R Guérout

M Aymar

O Dulieu

The ground state of the polar alkali-Strontium molecules: potential energy curve and permanent dipole moment

In this study, we investigate the structure of the polar alkali-Strontium diatomic molecules as possible candidates for the realization of samples of new species of ultracold polar molecules. Using a quantum chemistry approach based on Effective Core Potentials and Core Polarization Potentials, we model these systems as effective three valence electron systems, allowing for calculation of electronic properties with Full Configuration Interaction. The potential curve and the permanent dipole moment of the 2 Σ + ground state are determined as functions of the internuclear distances for LiSr, NaSr, KSr, RbSr, and CsSr molecules. These molecules are found to exhibit a significant permanent dipole moment, though smaller than those of the alkali-Rb molecules.

I. INTRODUCTION

The prospects of the realization of quantum degenerate gases composed of polar systems, i.e. exhibiting a permanent dipole moment, either magnetic or electric, are among the most fascinating ones in the context of researches on ultracold matter [1], related to many-body physics, quantum information, or quantum simulators of solid state physics. Indeed, neutral particles usually weakly interact via van der Waals short-range potentials varying with their mutual distance R as R -6 , which has been a key condition for the observation of Bose-Einstein condensation in weakly interacting gases of ultracold alkali atoms [2][3][4]. In contrast, particles with a permanent dipole moment interact through a long-range dipole-dipole potential varying as R -3 which dominates the van der Waals interaction. Ultracold gases of such particles are predicted to evolve in a entirely new regime of strong interactions with pronounced anisotropy. For instance, the Chromium atom has a large magnetic dipole moment of about 6µ B , and once condensed [5,6], the manifestation of anisotropic interactions has been observed experimentally [7,8]. Ground state polar molecules, having permanent dipole moment (in the body-fixed frame) ranging between a few tenths of a Debye like LiNa or KRb, up to several Debye like LiCs [START_REF] Aymar | sets[END_REF] are actually strongly interacting with larger forces than in the Chromium case, and are expected to be better candidates for studying strongly interacting degenerate gases. Up to now, several attempts to observe ultracold ground state polar molecules have been successful with bialkali molecules, namely KRb [10,11], LiCs [12], NaCs [13], RbCs [14]. However the achievement of quantum degeneracy of ultracold molecules is conditioned by the phase space density of molecules in a unique quantum state, preferably the absolute ground state, defined not only by their vibrational and rotational quantum numbers, but also by their hyperfine structure [15][16][17].

As the number of atomic species other than alkalis, which are laser-cooled and subsequently brought to quantum degeneracy is continuously increasing, the formation of novel species of polar molecules will soon be investigated in the ultracold regime [18]. For instance, photoassociation (PA) of Yb 2 [19,20] and YbRb [21] molecules has already been reported, while quantum degeneracy in Ytterbium [22,23], Calcium [24], and Strontium [25,26] atomic gases have recently been obtained. In the present paper, we investigate theoretically the structure of diatomic molecules composed of one Strontium atom and one alkali atom (Li, Na, K, Rb, Cs), for the first time for most of these species. In the following, we will refer to them as ASr molecules. In particular, we determined the permanent dipole moment of their ground state in order to provide guidance to the experimentalists to choose the appropriate combination of atomic species. In contrast with alkali dimers, such species also have a magnetic moment in the ground state due to their three valence electrons, which therefore makes them suitable for their manipulation with both electric and magnetic external fields. In Section II, we first recall our methodology based on quantum chemistry computations involving Effective Core Potentials (ECP), reducing the problem to an effective three valence electron system, for which Full Configuration Interaction can be achieved. Molecular potential curves and permanent dipole moments for the LiSr, NaSr, KSr, RbSr, and CsSr molecules in their electronic ground state are presented in Sections III and IV, emphasizing on the dipolar character of these molecules compared to bialkali molecules.

II. METHOD OF CALCULATION

We use the Configuration Interaction by Perturbation of a multi-configuration wave function Selected Iteratively (CIPSI) set of programs developed at the Université Paul Sabatier in Toulouse (France). The CIPSI package incorporates both the use of Effective Core Potentials (ECP) [27,28], and ℓ-dependent Core Polarization Potentials (CPP) [29,30]. Effective core potentials model the effect of inner shells electrons into a semi-empirical potential thus reducing the number of active electrons on each atom, namely one for the alkali atom, and two for the Strontium atom. Core polarization potentials embody the polarization effects of these effective cores with the valence ones. Thanks to the reduced number of active electrons, it becomes possible to perform a Full Configuration Interaction (FCI) in the valence space. This gives us a number of excited molecular states in addition to the lowest state in each symmetry. This method has proven to be efficient and accurate for alkali diatomics which are treated as two-electrons system [START_REF] Aymar | sets[END_REF]31], and we modified the CIPSI package accordingly for effective three-electron systems.

Effective core potentials are from ref. [32]. For the strontium atom, we use the socalled "large core" ECP for the 36 electrons of the Sr 2+ core, and basis sets composed of uncontracted Gaussian functions. The basis sets for alkali atoms are taken from ref. [START_REF] Aymar | sets[END_REF], where f gaussian have been removed to reduce the size of the configuration space. We checked on the alkali atoms that this has no influence on the lowest energy levels we are interested in here. The basis set for the strontium atom is taken from [33]. We actually used two slightly different basis sets: we first designed sets for ASr + ions, i.e. 8s7p4d for Lithium, 7s6p5d for Sodium, 7s5p7d for Potassium, 7s4p5d for Rubidium, 7s4p5d for Cesium, and 7s6p7d for Strontium ion whose exponents are reported in Table I. These results will be discussed in a separate publication. For the neutral systems ASr, we reduced the Sr + set by a few orbitals down to 5s5p6d, due to size constraints. The influence on the atomic energy levels remains small as it can be seen below.

In total, the number of configurations for the diatomic calculations is larger than 10 5 , and depends on the molecular symmetries. We use a recently modified version of the ℓ-dependent core polarization potential initially proposed by Foucrault et al. [30], which yields the correct asymptotic behavior of the potential energy at large internuclear distance [34], in contrast with most of the previous calculations performed on alkali dimers with this method. A set of cutoff radii, reported in Table II, are optimized to reproduce experimental values for the lowest s, p, and d atomic levels of the alkali atoms and of the strontium cation (Table III).

Polarizabilities for the relevant cores Li + , Na + , K + , Rb + , Cs + ,and Sr 2+ cores are taken from experimental and semi-empirical values of refs. [35,36].

Table III shows that such an optimization yields a satisfactory representation of the Strontium cation spectrum. The corresponding fitted levels of the alkali atoms are not reported here, as we are mainly interested into the lowest level of s, p, and d symmetry whose energies are represented exactly after the tuning of the cut-off radii of Table II.

Therefore the energies of a pair composed by one alkali atom and a Strontium cation in their lowest levels at infinite separations are well modeled here.

III. THE GROUND STATE POTENTIAL CURVE OF ALKALI-STRONTIUM

MOLECULES

As dissociation limits of ASr molecules involve a neutral alkali atom and a neutral Strontium atom, we first performed a first FCI calculation with the small and large basis sets and (b) the large basis set for Sr + (Table I), and their deviations ∆ E (in cm -1 ) from experiment [START_REF] Moore | Atomic energy levels[END_REF].

The ionization limit of Sr + is taken at 88965.18 cm -1 [42] to calculate the experimental binding energies in a.u.. We use the mass-corrected Rydberg constant 109736.63 cm -1 . The theoretical values of [41] have been spin-averaged.

involving two electrons, in order to calculate the lowest strontium energy levels. Results are given in Table IV, and are compared to experimental values. The differences range between less than 200 cm -1 for the ground state up to about 450 cm -1 for the lowest excited levels, as it was the case also for the Magnesium atom [37]. We note that such an accuracy is typical for this kind of calculations, as illustrated also by ECP+CPP FCI calculations on Calcium [38]. The use of the small basis set does not significantly affect the quality of the results.

We display in Figure 1(a) the potential energy curves (PEC) for the X 2 Σ + ground state of the ASr systems, relative to the same origin of energies fixed at the dissociation limit Ans+Sr(5s 2 1 S) for comparison purpose. The corresponding main spectroscopic constants are reported in Table V. The Strontium atom in its ground state is a closed-shell atom, so that the alkali-strontium molecules are expected to have a van der Waals character with a somewhat large equilibrium distance and weak binding energy, compared for instance I). The experimental values are averaged over fine structure energies when appropriate. We use the mass-corrected Rydberg constant 109736.63 cm -1 .

to alkali diatomics with comparable masses like alkali-rubidium molecules. This feature is clearly visible in the figure, as the typical binding energies are three to five times smaller than for the related A-Rb molecules. The equilibrium distances are also systematically larger for ASr than for ARb molecules, except for LiSr. The LiSr molecule is a bit peculiar, as its ground state is quite deep, with an equilibrium distance comparable to the LiRb one.

The potential depths of the ASr molecules immediately show that in ultracold conditions these molecules will not be stable against collisions between them, just like KRb molecules [43]. The reaction channel yielding a Sr 2 molecule and an alkali dimer is energetically open for all alkali species. Indeed, the Sr 2 well depth is about 1061 cm -1 [44], while those of the alkali dimers are 8517 cm -1 [45], 6022 cm -1 [46], 4451 cm -1 [47], 3993 cm -1 [48], 3649 cm -1

[49], for Li 2 , Na 2 , K 2 , Rb 2 , Cs 2 , respectively.

From the long range part of these curves we can estimate the coefficient C 6 of the leading term of the van der Waals interaction

IV. THE PERMANENT DIPOLE MOMENT OF ALKALI-STRONTIUM MOLECULES

As stated in the introduction, an important property of these molecules, in the perspective of cooling and trapping them at ultracold temperatures is the permanent dipole moment (PDM), which are drawn in Figure 1(b) and reported as well in Table V. The PDM for ground state ASr molecules is predicted to be noticeable, even if they do not reach such high values than those of the alkali dimers [START_REF] Aymar | sets[END_REF]. It is worthwhile to mention that the relation between the magnitude of the PDM and the difference in the mass (and then in the size) of the constituting atoms is inverted compared to alkali dimers: the PDM of LiCs and LiRb are the largest ones among all alkali pairs, while the PDM of LiSr is by far the smallest D e (cm -1 ) R e (a.u.) ω e (cm -1 ) B e (cm one compared to the other ASr species. This feature is amplified by the mismatch of the minimum of the PEC of LiSr and NaSr, and the maximum of the PDM curve, in contrast with the other species.

V. CONCLUSION

In this paper we investigate for the first time the electronic structure of the alkali-Strontium molecules with a quantum chemistry approach which accurately treat correlation between valence electron through a Full Configuration Interaction, while the correlation between valence and core electrons is accounted for through effective potentials. This approach has proven to be powerful for similar calculations on alkali dimers. The potential curve and the main spectroscopic constants, as well as the permanent dipole moment (PDM) of the 2 Σ + ground state have been determined for LiSr, NaSr, KSr, RbSr, and CsSr molecules.

Though their PDM is generally smaller than the alkali-Rb molecules, these systems are possible candidates for achieving a new kind of ultracold molecular sample with anisotropic interactions. Just like heteronuclear alkali dimers, ultracold molecules in their ground state can probably be created by photoassociation, and this will be the topic of a further study.

While completing this paper, Żuchowski, Aldegunde and Hutson informed us about their study about the structure of the RbSr ground state [51], using an all-electron quantum chemistry approach. Their results are in good agreement with ours. For instance, they obtained an equilibrium distance R e = 8.86 a.u., a well depth of about 1000 cm -1 , and a PDM done for Cs 2 [17,52]and KRb [15] molecules.

3

 3 P o -0.54765155 -0.548880 -269 -0.548899 -273 14702.6 14613 -87 14613 -88 5s4d 3 D e -0.53147099 -0.529868 351 -0.529907 343 18253.7 18779 533 18781 528 5s4d 1 D e -0.52283208 -0.520684 471 -0.520733 460 20149.7 20793 653 20795 645 5s5p 1 P o -0.51577530 -0.517756 -434 -0.517792 -442 21698.5 21447 -252 21440 -257 TABLE IV. Computed Strontium binding energies E b (in a.u. relative to the double threshold of Strontium) and excitation energies E e (in cm -1 ) compared to the experimental values of ref.[39] (E exp b and E exp e ), and their differences (δ b = E b -E exp b and δ e = E e -E exp e ) in cm -1 , resulting from a two-electron FCI calculation with (a) the large basis set, and (b) the small basis set for Sr + (Table

FIG. 1 .

 1 FIG. 1. (a) Potential energy curves and (b) permanent dipole moments (PDM) for the X 2 Σ + ground state of the ASr molecules (A=Li, Na, K, Rb, Sr). Vertical lines guide the eye to locate the value of the PDM at the equilibrium distance.

of 1 .

 1 36 D at R e (compared to our values R e = 8.69 a.u., D e = 1073 cm -1 , and d e = 1.54 D). The slight differences are probably due to the sensitivity of the results on the treatment of electron correlation, and further experiment should help to clarify the situation. In their paper, Żuchowski et al. demonstrated the existence of Feshbach resonances in RbSr. Therefore, our next study on excited states of these molecules should guide experimentalists to design ways for achieving adiabatic population transfer from molecules created by Feshbach association down to the lowest energy level of the molecule, just like it has been recently

TABLE II .

 II Optimized cutoff radii ρ ℓ (in atomic units a 0 ) and core polarizabilities α of the relevant ionic cores Li + , Na + , K + , Rb + , Cs +[35], Sr 2+[36] entering into the Core Polarization Potentials

		Li angular momentum	Li	Na	Na	K	K	Rb	Cs Rb	Sr + Cs	Sr +
		s	ρ s 1.4519565 1.450275 2.10816 2.5365 2.85585 2.13999 2.464 2.8357 0.9312 1.292561 0.328926 0.79174
		ρ p 1.013 1.6452591 1.9722 2.279 2.544 2.183 1.991 0.49318 0.2676 0.824992 0.241529 0.316178
		ρ d	0.6	1.5 0.582 0.072085 0.0427 0.234682 0.050502 0.066565 1.9405 2.5217 2.89815 1.706
				Li +	Na + 0.200 0.036061 0.03915 0.032072 0.029302 0.02699 K + Rb + Cs + Sr 2+
			α 0.1997	0.9987 0.070 0.016674 0.01448 0.013962 0.013282 0.013495 5.472 9.245 16.33 5.67
					0.031 0.00693 0.0055 0.00575 0.00528	0.009
					0.015 0.00287 0.0026 0.0025	0.003	0.003
					0.007
	(CPP).	p			0.630		0.431		0.133	0.128	0.1	0.225825
					0.240 0.09276 0.05128 0.040097 0.0405 0.095691
					0.098 0.03562 0.01642 0.014261 0.0162 0.042077
					0.043 0.01447 0.0052 0.00485 0.00443 0.018077
					0.020		0.0058 0.0022	0.0090385
					0.010 0.00023			0.005
					0.005
		d			0.180		0.292		1.255 0.408807 0.196894 3.618081
					0.080 0.06361 0.343 0.096036 0.067471 0.999656
				0.22796 0.02273 0.109 0.026807 0.027948 0.390735
				0.008574 0.008852 0.0294 0.009551 0.010712 0.12277
							0.00352 0.01013 0.004	0.003 0.036655
									0.0039	0.018327
									0.0018	0.009
		symmetry		LiSr		NaSr		KSr	RbSr	CsSr
		{Σ + , ∆ x 2 -y 2 }	129945 132792 161703 110337 110337
		Π	120032 123684 151478 102540 102540
		{Σ -, ∆ xy }	110240 114840 142138 95457	95457
							4

TABLE I .

 I Gaussian basis set exponents used to represent the effective one-electron systems of

	State Exp [39]	(a)	∆ E	(b)	∆ E	[40]	∆ E	[41]	∆ E
	5s -0.4053569 -0.405354 0 -0.405358 0 -0.405522 36 -0.40839 666
	4d -0.3382685 -0.338269 0 -0.338269 0 -0.338247 -4 -0.341908 799
	5p -0.2948674 -0.294868 0 -0.294869 0 -0.294854 -2 -0.29588 222
	6s -0.1878519 -0.187521 -73 -0.187544 -68 -0.187469 -84
	5d -0.1623282 -0.160856 -323 -0.160947 -303 -0.161237 -239
	6p -0.1503744 -0.150234 -31 -0.150237 -30 -0.150150 -49
	7s -0.1093568			-0.109138 -48
	6d -0.9758806			-0.096543 -230
	7p -0.921336			-0.091920 -46
	8s -0.7166203			-0.075047 -34

the present work, and resulting number of configurations representing the effective three-electron diatomic systems A-Sr (with A ≡ Li, Na, K, Rb, Cs) for the relevant molecular symmetries. The actual basis sets used for ASr neutral molecules include all exponents but the ones in italic, while the whole set has been used for ASr + systems. The three lowest lines provide the size of the hamiltonian for the Full Configuration Interaction. TABLE III. Binding energies (in a.u.) of Sr + levels obtained with (a) the small basis set, and

  -1 ) d e (Debye) d 0 (Debye)

	LiSr	2587	6.57	184.9	0.21	0.34	0.34
	NaSr	1597	7.22	85.4	0.063	0.62	0.63
	KSr	1166	8.33	52.4	0.032	1.52	1.50
	RbSr	1073	8.69	32.3	0.018	1.54	1.53
	CsSr	1084	9.06	33.8	0.013	1.91	1.91
	LiRb	13759	6.49	210		4.42
	NaRb	5076	6.82	107		3.41
	KRb	4199	7.63	76		0.62
	CsRb	3907	8.29		1.28

TABLE V .

 V Main spectroscopic constants for the lowest electronic states of the ASr molecules (A=Li, Na, K, Rb, Sr): well depth D e , equilibrium distance R e , harmonic constant ω

e , and rotational constant B e . The value of the dipole moment d e at the equilibrium distance, and averaged for the v = 0 level (d 0 ) are also reported. The well depth, equilibrium distance, and permanent dipole moment at equilibrium of the related ARb molecules are displayed for comparison, following our computations reported in Refs.

[START_REF] Aymar | sets[END_REF]31,50]

.

ACKNOWLEDGMENTS R.G. gratefully acknowledges support from Institut de Recherches sur les Atomes Froids (IFRAF). This work has been performed in the framework of the network "Quantum Gases of Dipolar Molecules" (QuDipMol) of the EUROQUAM program of the ESF.


Dr Edith Pomarol-Clotet

Erick Jorge Canales-Rodriguez

Raymond Salvador

Salvador Sarró

Jesús J Gomar

Fidel Vila

Jordi Ortiz-Gil

Yasser Iturria- Medina

Antoni Capdevila

Peter J Mckenna

Benito Menni

Medial prefrontal cortex pathology in schizophrenia as revealed by convergent findings from multimodal imaging

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche

Medial prefrontal cortex pathology in schizophrenia as revealed by convergent findings from multimodal imaging

Edith Pomarol-Clotet, Erick Canales Rodgriguez, Raymond Salvador, Salvador Sarro, Jesus Gomar, Fidel Vila, Jordi Ortiz-Gil, Yasser Iturria Among the many lines of investigation undertaken to characterise the brain pathology of schizophrenia, one of the most productive has been neuroimaging. Early studies using CT established beyond doubt that there is lateral ventricular enlargement in the disorder [START_REF] Van Horn | Ventricular enlargement in schizophrenia. A metaanalysis of studies of the ventricle:brain ratio (VBR)[END_REF] , and MRI studies have shown that this is coupled with a small degree of brain tissue volume reduction, of around 2% [START_REF] Wright | Meta-analysis of regional brain volumes in schizophrenia[END_REF] . MRI studies have also suggested that brain volume loss in schizophrenia, while widespread, is not homogeneous, but is instead most pronounced in medial temporal lobe structures [START_REF] Wright | Meta-analysis of regional brain volumes in schizophrenia[END_REF] and in the grey matter of the superior temporal cortex [START_REF] Mccarley | MRI anatomy of schizophrenia[END_REF] . Recent studies using voxel-based morphometry (VBM), which identifies clusters of difference between groups of subjects in an unbiased way without the necessity of preselecting regions of interest, have confirmed that cortical grey matter volume reductions are prominent in parts of the temporal lobe cortex [START_REF] Honea | Regional deficits in brain volume in schizophrenia: a meta-analysis of voxel-based morphometry studies[END_REF] .

However, these studies have also found evidence of volume reductions in other areas, including the anterior cingulate cortex, the insular cortex, the left middle frontal gyrus and the postcentral gyrus [START_REF] Glahn | Meta-analysis of gray matter anomalies in schizophrenia: application of anatomic likelihood estimation and network analysis[END_REF] .

While structural imaging has implicated a variety of brain regions in schizophrenia, the emphasis in functional imaging studies has been and continues to be on the frontal lobes. The original functional imaging finding of hypofrontality, while not consistently replicated, has been supported by meta-analysis both at rest and under conditions of neuropsychological task activation [START_REF] Hill | Hypofrontality in schizophrenia: a meta-analysis of functional imaging studies[END_REF] . At the same time, it is increasingly clear that the prefrontal cortex dysfunction in schizophrenia goes beyond any simple concept of hypofunction. Thus, rather than hypofrontality, a number of studies have found evidence of increased activation in the prefrontal cortex (PFC) during performance of working memory tasks [START_REF] Manoach | Schizophrenic subjects activate dorsolateral prefrontal cortex during a working memory task, as measured by fMRI[END_REF][START_REF] Callicott | Physiological dysfunction of the dorsolateral prefrontal cortex in schizophrenia revisited[END_REF][START_REF] Tan | Dysfunctional prefrontal regional specialization and compensation in schizophrenia[END_REF][START_REF] Callicott | Complexity of prefrontal cortical dysfunction in schizophrenia: more than up or down[END_REF] . This 'hyperfrontality' has been found in dorsolateral and ventral prefrontal regions, and whether it is seen appears to depend on the nature of the task used, and how well the patients perform it [START_REF] Tan | Dysfunctional prefrontal regional specialization and compensation in schizophrenia[END_REF][START_REF] Callicott | Complexity of prefrontal cortical dysfunction in schizophrenia: more than up or down[END_REF][START_REF] Manoach | Prefrontal cortex dysfunction during working memory performance in schizophrenia: reconciling discrepant findings[END_REF][START_REF] Glahn | Beyond hypofrontality: a quantitative meta-analysis of functional neuroimaging studies of working memory in schizophrenia[END_REF][START_REF] Tan | Dysfunctional and compensatory prefrontal cortical systems, genes and the pathogenesis of schizophrenia[END_REF] . Complicating matters further, two recent studies have found that schizophrenic patients show a failure of task-related deactivation in the medial frontal cortex [START_REF] Pomarol-Clotet | Failure to deactivate in the prefrontal cortex in schizophrenia: dysfunction of the default mode network?[END_REF][START_REF] Whitfield-Gabrieli | Hyperactivity and hyperconnectivity of the default network in schizophrenia and in first-degree relatives of persons with schizophrenia[END_REF] . This medial frontal area corresponds to part of the so-called default mode network, a series of interconnected regions that are highly active at rest but which de-activate during performance of a wide range of cognitive tasks [START_REF] Raichle | A default mode of brain function[END_REF][START_REF] Buckner | The brain's default network: anatomy, function, and relevance to disease[END_REF] .

A third imaging technique which is increasingly being applied to schizophrenia is diffusion tensor imaging (DTI). This indexes white matter abnormality by means of decreased fractional anisotropy (FA) [START_REF] Basser | Microstructural and physiological features of tissues elucidated by quantitative-diffusion-tensor MRI[END_REF] ; tractography algorithms can also be employed to identify which particular tracts are affected. Over 20 studies have indicated that schizophrenia is associated with decreased FA, particularly in white matter tracts connecting temporal and prefrontal regions. However, to date there is a lack of convergence in the findings, and the majority of studies have used a region-of-interest (ROI) approach rather than whole-brain-based examination [START_REF] Calhoun | Method for multimodal analysis of independent source differences in schizophrenia: combining gray matter structural and auditory oddball functional data[END_REF][START_REF] Lui | Association of cerebral deficits with clinical symptoms in antipsychotic-naive first-episode schizophrenia: an optimized voxel-based morphometry and resting state functional connectivity study[END_REF] .

It has been suggested that further understanding of brain pathology in schizophrenia will depend on integration of findings from voxel-based structural techniques with those from functional imaging and white matter tractography using DTI [START_REF] Miyata | Reduced white matter integrity correlated with cortico-subcortical gray matter deficits in schizophrenia[END_REF][START_REF] Kalus | Volumetry and diffusion tensor imaging of hippocampal subregions in schizophrenia[END_REF] . To date, however, relatively few such 'multimodal' imaging studies have been carried out, and these have either employed only two imaging techniques [START_REF] Calhoun | Method for multimodal analysis of independent source differences in schizophrenia: combining gray matter structural and auditory oddball functional data[END_REF][START_REF] Lui | Association of cerebral deficits with clinical symptoms in antipsychotic-naive first-episode schizophrenia: an optimized voxel-based morphometry and resting state functional connectivity study[END_REF][START_REF] Miyata | Reduced white matter integrity correlated with cortico-subcortical gray matter deficits in schizophrenia[END_REF] or have focused on discrete brain structures such as the hippocampus and amygdala [START_REF] Kalus | Volumetry and diffusion tensor imaging of hippocampal subregions in schizophrenia[END_REF][START_REF] Kalus | New evidence for involvement of the entorhinal region in schizophrenia: a combined MRI volumetric and DTI study[END_REF][START_REF] Kalus | The amygdala in schizophrenia: a trimodal magnetic resonance imaging study[END_REF] . In this study we report, for the first time, use of a whole brain approach combining all three imaging modalities, in order to determine what, if any, common sites of pathology they identify in the disorder.

Method

Subjects

The patient sample consisted of 32 schizophrenic patients recruited from two hospitals.

They all met DSM-IV criteria for schizophrenia, based on interview plus review of clinical history. Patients were excluded if: a) they were younger than 18 or older than 65, b) had a history of brain trauma or neurological disease, and c) had shown alcohol/substance abuse within 12 months prior to participation. Twenty-seven were inpatients and 5 were living outside the hospital with relatives or in supported accommodation. They all had chronic illnesses (range 5-39 years), were symptomatic (mean PANSS score 71.97±17.01) and had on average moderately severe illness (Global Assessment of Function [GAF] score = 44.03±10.89). They were all scanned when in relatively stable condition (ie outside any period of acute relapse). All were taking neuroleptic medication (clozapine N=7, other atypicals N=10, typical neuroleptics N=3, combined typical and atypical treatment N=12). fMRI findings on this sample have previously been described by Pomarol-Clotet et al [START_REF] Pomarol-Clotet | Failure to deactivate in the prefrontal cortex in schizophrenia: dysfunction of the default mode network?[END_REF] .

The controls consisted of 32 healthy individuals selected to be age-and sex-matched to the patients and met the same exclusion criteria. Subjects were recruited from nonmedical staff working in the hospital, their relatives and acquaintances, plus from independent sources in the community. They were questioned and excluded if they reported a history of mental illness and/or treatment with psychotropic medication.

Written informed consent was obtained from all participants. The study was approved by the local hospital ethics committee.

Procedure

All subjects underwent structural and functional MRI scanning in a single session, using the same 1.5 Tesla GE Signa scanner (General Electric Medical Systems, Milwaukee, Wis) located at the Sant Joan de Déu Hospital in Barcelona (Spain). Structural data were analysed with FSL-VBM, an optimized voxel-based morphometry style analysis [START_REF] Beckmann | Applying FSL to the FIAC data: model-based and model-free analysis of voice and sentence repetition priming[END_REF][START_REF] Smith | Tract-based spatial statistics: voxelwise analysis of multi-subject diffusion data[END_REF] carried out with FSL tools [START_REF] Smith | Advances in functional and structural MR image analysis and implementation as FSL[END_REF] ; this yields a measure of difference in local grey matter volume. In a first step, structural images were brain-extracted using BET [START_REF] Smith | Fast robust automated brain extraction[END_REF] . Next, tissue-type segmentation was carried out and the resulting grey-matter partial volume images were aligned to the MNI152 standard space using the FSL tools FLIRT and FNIRT. The resulting images were averaged to create a study-specific template, to which the native grey matter images were non-linearly re-registered. These images were modulated (to correct for local expansion or contraction) by dividing by the Jacobian of the warp field, and they were later smoothed with an isotropic Gaussian kernel with a sigma of 4 mm. Finally, group comparisons between patients and controls were carried out with permutation-based non-parametric tests. These were made with the randomise function implemented in FSL, using the recently developed threshold free cluster enhancement method (TFCE), for proper statistical inference of spatially distributed patterns [START_REF] Smith | Threshold-free cluster enhancement: addressing problems of smoothing, threshold dependence and localisation in cluster inference[END_REF] .

fMRI: The paradigm used has been described in Pomarol et al [START_REF] Pomarol-Clotet | Failure to deactivate in the prefrontal cortex in schizophrenia: dysfunction of the default mode network?[END_REF] . Scanning was carried out while participants performed a sequential-letter version of the n-back task [START_REF] Gevins | Spatiotemporal dynamics of component processes in human working memory[END_REF] . Two levels of memory load (1-back and 2-back) were presented in a blocked design manner.

Each block consisted of 24 letters which were shown every 2 seconds (1 s on, 1 s off) and all blocks contained 5 repetitions (1-back and 2-back depending on the block) located randomly within block. Individuals had to detect them and inform by pressing a button. Four 1-back and four 2-back blocks were presented in an interleaved way, and between them, a baseline stimulus (an asterisk flashing with the same frequency as the letters) was always presented for 16 seconds. In order to identify which task had to be performed, characters were shown in green in 1-back blocks and in red in the 2-back blocks. All participants first went through a training session, outside the scanner.

In fMRI image analyses were performed with the FEAT module, included in FSL software [START_REF] Smith | Tract-based spatial statistics: voxelwise analysis of multi-subject diffusion data[END_REF] . At a first level, images were corrected for movement, were coregistered to a common stereotaxic space (Montreal Neurologic Institute template), and were spatially smoothed with a Gaussian filter (FWHM = 5 mm). To minimise unwanted movement related effects, individuals with an estimated maximum absolute movement over 3.0 mm, or an average absolute movement higher than 3 mm were discarded from the study. Finally, group comparisons between patients and controls were performed using the same FEAT module, by means of mixed-effects GLM models [START_REF] Beckmann | Applying FSL to the FIAC data: model-based and model-free analysis of voice and sentence repetition priming[END_REF] . A z-threshold of Additionally, the output from the DTI analysis was used to explore potential differences in white matter structural connectivity. For this we used the voxel-based methodology described by Iturria-Medina et al [START_REF] Nelson | The Revised National Adult Reading Test[END_REF][START_REF] Ser | Estimation of premorbid intelligence in Spanish people with the Word Accentuation Test and its application to the diagnosis of dementia[END_REF] , which uses Dijkstra's graph theory algorithm to find the most probable route of connection between any pairs of voxels in the brain.

First, the statistical map resulting from TBSS was automatically partitioned into nonoverlapping clusters. Next, four of these clusters were selected as representative ROIs, after considering their central location in each of the significant tracts, and avoiding other clusters containing fibre intersections (which would make the interpretation of results difficult). Every ROI was used separately as a seed mask by an optimized tractography algorithm [START_REF] Iturria-Medina | Characterizing brain anatomical connections using diffusion weighted MRI and graph theory[END_REF] , delivering three-dimensional images that quantified the degree of anatomical connection between a particular ROI and each voxel in the brain [START_REF] Iturria-Medina | Studying the human brain anatomical network via diffusion-weighted MRI and Graph Theory[END_REF] .

Finally, all individual maps were aligned into a common space and they were smoothed with an isotropic Gaussian kernel with a sigma of 4 mm. This allowed comparing connectivity patterns between patients and controls using the same permutation-based randomise function from FSL.

Statistical thresholds

In the three principal analyses comparing patients and controls, a threshold of p=0.01, corrected for multiple comparisons across space, was used. We applied this relatively conservative threshold in order to minimise false positive findings arising from the analysis of several modalities and from different sets of images. Using this threshold on the three main comparisons leads to an overall probability of finding one (or more) false positives of 0.03. Results applying a corrected p = 0.05 in the individual tests are reported in the supplementary online material. However, these results should be treated with caution, as they imply an overall probability of 0.14 for false positives in the three main comparisons.

Results

Demographic findings

Demographic findings are shown in Table 1. The patients and controls were selected to be matched for age and sex. There were also no significant differences between their score on the Word Accentuation Test (TAP), a test designed to estimate IQ (premorbid IQ in the patients) analogous to the National Adult Reading Test (NART) in English [START_REF] Nelson | The Revised National Adult Reading Test[END_REF] , based on pronunciation of low-frequency Spanish words whose accents are removed [START_REF] Ser | Estimation of premorbid intelligence in Spanish people with the Word Accentuation Test and its application to the diagnosis of dementia[END_REF] .

As typically found in schizophrenia, the patients, however, had a lower current IQ than the controls.

VBM

Due to poor image quality, two individuals (1 control and 1 patient) were excluded from the VBM analyses. At a p=0.01, only two areas of the brain showed significant differences in volume between patients and controls (see Figure 1A). One of these was centred in the medial frontal cortex [peak in Brodmann area 32 (BA 32), Talairach (-8, 14, 46), z score=5.95, p<0.001], bilaterally including parts of the gyrus rectus, anterior cingulate, medial superior frontal gyrus, and extending posteriorly to the supplementary motor area. The second significant area was located in the right hemisphere, partially covering the dorsolateral prefrontal cortex and extending to inferior frontal cortical -11 -regions and the precentral gyrus with a maximum in BA 44 [Talairach (50, 8, 24), z score=4.7, p<0.0197].

[Figure 1 Additionally, patients showed significant failure to de-activate in two clusters (Figure 1B, shown in orange). One of these extended over a large medial frontal area including, bilaterally, the gyrus rectus, the anterior cingulate cortex and parts of the superior medial frontal cortex and related frontomedial structures [peak activation in BA 11, Talairach (-2, 38, -2), z score=4.91, p<1. 78 10 -9 ]. This cluster clearly overlapped with the region of volume reduction identified in the VBM analysis (Figure 1A). The other cluster where there was significant failure to deactivate was smaller, and contained parts of the hippocampal complex and neighbouring anterior temporal regions with maximum activation in BA 48 [Talairach (46, -8,-12), z score=4.04, p<0.000798].

DTI

Due to excessive movement only 25 patients and 28 controls could be included in this analysis. At p= 0.01 corrected, the major FA differences between the patients and controls were found in the corpus callosum [maximum in Talairach space (22, 37, -1), p<0.00701] (see Figure 2A). In particular, alterations were seen in the anterior portion of this structure, extending from below the genu to include the rostral and anterior midbody. This area of significant difference also included the anterior corona radiata bilaterally (visible particularly in the left-hand figure).

A further anomalous region was located posteriorly in the splenium of the corpus callosum on the left, also involving the posterior thalamic radiation (including the optic radiation) and to a lesser extent the posterior corona radiata [maximum at Talairach coordinates (-21, -83, 10), p<0.007].

In order to examine the relationship of the anterior callosal FA differences to the overlapping areas of structural and functional MRI abnormality in the medial prefrontal cortex, we performed a connectivity/tractography analysis (see Methods). For this, four ROIs were selected from an automatic parcellation of all areas with significant differences in FA at p=0.01. ROI#1 corresponded to the genu of the corpus callosum in the midline; ROI2# and ROI#3 were components of the left and right parts of the body of the corpus callosum anteriorly; ROI#4 was located within the posterior thalamic radiation. In this analysis we first applied a less conservative threshold of 0.05 rather than the 0.01 used in all other analyses: we expected higher levels of noise inherent to limitations in both the diffusion tensor model [START_REF] Frank | Characterization of anisotropy in high angular resolution diffusionweighted MRI[END_REF] and the tractography algorithm to reduce the statistical power of the connectivity analyses.

The three anteriorly placed seed regions (ROI#1, ROI#2, ROI#3) showed significant connectivity differences between patients and controls which affected principally a large expanse of the medial frontal cortex (see Figure 2B). Noticeably, there is a clear overlap between these results and areas showing failure to deactivate in fMRI and regions with volume reduction in VBM (Figure 1A andB). The seed placed in the left side of the body of the corpus callosum also showed differential connectivity with the left dorsolateral prefrontal cortex. The fourth seed, located posteriorly in the posterior thalamic radiation, did not result in any differential connectivity between the schizophrenic patients and the controls.

Repeating the analyses at a threshold of 0.01 corrected had similar results, but the area of differential structural connectivity was less extensive. In particular, only the seed region ROI#3 in the right part of the body of the corpus callosum continued to show significant differences between patients and controls. These affected areas very similar to those depicted in the lower panel of Figure 2B, but unilaterally on the right side of the brain.

Discussion

In this study three different whole-brain voxel-based imaging techniques identified the medial prefrontal cortex as a prominent site of abnormality in schizophrenia. This region has not previously been a focus of interest in the disorder, although some post-clusters of reduced volume in the medial prefrontal cortex and the dorsolateral prefrontal cortex, these were accompanied by other clusters, notably in the insula/inferior frontal cortex and the medial temporal lobes. Some of these additional areas were also evident in our analysis using a threshold of p=0.05 (see supplementary online material).

On the other hand, there are grounds for believing that VBM abnormality in schizophrenia may not be as widespread as originally thought. When the technique was originally introduced in 2000-2001 [START_REF] Ashburner | Voxel-based morphometry--the methods[END_REF][START_REF] Good | A voxel-based morphometric study of ageing in 465 normal adult human brains[END_REF] , it utilized a measure of grey matter concentration or density, the proportion of grey matter within a given voxel after spatial normalization of the images. Later, a modulated or 'optimized' method became available which gives a more intuitive estimate of grey matter volume. Fornito et al [START_REF] Fornito | Mapping grey matter reductions in schizophrenia: an anatomical likelihood estimation analysis of voxel-based morphometry studies[END_REF] meta-analyzed studies using measures of grey matter concentration in schizophrenia and found clusters of significant volume reduction in the medial and lateral frontal cortex, temporal cortex and insula bilaterally. However, meta-analysis of studies using the volume measure resulted in a more restricted pattern of differences: changes in the temporal lobe and insula were no longer seen, and the largest areas of reduced volume were in the medial aspect of the left superior frontal gyrus plus the left orbitofrontal and fusiform regions.

DTI studies of schizophrenia have found evidence of abnormality in many different white matter areas, although these include the corpus callosum [START_REF] Calhoun | Method for multimodal analysis of independent source differences in schizophrenia: combining gray matter structural and auditory oddball functional data[END_REF][START_REF] Lui | Association of cerebral deficits with clinical symptoms in antipsychotic-naive first-episode schizophrenia: an optimized voxel-based morphometry and resting state functional connectivity study[END_REF] , especially in recent studies [START_REF] Miyata | Reduced white matter integrity correlated with cortico-subcortical gray matter deficits in schizophrenia[END_REF][START_REF] Rotarska-Jagiela | The corpus callosum in schizophrenia-volume and connectivity changes affect specific regions[END_REF] . Once again, however, there are grounds for believing that the true pattern may be more restrictive: Ellison-Wright and Bullmore 42 meta-analyzed 15 studies which used a whole brain, voxel-based approach and found that only two locations were consistently identified across studies. One of these was in the deep white matter of the left frontal lobe, close to the genu of the corpus callosum. The other area was in the left temporal lobe white matter. These areas are strikingly similar to those we found using a threshold of p=0.01 corrected.

The linchpin for the convergence of evidence found in our study is the failure of deactivation in the medial frontal cortex, which was equally prominent at thresholds of p=0.05 or p=0.01. One of the most important functional imaging findings to emerge in recent years has been that prefrontal cortex dysfunction in schizophrenia goes beyond any simple concept of hypofrontality, with a series of studies documenting areas of increased activation ('hyperfrontality') during performance of working memory tasks 7-

Legends for figures

  Medina, Antoni Capdevila, Peter MckennaTo cite this version:Edith Pomarol-Clotet, Erick Canales Rodgriguez, Raymond Salvador, Salvador Sarro, Jesus Gomar, et al.. Medial prefrontal cortex pathology in schizophrenia as revealed by convergent findings from multimodal imaging. Molecular Psychiatry, 2010, n/a (n/a), pp.n/a-n/a. 10.1038/mp.2009.146. hal-00499663

Structural imaging:

  High resolution structural T1 MRI data were acquired with the following acquisition parameters: Matrix size 512x512; 180 contiguous axial slices; voxel resolution 0.47x0.47x1 mm 3 ; echo (TE), repetition (TR) and inversion (TI) times, (TE/TR/TI) = 3.93 ms/2000 ms/710 ms respectively; flip angle 15 degrees.

  each individual scanning session 266 volumes were acquired. A gradient echo echoplanar (EPI) sequence depicting the blood-oxygenation-level-dependent (BOLD) contrast was used. Each volume contained 16 axial planes acquired with the following parameters: TR = 2000 ms, TE = 20 ms, flip angle = 70 degrees, section thickness = 7 mm, section skip =.7 mm, in-plane resolution = 3 x 3 mm 2 . The first 10 volumes were discarded to avoid T1 saturation effects.

2. 3 ( 9 -

 39 the default in FSL) was used to generate the initial set of clusters. FEAT uses Gaussian Random Field theory to properly account for the spatially distributed patterns when performing statistical tests.DTI:Whole brain diffusion-weighted images were recorded along 25 gradient directions using three different b-values (500, 750 and 1000 s/mm 2 ) together with three unweighted (b = 0) images (78 images in total). For each image we used the following parameters: field of view FOV=289x289 mm 2 ; matrix size 128x128; number of slices 28; voxel resolution 1.13x1.13x5 mm 3 ; TE = 107 ms; TR = 8000 ms. DTI datasets were analyzed with FSL-TBSS[START_REF] Smith | Tract-based spatial statistics: voxelwise analysis of multi-subject diffusion data[END_REF] , a Tract-Based Spatial Statistics analysis carried out with FSL tools. In a first step, FA images were created by fitting a tensor model to the raw diffusion data using FDT, and then brain-extracted using BET[START_REF] Smith | Fast robust automated brain extraction[END_REF] . All subjects' FA data were then aligned into a common space using the nonlinear registration tool FNIRT [J.L.R. Andersson, M. Jenkinson and S. Smith. Non-linear optimisation: FMRIB technical report TR07JA1 from www.fmrib.ox.ac.uk/analysis/techrep; J.L.R. Andersson, M. Jenkinson and S. Smith.Non-linear registration, aka Spatial normalisation: FMRIB technical report TR07JA2 from www.fmrib.ox.ac.uk/analysis/techrep], which uses a b-spline representation of the registration warp field[START_REF] Rueckert | Non-rigid registration using free-form deformations: Application to breast MR images[END_REF] . Next, the mean FA image was created and thinned to create a mean FA skeleton which represents the centres of all tracts common to the group. Each subject's aligned FA data was then projected onto this skeleton. As in the VBM analysis, group comparisons between patients and controls were performed using the randomise function implemented in FSL, which carries out permutation based, non parametric comparisons.

  about here] fMRI While the 1-back vs baseline contrast did not reveal any significant differences in activation, the 2-back vs baseline contrasts revealed several areas of differential activation between the two groups. The patients showed significantly reduced activation compared to controls in two areas (Figure 1B, shown in blue). One of these areas comprised two distinct but clearly related clusters [cluster1: peak activation in BA 8, Talairach (2, 26, 50), z score=4.35, p<1.19 10 -7 ; cluster2: peak activation in BA 6, Talairach (-46, -2, 28), z score=4.12, p<0.00131]. These clusters included parts of the frontal operculum bilaterally, both precentral gyri and the supplementary motor areas. They also it reached some sections of the right dorsolateral prefrontal cortex and the left basal ganglia. The other area was located in the cerebellum [peak activation in Talairach coordinates (2, -56, -24), z score=5.96, p<1.91 10 -8 ].

Figure 1 .

 1 Figure 1. Top panel (A) VBM findings: regions showing significant volume reduction thresholded at p=0.01 in the schizophrenic patients are shown in orange. Bottom panel (B) fMRI findings: regions are shown where there were significant differences between patients and controls during performance of the n-back task (2-back vs baseline comparison), thresholded at p=0.01. Blue indicates hypoactivation, ie areas where controls activated significantly more than patients. Orange indicates areas where the schizophrenic patients showed failure to de-activate in comparison to controls. The right side of the images represents the left side of the brain.

Figure 2 :

 2 Figure2: DTI findings. Top panel (A) shows areas of significant FA reduction in the schizophrenic patients identified using TBSS thresholded at p=0.01. Bottom panels (B) show areas of structural connectivity which differed significantly between the schizophrenic patients and controls based on the seed placed in the genu of the corpus callosum (upper, shown in red), and the seeds placed in the body of the corpus callosum, right and left (lower, shown in orange). A threshold of p=0.05 corrected was used for this analysis. The right side of the images represents the left side of the brain.

. The leading interpretation of this finding has been that of cortical inefficiency: even when schizophrenic patients are able to perform a cognitive task normally, they have to 'work harder to keep up' with its demands, and this leads to a compensatory brain functional response characterized by greater and/or wider activation of relevant cortical regions than in healthy subjects[START_REF] Callicott | Complexity of prefrontal cortical dysfunction in schizophrenia: more than up or down[END_REF][START_REF] Tan | Dysfunctional and compensatory prefrontal cortical systems, genes and the pathogenesis of schizophrenia[END_REF] . However, a meta-analysis of fMRI studies using the n-back task[START_REF] Glahn | Beyond hypofrontality: a quantitative meta-analysis of functional neuroimaging studies of working memory in schizophrenia[END_REF] casts doubts on this interpretation, since a) hyperfrontality was found in the medial prefrontal cortex, different from the dorsolateral and other lateral areas where hypofrontality was seen; and b) this medial frontal area was not activated in the meta-analysis of either patients alone or controls alone. Subsequently, findings from two studies suggest that the hyperfrontality seen in medial frontal cortex in schizophrenia actually represents a failure to de-activate[START_REF] Pomarol-Clotet | Failure to deactivate in the prefrontal cortex in schizophrenia: dysfunction of the default mode network?[END_REF][START_REF] Whitfield-Gabrieli | Hyperactivity and hyperconnectivity of the default network in schizophrenia and in first-degree relatives of persons with schizophrenia[END_REF] (because of 'reverse subtraction' from a high baseline, this can result in apparent hyperactivation, see Gusnard and Raichle[START_REF] Gusnard | Searching for a baseline: functional imaging and the resting human brain[END_REF] ).

Supported by the Instituto de Salud Carlos III, Centro de Investigación en Red de Salud Mental, CIBERSAM. Edith Pomarol-Clotet was supported by a Marie Curie European Reintegration Grant (MERG- CT-2004-511069). This work will will be included as part of Salvador Sarró's doctoral thesis in the Universitat Autònoma de Barcelona.

mortem studies have noted microstructural abnormalities in the anterior cingulate cortex [START_REF] Fornito | Anatomical Abnormalities of the Anterior Cingulate Cortex in Schizophrenia: Bridging the Gap Between Neuroimaging and Neuropathology[END_REF] , and it is an area where apparent hyperactivation [START_REF] Glahn | Beyond hypofrontality: a quantitative meta-analysis of functional neuroimaging studies of working memory in schizophrenia[END_REF] , and more recently failure of de-activation [START_REF] Pomarol-Clotet | Failure to deactivate in the prefrontal cortex in schizophrenia: dysfunction of the default mode network?[END_REF][START_REF] Whitfield-Gabrieli | Hyperactivity and hyperconnectivity of the default network in schizophrenia and in first-degree relatives of persons with schizophrenia[END_REF] has been found in the disorder (see below). We also found evidence of convergent abnormality in the dorsolateral prefrontal cortex, which is an area of longstanding interest in schizophrenia. Here, however, the laterality was less consistent across techniques.

Our findings differ from two other studies which have applied whole-brain multimodal imaging to schizophrenia [START_REF] Calhoun | Method for multimodal analysis of independent source differences in schizophrenia: combining gray matter structural and auditory oddball functional data[END_REF][START_REF] Lui | Association of cerebral deficits with clinical symptoms in antipsychotic-naive first-episode schizophrenia: an optimized voxel-based morphometry and resting state functional connectivity study[END_REF] . Calhoun et al [START_REF] Calhoun | Method for multimodal analysis of independent source differences in schizophrenia: combining gray matter structural and auditory oddball functional data[END_REF] examined 15 chronic schizophrenic patients and 15 controls using VBM and fMRI during performance of an auditory oddball task. They used joint independent component analysis (jICA) of both modalities to determine areas of difference between both groups. Significant differences for VBM and fMRI were located in clearly different cortical regions, and there was no anatomical convergence. Lui et al [START_REF] Lui | Association of cerebral deficits with clinical symptoms in antipsychotic-naive first-episode schizophrenia: an optimized voxel-based morphometry and resting state functional connectivity study[END_REF] carried out VBM on 68 patients with first-episode schizophrenia and 68 controls. Like us, they found a cluster of grey matter volume reduction in the anterior cingulate cortex (although on the right only), along with two other clusters in the right superior and right middle temporal gyri. However, when the authors used these three regions as seeds for a functional connectivity analysis using resting fMRI, no differences between the patients and the controls emerged.

Our findings are also different from those of other studies using single modalities of brain imaging. In particular, we found a considerably less extensive pattern of brain abnormality in the VBM and DTI analyses than in previous studies. On the one hand, this undoubtedly reflects our use of a conservative threshold of p=0.01 corrected. Thus, while two recent meta-analyses of VBM studies in schizophrenia [START_REF] Glahn | Meta-analysis of gray matter anomalies in schizophrenia: application of anatomic likelihood estimation and network analysis[END_REF][START_REF] Fornito | Mapping grey matter reductions in schizophrenia: an anatomical likelihood estimation analysis of voxel-based morphometry studies[END_REF] found, like us, What is the function of this medial prefrontal area identified by multimodal imaging?

As mentioned above, it includes, but is not limited to, the anterior cingulate cortex, an area which has been implicated in mood, attention, emotional regulation, error detection and decision making [START_REF] Fornito | Anatomical Abnormalities of the Anterior Cingulate Cortex in Schizophrenia: Bridging the Gap Between Neuroimaging and Neuropathology[END_REF][START_REF] Devinsky | Contributions of anterior cingulate cortex to behaviour[END_REF] . Perhaps more significantly, it corresponds closely to one of the two midline nodes of the default mode network, a system of brain regions which are active at rest but de-activate during performance of a wide range of attention demanding cognitive tasks [START_REF] Raichle | A default mode of brain function[END_REF] . The default mode network has been proposed to be involved in functions like conceiving the perspectives of others, retrieving autobiographical memories and envisioning the future, processes which can be subsumed under a broad heading of mentation detached from the external world [START_REF] Buckner | The brain's default network: anatomy, function, and relevance to disease[END_REF] . Going further, it has been argued that such functions underlie the experience and maintenance of one's sense of self [START_REF] Gusnard | Being a self: considerations from functional imaging[END_REF] . A further possibility is that the default mode network underlies a state of 'watchfulness', a passive, low-level monitoring of the external environment for unexpected events in conditions when active attention is relaxed [START_REF] Buckner | The brain's default network: anatomy, function, and relevance to disease[END_REF] . Any and all of these possibilities appear to have scope for explaining the symptoms of schizophrenia.