpertz, 2007; Lai et al., 2007). However, although treat-ment cannot definitively be excluded as having influencedour findings, both pharmacological and psychotherapeutictreatments tend to improve the neurofunctional deficitsobserved in the study, so the fact that with a small sampleit is still possible to find significant differences and cleartendencies to significance in relation to controls in the senseof the established hypothesis, even under treatment, lendscredence to the effects found. Regarding generalizability ofour findings, the presence of active depressive or anxiousstates in the patient's group would have interfered in theevaluation of personality traits or dimensions of emotionaldysregulation affecting generalizability in a small sample asthe one analyzed, so we were interested in obtaining ahomogeneous sample, ruling out active Axis I affective andanxiety disorders (highly comorbid with BPD) so that thefindings were related to affective cluster personality traitscharacteristic of these patients (affective instability, inappro-priate intense anger, feelings of emptiness, etc.). On the onehand, the observed 18F-FDG uptake differences betweencontrols and BPD patients can arise from several factors orcombination of factors such as impulsivity, aggressiveness orgender. However, given the relatively low sample size (N=8)in our study and the predominance of females (6 females, 2males), it was not feasible for us to directly assess the impactof such factors in our findings. Soloff et al. (2005) found thatmale BPD subjects showed areas of increased glucoseutilization in large areas of parietal and occipital cortex,bilaterally. In response to fenfluramine (relative to placebo),significant decreases in glucose uptake were found in maleBPD subjects, centered in the left temporal lobe. Theseglucose changes did not occur in female patients. Moreover,
female, but not male, control subjects showed significantlydecreased uptake in areas of right frontal and temporalcortex. In our study, the most noticeable difference in glucoseutilization between BPD patients and controls is a markeddecrease in the right frontal cortex, which would be inagreement with the preponderance of females in our sample(6 to 2). However, we also observed increased glucose uptakein the bilateral parietal and occipital cortices of the patients.On the other hand, one open question from these type ofstudies is if there are BPD subgroups regarding baselineprefrontal metabolism (e.g. predominantly impulsive vs.predominantly anxious borderline patients) and althoughBDI, STAI, BIS-11, SSS-FV and BDHI scores were assessed, thusconsidering important clinical factors such as impulsivity andemotional state at the time of evaluation, the current studycannot address this question because of the small sample sizewhich does not allow us to calculate correlations betweenthese measures.
In summary, this study shows that BPD patients may havea frontolimbic network dysfunction characterized by amarked hypo-metabolism in frontal lobe and hyper-metab-olism in motor cortex (paracentral lobules and post-centralcortex), medial and anterior cingulus, occipital lobe, temporalpole, left superior parietal gyrus and right superior frontalgyrus. These findings may explain some of the features ofBPD.
Role of funding sourceNone.
Conflict of interestNone to declare as regards to this work.
Acknowledgements
None.
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