The measured TCD waveforms were compared to those derived from Vx(t), an illustrative Kolmogorov-Smirnov test was employed to determine the validity. The results showed that the TCD waves could been reconstructed for patients with different CBFVs by implementing their variable heart rates and the formulated maximum/minimum of Vx(t). Comparisons between derived and measured TCD waveforms suggest that the two waveforms are very similar. The results confirm that CBFV can be well-modeled through an eighth-order Fourier function. This function Vx(t) can be used extensively for a prospective study of cerebral hemodynamics in geriatric patients with suspected cerebrovascular disease.Cerebral blood flow velocity(CBFV) is an important parameter for study of cerebral hemodynamics. However, a simple and highly similar mathematical model has not yet been established for analyzing CBFV. To alleviate this issue, through TCD examination in 100 geriatric patients with suspected cerebrovascular disease , we established a representative eighth-order Fourier function V Cerebrovascular disease has become the second leading cause of death and the leading cause of adult disability worldwide135et al.9However, a simple and highly similar mathematical model for CBFV has not yet been established. Olufsen and colleaguesmax/CBFVmin ranged to 30–120/15–90 cm/s, and the heart rate were within a range of 60–100 beats/min. Patients with any stenotic or occlusive disease of the carotid, vertebro-basilar and intracranial arteries along with patients acquiring arrhythmias were excluded from the study. Patients who had a recent onset of moderate to severe stroke, defined as NIHSS score > 4 points were also excluded from the study.The study was approved by the Ethics Committee of Chongqing Medical University. Written informed consents were obtained from all participants themselves, the methods were carried out in accordance with the approved guidelines. Our study included patients with suspected cerebrovascular disease who underwent Transcranial Doppler(TCD) examination from January 2014 to December 2014 at our institution. The inclusion criteria were as follows: 1) Patients had signs and symptoms suggestive of cerebrovascular disease. 2) Patients had to undergo TCD examinations. 3) The CBFVAfter attaining the TCD results, a sum of nine CBFV waves were bilaterally recorded for each patient: two from the (left and right) anterior cerebral arteries, two from the (left and right) middle cerebral arteries, two from the (left and right) posterior cerebral arteries, two from the (left and right) vertebral arteries and one from the basilar artery.A TCD wave is an irregular periodic wave . Considemax/CBFVmin to 80/50 cm/s.Since the TCD waves were significantly variable for all the participating patients, it was necessary to standardize all waves to derive at one representative Fourier function with 18 representative coefficients. To accomplish that, 100 patients were randomly selected followed by the standardization of all waves of these patients using the following methods: (1) the abscissa (time) was set up to 0 s at the first nadir; (2) the abscissa (time) to 0.8 s at the second nadir; (3) the ordinate of the nadir to 50 cm/s; and (4) the ordinate of the zenith to 80 cm/s Fig. . Eventua0(t)  was derived by lengthening and/or shortening of V0(t) in the longitudinal and transverse directions (x(t) model, 100 new included patients were chosen randomly with completed TCD examination. The CBFV waves were assessed for each patient by the Fourier function model Vx(t). Comparisons between derived and measured TCD waveforms were tested for the validity.After this standardization procedure, the 18 standardized coefficients  were obtained by calculating the mean of each coefficient of all new fitted functions. Based on the standardized coefficients, we were able to derive a representative eighth-order Fourier function V(t) Fig. . A functrections . To valiAll statistical analysis was performed by using SPSS 20.0.Definite integral of the absolute value of the differential function in  was implemented to compare the coherent function. The single sample Kolmogorov-Smirnov test was employed to test A total of 200 patients were included in our study and the demographic data was listed in max/CBFVmin to 80/50 cm/s. MATLAB 7.0 was able to construct eighth-order Fourier functions so as to fit all the standardized TCD waveforms. After the above procedure, we gained an aggregate of 900 fitting functions  and on observation, all these new functions demonstrated as follows: these functions not only had the same maximum, minimum and rhythm, but also possessed a consistent waveform morphology; further all corresponded to a single underlying function i.e. V0(t) pathway.In order to obtain the common feature of these waveforms, all 900 TCD waves belonging to the derivation group  were standardized with all cardiac cycles customized to 0.8 s and all CBFV0(t), the 18 standardized coefficients  were derived by calculating the mean of each coefficient from the 900 newly fitted functions (0(t) = 64.5 − [5.154cos(7.85t) − 10.962sin(7.85t)] − [5.4516cos(2 * 7.85t) − 1.7574sin(2 * 7.85t)] − [1.731cos(3 * 7.85t) + 0.846sin(3 * 7.85t)] − [1.5684cos(4 * 7.85t) + 0.23976sin(4 * 7.85t)] − [0.50328cos(5 * 7.85t) + 1.0524sin(5 * 7.85t)] − [0.10014cos(6 * 7.85t) + 0.30504sin(6 * 7.85t)] − [0.035316cos(7 * 7.85t) + 0.3963sin(7 * 7.85t)] + [0.16248cos(8 * 7.85t) − 0.17118sin(8 * 7.85t)] (0(t) has a cycle of 0min = 50 cm/s, CBFV0max = 80 cm/s.In order to establish the standardized function Vunctions . Based o 7.85t)] . V0(t) h0(t) in the longitudinal and transverse directions, the V0(t) function was manipulated to fit the TCD waves for the varying CBFVs and heart rates (max/CBFVmin as M/N (cm/s) and the heart rate as H (beats/min). According to the Fourier function, based on the function V0(t); CBFV function Vx(t) of this patient X, should be able to conform to the following relationship:On lengthening and/or shortening of Vrt rates . Thus, ix(t) has an average value of (1/30)(14.5 M + 15.5 N) (cm/s), with an ordinate range from M to N, and a cycle of 60/H (s)  .x(t) model, a validation group  were randomly selected for TCD examinations, and later all TCD waves were function-fitted using MATLAB 7.0. The TCD waveforms were also assessed in each patient by the Fourier function model Vx(t). The estimated TCD waveform and the actual waveform were calculated by using x(t) model can be used for normal subjects. A total of 100 normal subjects  were randomly selected for TCD examinations and all TCD waves were assessed by the Fourier function model. The single sample Kolmogorov-Smirnov test of nine definite integrals in 100 normal subjects were illustrated in To validate this V similar . We furtx(t) has successfully derived on the basis of these reliable tests.Transcranial Doppler (TCD) is a noninvasive method that is commonly used for detection of the cerebral hemodynamics in patients with suspected neurovascular diseases. It is commonly used in clinical practice due to its relatively very simple operation and good reproducibility. In recent years, TCD has been widely used for measurement of cerebrovascular hemodynamics1517Fourier first proposed that any periodic function could be expressed via an arithmetic sum of the constituent sine and cosine functions, which is commonly known as the Fourier series (French: Série de Fourier)1920max/CBFVmin to 80/50 cm/s in order to obtain the common feature of these TCD waveforms. All standardized TCD waveforms shared a common feature that was very close to V0(t) pathway and vice versa. Therefore, the Vx(t) function might have been beneficial only to our participants. Further studies are required to demonstrate whether this function could be used for other populations and confirm its reliability. We have selected 100 normal geriatric subjects with a quantitative assessment of sitting errors. The results suggested that the Vx(t) function was quite similar with the actual waveform. The age group of our participants was between 60–80 years old which was the high incidence age of cerebrovascular diseasex(t) could be used widely in the study of cerebrovascular disease.We standardized all variant cardiac cycles to 0.8 s and all CBFVx(t) could be utilized to achieve a double benefit with a reduced effort. In addition, while studying cerebrovascular hemodynamics, we require the function expression instead of raw data points. Vx(t) could also be used in the study of cerebral perfusion pressure(CPP) and/or cerebral vascular resistance(CVR). CPP and CVR changes are slightly complex issues. The CBFV was increased when CPP > CVR and vice versa. The first derivative of Vx(t) was V’x(t), which could directly manifest changes between CPP and CVR.For the study of cerebrovascular hemodynamics in a particular patient, the CBFV data can directly make use of TCD or MRI. But these data have continuous data points and are not conducive for the subsequent calculations. Therefore, a combined use of the measured data and Vx(t) can be used extensively for a prospective study of cerebral hemodynamics in geriatric patients with suspected cerebrovascular disease.Based on the TCD data, CBFV can be well-modeled through an eighth-order Fourier function using MATLAB 7.0. This function VHow to cite this article: Liu, B. et al. A Highly Similar Mathematical Model for Cerebral Blood Flow Velocity in Geriatric Patients with Suspected Cerebrovascular Disease. Sci. Rep.5, 15771; doi: 10.1038/srep15771 (2015).


Importance. There is a conflict about the content of the macular folds in nanophthalmic eyes in the literature. Our study clearly demonstrated that papillomacular folds seen in nanophthalmos or posterior microphthalmos were only composed of neurosensory retina without involvement of retinal pigment epithelium and choroid. Observations. This is a report of two consecutive nanophthalmic patients with macular folds at Maltepe University School of Medicine, Department of Ophthalmology, from January to June 2012. Anterior segment dimensions were near normal. The axial lengths of the eyes were short with markedly shortened posterior segment. A macular fold extending from the center of the fovea towards the optic nerve head was present in all eyes. Optic coherence tomography clearly demonstrated that folds were only composed of neurosensory retina. Binocular visual acuities and refractive errors of the cases were 0.3, 0.2 and +16.00, +15.75 diopters, respectively. Conclusions and Relevance. Our study proposes a surgical option to treat these folds like serous retinal detachments by showing the true content of the folds, although there is not any surgical operation accepted for this condition yet. Further studies dealing with the surgical interventions of these folds should be performed to support this option. Nanophthalmos is a rare condition and results from the developmental arrest of the globe in all dimensions without other major malformations . NanophtDifferent funduscopic appearances have been shown in nanophthalmic eyes, including pigmentary changes from retinal flecks to bone spicules, bull's eye maculopathy, macular hypoplasia, retinal and macular cysts, and papillomacular folds , 3.We describe two cases of bilateral nanophthalmos with yellow pigmented macular folds and high hyperopia.μ, 2282 μ and 1658 μ, 2312 μ, respectively. Choroidal thicknesses of OD and SO were 405 μ and 389 μ, respectively. OCT demonstrated papillomacular fold of sensorial retina without involvement of underlying retinal pigment epithelium and choroid  refractive errors in both eyes. Axial lengths were 14.20 mm OD and 14.50 mm OS. Horizontal and vertical corneal diameters were 9.5 mm and 9.8 mm in right eye and 9.2 mm and 9.6 mm in left eye, respectively. The intraocular pressure was measured as 16 mmHg OD, 18 mmHg OS. Pachymetry and anterior chamber angle measurements were performed by optical coherence tomography (OCT). Central corneal thicknesses of right and left eye were 527 microns and 534 microns, respectively. Temporal anterior chamber degrees of right and left eye were 32.59 degrees and 35.44 degrees, respectively. Funduscopic examination showed crowded discs with blurred margins along with horizontal macular folds emanating from the fovea and extending nasally to the optic disc . Horizon choroid .μ, 2209 μ and 1138 μ, 1442 μ, respectively. Choroidal thicknesses of OD and SO were 406 μ and 399 μ, respectively. OCT demonstrated papillomacular fold of sensorial retina without involvement of underlying retinal pigment epithelium and choroid (A 30-year-old male presented with best corrected visual acuity of 0.2 OU with +1.50 D at 125 cylindrical degree refractive errors in OD and with +15.75 D spherical and +1.00 D at 42 degree cylindrical degree refractive errors in OS. Previously, he had clear lens cataract extraction to correct the refractive error in OD in another center. Axial lengths were 14.40 mm OD and 14.60 mm OS. Horizontal and vertical corneal diameters were 9.7 mm and 10.2 mm in right eye and 9.8 mm and 10.2 mm in left eye, respectively. The intraocular pressure was measured as 14 mmHg OD, 15 mmHg OS. Central corneal thicknesses of right and left eye were 538 microns and 544 microns, respectively. Temporal anterior chamber degrees of right and left eye were 36.19 degrees and 31.44 degrees, respectively. Fundus examination showed crowded discs with blurred margins along with horizontal macular folds emanating from the fovea and extending nasally to the optic disc . Horizon choroid .Various macular changes including papillomacular folds and macular radial folds have been described with nanophthalmic eyes . Foveal Our patients had axial lengths less than 16 mm; therefore crowded discs, yellowish reflex, and macular folds were seen because of the crowding of the posterior segment. Visual acuities of the patients were 0.3 and 0.3. Early detection of this condition is very important for the amblyopia therapy.Vision may be affected in these patients due to high refractive amblyopia and/or structural macular changes. Papillomacular folds, which are common among patients with posterior microphthalmos, are also seen in patients with nanophthalmos. The OCT scans of patients with posterior microphthalmos and retinal folds have demonstrated that the neurosensory retina was folded; however the retinal pigment epithelium layer and choroid were intact without folding . It is pCrowded posterior segment in nanophthalmic eyes may lead to retinal changes described in our cases. OCT clearly demonstrated that only neurosensory retina was involved in papillomacular folds in nanophthalmos. High refractive amblyopia and chorioretinal changes are the major causes of low vision in these patients.


Autism Res2015, 8: 534–544. © 2015 International Society for Autism Research, Wiley Periodicals, Inc.Recent research has shown that adults with autism spectrum disorders (ASD) have difficulty interpreting others' emotional responses, in order to work out what actually happened to them. It is unclear what underlies this difficulty; important cues may be missed from fast paced dynamic stimuli, or spontaneous emotional responses may be too complex for those with ASD to successfully recognise. To explore these possibilities, 17 adolescents and adults with ASD and 17 neurotypical controls viewed 21 videos and pictures of peoples' emotional responses to gifts , then inferred what gift the person received and the emotion expressed by the person while eye movements were measured. Participants with ASD were significantly more accurate at distinguishing who received a chocolate or homemade gift from static (compared to dynamic) stimuli, but significantly less accurate when inferring who received Monopoly money from static (compared to dynamic) stimuli. Both groups made similar emotion attributions to each gift in both conditions . Participants with ASD only made marginally significantly fewer fixations to the eyes of the face, and face of the person than typical controls in both conditions. Results suggest adolescents and adults with ASD can distinguish subtle emotion cues for certain emotions (genuine from feigned positive) when given sufficient processing time, however, dynamic cues are informative for recognising emotion blends (e.g. smiling in confusion). This indicates difficulties processing complex emotion responses in ASD.  Although current diagnostic criteria for autism spectrum disorders (ASD) includes difficulties interpreting other's emotions and responding appropriately APA, , emotionTo accomplish this, Cassidy et al.  developeIt is unclear how individuals with ASD process the spontaneous emotional responses we typically encounter in everyday life. Spontaneous emotional responses are subtle, can show more than one emotion, and are subject to display rules, such as trying to show a positive, as opposed to a negative façade to a social interaction partner  = 10.1, P < 0.001). There was no significant effect of gender on task performance in the control group.The ASD group was comprised of 17 adolescents and adults  aged 14–21 years, recruited from specialist schools and colleges for individuals with ASD across the UK. Two participants in the ASD group met the recommended cut‐off (>32) on the autism spectrum quotient (AQ) . The static condition included 21 pictures taken from one frame of each video. Stimuli were presented on the Tobii (1750) eye‐tracker in high definition (1920 × 1080i). Eye movements were recorded using Tobii Studio at a rate of 50 recordings per second.Full details of the stimuli set are available in Cassidy et al. . There wK = 0.86). These pictures were extracted in full colour high definition format using Final Cut Pro.One frame of each video clip was chosen by the researchers for use in the current study. This was judged by extracting the frame at the peak of the person's expression; after they had seen the gift, and their face had fully formed their reaction. Four independent judges rated whether the static picture chosen by the researcher represented the peak of the expression shown in the video. Cohen's Kappa showed a high level of agreement between judges , and state the emotion of the target on being offered the gift. All responses were verbal and digitally recorded.In the dynamic condition, each trial presentation sequence consisted of a 500 ms blank screen preceding the video, followed by a fixation cross in the middle of the screen which participants were asked to fixate on while they gave their response. In the static condition, a fixation cross appeared in the middle of the screen for 5 sec before the picture appeared. The picture remained on the screen until the participant answered the test questions. Then, the experimenter would move onto the next trial by a key press. All pictures and videos were presented in random order.The researcher then asked the participant ‘do you think the person got a box of chocolates, a tacky glitter card made especially for them, or some fake money?’ The participant was given as much time as they needed to respond to the test question. After giving a response the participant was then asked ‘How do you think the person felt when they got the [participant's gift response]?’ After the participant had responded to both of the test questions, the researcher asked if the participant was ready and started the next trial by a key press.As participants' estimations of the target's emotion were free response, to analyse these data the experimenter used the same coding scheme as described in Cassidy et al. , to codePositive: Any label which had a positive connotation; happy, glad, pleasantly surprised, pleased.Negative: Any label which had a negative connotation; displeased, unhappy, disappointed, angry, upset.Pretend: Any label which referred to the participant concealing negative emotions; hiding disappointment, fake smile, politely accepting.Confused: Any label which did not have an explicit positive or negative connotation. For example, surprised, confused, puzzled, thoughtful.Are individuals with ASD less accurate when inferring gift in both conditions? Table F = 0.3, P = 0.9) or group  = 2.4, P = 0.1). There was a three way interaction between group, condition and gift  = 7.2, P < 0.001). Simple main effects analysis showed participants with ASD were only significantly less accurate than controls when inferring who received Monopoly money in the static condition  = 8.5, P < 0.01).A three way mixed ANOVA compared group , condition  and percentage of correct gift responses . There was no significant effect of condition  = 8.1, P < 0.01), and significantly less accurate when inferring who received Monopoly money  = 18.1, P < 0.001) in the static (compared to the dynamic) condition. There was no significant difference in correct homemade gift inferences between the two conditions  = 2.1, P = 0.1).Simple main effects analysis showed participants with ASD were significantly more accurate when inferring who received a chocolate gift  = 9.9, P < 0.01), and marginally significantly less accurate when inferring who received a homemade gift  = 0.8, P < 0.05) in the static (compared to the dynamic) condition. There was no significant difference in correct Monopoly money  = 1.4, P = 0.2) inferences between the two conditions.The typical control group were significantly more accurate when inferring who received a chocolate gift  = 9.8, P < 0.01), regardless of gift type  = 2, P = 0.14).A two way mixed ANOVA showed that the static picture was displayed longer in the ASD than the typical control group  = 4.1, P < 0.01). To explore this interaction, simple main effects analysis compared the percentage of correct to incorrect responses in each condition and group separately, followed up with Bonferroni corrected t‐tests.Table P < 0.001) and homemade (P < 0.001) inferences  = 18.1, P < 0.001); significantly more correct homemade inferences than incorrect Monopoly money (P < 0.01), but not chocolate (P = 0.9) inferences  = 20.7, P < 0.001); participants with ASD did not give significantly more correct chocolate inferences than incorrect homemade or Monopoly money inferences  = 0.8, P = 0.5).Participants with ASD gave significantly more correct Monopoly money inferences than incorrect chocolate (P < 0.001) and homemade (P < 0.001) inferences  = 26, P < 0.001); significantly more correct homemade inferences than incorrect Monopoly money (P < 0.001), but not chocolate (P = 1) inferences  = 39.3, P < 0.001); typical controls did not give significantly more correct chocolate inferences than incorrect homemade or Monopoly money inferences  = 0.4, P = 0.7).Typical controls gave significantly more correct Monopoly money inferences than incorrect chocolate  = 0.01, P = 0.9). Participants with ASD gave significantly more correct homemade inferences than incorrect chocolate inferences (P < 0.05), but not incorrect Monopoly money (P = 0.053) inferences  = 4.3, P < 0.05); and significantly more correct chocolate inferences than incorrect homemade inferences (P < 0.01), but not incorrect Monopoly money (P = 1) inferences  = 7.1, P < 0.01).Participants with ASD did not give significantly more correct Monopoly money inferences than incorrect chocolate or homemade inferences (P < 0.001) and homemade (P < 0.01) inferences  = 11.1, P < 0.001); significantly more correct chocolate inferences than incorrect homemade (P < 0.05) and incorrect Monopoly money (P < 0.001) inferences  = 13.3, P < 0.001); but not significantly more correct homemade inferences than incorrect Monopoly money or chocolate inferences  = 1, P = 0.4).Typical controls gave significantly more correct Monopoly money inferences than incorrect chocolate (In the static (compared to the dynamic) condition, both groups made significantly more correct chocolate inferences, but individuals with ASD gave significantly less correct Monopoly money inferences. This is reflected in the pattern of participants' errors; participants with ASD could only distinguish reactions to chocolate and homemade in the static condition, and reactions to Monopoly money from chocolate and homemade in the dynamic condition.A similar analysis approach to Cassidy et al.  is adopt2(1) = 17.6, P < 0.01; ASD group, Lχ2(1) = 12.1, P < 0.01) and dynamic condition  = 24.4, P < 0.01; ASD group, Lχ2(1) = 13.77, P < 0.01), or when the gift inferred was incorrect in the static  = 13.85, P < 0.01; ASD group, Lχ2(1) = 14.1, P < 0.01) and dynamic condition  = 15.8, P < 0.01; ASD group, Lχ2(1) = 8.9, P < 0.05).Results showed that both groups gave significantly more consistent and less inconsistent gift and emotion inferences than predicted by the model, when the gift inferred was correct in the static  in the static condition as to the eyes, mouth and body. In the dynamic condition, fixations were visually coded as to the eyes, mouth or body by the experimenter. Perusal of the raw eye‐tracking data showed loss of calibration (indicated by fixations made outside of the eye‐tracking area) was more prevalent in the ASD group. To control for differences in calibration quality between groups, ratios were calculated for attention to the eyes of the face (eye:mouth ratio = eyes / eyes + mouth) and to the face of the person (face:person ratio = eyes + mouth / eyes + mouth + body). Higher values for the eye to mouth ratio denote a greater proportion of fixations/duration of fixations on the eyes of the face. Higher values for the face to person ratio denote a greater proportion of fixations/duration of fixations to the face of the person.A three way mixed ANOVA compared group as a between subjects factor with two levels , condition as a within subjects factor with two levels  and ROI as another within subjects factor with two levels , for the percentage number/duration of fixations. Data were collapsed across the three gifts as the pattern of results did not significantly differ between gift types Table .F = 4.3, P = 0.046). There was a significant main effect of ROI; proportion of fixations were significantly higher to the face of the person (89.3%) than the eyes of the face  = 208, P < 0.001). The interaction between condition, ROI and diagnosis failed to reach significance  = 3.2, P = 0.08); those with ASD tended to be less focused on the eyes of the face in the dynamic condition, and to the face of the person in the static condition  = 3.8, P = 0.058).For percentage number of fixations there was a significant main effect of condition; percentage number of fixations to the eyes of the face and face of the person were significantly higher in the dynamic (69.8%) than the static 65%) condition  = 177, P < 0.001). The interaction between condition, ROI and diagnosis failed to reach significance  = 3, P = 0.09); those with ASD tended to spend less time looking to the eyes of the face in the dynamic condition, and to the face of the person in the static condition  = 2.6, P = 0.1).For proportion of fixation duration, there was a significant main effect of ROI; proportion of fixation duration was significantly longer to the face of the person (92.3%) than the eyes of the face  condition, and significantly less accurate than controls, despite viewing the pictures for significantly longer than typical controls. The pattern of errors reflects this significant change in performance between the two conditions. In the dynamic condition participants with ASD were more likely to confuse reactions to chocolate and homemade gifts but not Monopoly money, similar to the results found in Cassidy et al. . HoweverBoth groups systematically attributed different emotions to each gift in both conditions. This suggests , or a static picture of a mixed emotional expression in the absence of informative speech content (smiling in confusion). However, adults with ASD can process subtle visual cues distinguishing genuine from feigned smiles if given time to peruse these. These subtle difficulties cannot be revealed using static stimuli. Future studies must explore what factors contribute to the emotion processing difficulties adults with ASD experience using real life social situations.


Symbiosis is one of the most fundamental relationships between or among organisms and includes parasitism (which has negative effects on the fitness of the interacting partner), commensalism (no effect), and mutualism (positive effects). The effects of these interactions are usually assumed to influence a single component of a species’ fitness, either survival or fecundity, even though in reality the interaction can simultaneously affect both of these components. I used a dual lattice model to investigate the process of evolution of mutualistic symbiosis in the presence of interactive effects on both survival and fecundity. I demonstrate that a positive effect on survival and a negative effect on fecundity are key to the establishment of mutualism. Furthermore, both the parasitic and the mutualistic behaviour must carry large costs for mutualism to evolve. This helps develop a new understanding of symbiosis as a function of resource allocation, in which resources are shifted from fecundity to survival. The simultaneous establishment of mutualism from parasitism never occurs in two species, but can do so in one of the species as long as the partner still behaves parasitically. This suggests that one of the altruistic behaviours in a mutualistic unit consisting of two species must originate as a parasitic behaviour.The online version of this article (doi:10.1007/s00114-014-1175-1) contains supplementary material, which is available to authorized users. Serratia symbiotica, reduces its host’s fecundity and growth rate under normal conditions, but promotes its survival after the removal of an essential obligate endosymbiont, Buchnera  and mutualistic (positive) effects on the partner are equal. I focus on a situation where mutualism never evolves in a well-mixed population, but by incorporating spatial structure, I show that mutualism can evolve from parasitism in a host-symbiont system. This can occur if the symbiont’s parasitic behaviour benefits its survival by exploiting the host’s resources while it simultaneously devotes its resources to its host’s survival. I also show that mutualism never becomes established simultaneously in two parasitic species.AE, AP, and AM and those for Sp. B BE, BP, and BM. The total frequency for each species must be equal to one, as follows:I constructed a dual lattice space model in which the two species, Sp. A and Sp. B, each inhabit one lattice. Lattices exist in parallel, following previous studies  b′A, respectively, where (0 ≤ qA ≤ 1). The sum of these two quantities is b′A. Parasitism by Sp. A enhances its fecundity and survival, denoted pAbA and (1−pA) bA, respectively, where (0 ≤ pA ≤ 1). The sum of these quantities is bA. In other words, when Sp. B is a neutral host , the interaction with parasitic Sp. A results in reproductive rates of rA + pAbA and rB − qAb′A for Sp. A and Sp. B, respectively. Similarly, the mortality rates of Sp. A and Sp. B become dA − (1 − pA ) bA and dB + (1 − qA ) b′A, respectively. The quantities qA and pA represent the relative effects of parasitism on the fecundity and survival of the parasite and recipient, respectively. The total cost to Sp. B (b′A) of the parasitism does not necessarily equal the total advantage to the parasite, Sp. A (bA).When an individual of Sp. A is a parasite, its interaction with an individual of Sp. B takes the form of exploitation. This results in a reduction in fecundity and survival for Sp. B, denoted uAcA and (1−uA) cA, respectively, where (0 ≤ uA ≤ 1). The sum of these two quantities is cA, which is the total quantity of the resource available to Sp. B. These resources increase the fecundity and survival of Sp. B by vAc′A and (1−vA) c′A, respectively, where (0 ≤ vA ≤ 1). When mutualistic Sp. A interacts with naïve host Sp. B, their reproductive rates become rA + pAbA − uAcA and rB − qAb′A + vAc′A, respectively. Similarly, their mortality rates become dA − (1 − pA) bA + (1−uA) cA and dB + (1 − qA) b′A−(1−vA) c′A, respectively. A symbiotic relationship with a mutualistic strain of Sp. A is therefore effectively commensalism for Sp. B if qA = vA and c′A = b′A, because the overall effect of such a mutualist on its partner is zero. Similar notation is applied to the parasitic and mutualistic strains of Sp. B, i.e., rB , dB, bB, pB, b′B, qB, cB, uB, c′B, and vB . In reproductive and mortality rates , the first subscript represents the symbiotic recipient, and the second represents the actor. The corresponding equations for BP and BM can be formulated in a similar manner.The subscript From Eqs.  and 12, AM continuously decreases. The population of the mutualist strain therefore never increases for any parameter values under unlimited dispersal conditions. This result also applies to Sp. B. Thus, mutualism cannot evolve in either species in this system.Because the right-hand side of Eq.  is alwayRA/4 for each empty neighbouring site, where RA is the reproductive rate of the parent individual. This rate depends on the status of the corresponding site on lattice B. (3) If there is an individual of Sp. B present at the corresponding site on lattice B, the same process is applied to this individual. (4) The Sp. A individual is killed with probability DA, which depends on the status of the corresponding site on lattice B. (5) The same procedure is conducted for the corresponding Sp. B individual. (6) The above process is repeated 25 × 25 times. Mutant individuals are then introduced at random, irrespective of whether the site is occupied or not, at a frequency of 0.04 . If a wild-type individual is present, it is replaced by the mutant individual. After running this simulation for 1,000 generations, the frequency of mutant individuals in the wild-type population is noted. I ran the above procedure 100 times to derive the ensemble mean of the resulting frequencies. The invasiveness of the mutualistic strain was examined by recording the frequency with which its population increased after the introduction. The invasiveness of mutant parasitic individuals into a wild-type mutualistic population  is also examined to check the robustness of mutualism.Now, consider the case for limited dispersal. I employed a simulation to investigate the ability of the mutant strains to invade populations of the “wild-type” strains, using Monte-Carlo simulations following the procedure described by Yamamura et al. . I constbX = b′X and cX = c′X , and ran the simulation as coded above, using several values for cX and bX. I restricted the parameters pX, qX, uX, and vX to either zero or one, because the number of possible combinations of intermediate values between zero and one is unfeasibly large. I also assume symmetry between the effects of parasitism and mutualism, i.e., cA = bB and cB = bA, and between the reproductive and mortality rates of each species, i.e., rA = rB = 0.5 and dA = dB = 0.2.In this study, I focus on evolutionary conditions that cause differential influences of interspecific interaction on the two fitness components: fecundity and survival. For simplicity, I therefore assume symmetry between the quantities of resources that are lost and gained by each species, i.e., cA = bA = 0 , whereas Sp. B behaves as either a parasite or a mutualist with respect to Sp. A, depending on the values of pB, qB, uB, and vB. I examined the ability of a mutualistic strain , described by pB, qB, uB, and vB , to invade a population of the parasitic strain (Sp. BP), described by pB and qB , under the condition that the behaviour of their neutral host, Sp. A, is fixed as cA = bA = 0. In most cases, the mutualistic strain failed to invade into the parasite population. However, when  =  for both strains and  =  for the mutualistic strain, the results were more interesting. In this scenario, Sp. BP used resources affecting the fecundity of Sp. A for its survival, but Sp. BM increased the survival of Sp. A by reducing its own fecundity. I conducted a test of reciprocal invasiveness under this scenario, i.e., the invasion of Sp. BP into a Sp. BM population. Figure BM) 1,000 generations after the generation in which it was introduced into a population of Sp. BP. The mutualists achieved higher frequency when both the exploitation by Sp. B (bB) and the contribution made by Sp. BM (cB) were high. Figure c′B > cB  = 0,  for bothcB = bB = 0). On the horizontal axis, the situation is identical to Sp. A interacting with Sp. BP, because Sp. BM does not incur any cost for its mutualistic behaviour . In fact, Sp. A increases its population when Sp. BM is strongly exploitative and also pays a large cost, whereas Sp. A’s population decreases when the mutualistic strain is strongly exploitative and pays a small cost. Figure bB and cB are high, as does that of its host, Sp. A. Paying a cost greater than the benefit derived from exploiting Sp. A results in a decrease in the population of Sp. BM. This leads to an increase in the population of Sp. BP after it invades the mutualist population , (qA = qB), (uA = uB), and (vA = vB). In this simulation, the mutualistic strains each pay the same cost (cA = cB = 0.1). Under these conditions, the mutualistic strains never increase their populations after invasion except when  =  =  and  =  = . Here, I define success in the establishment of mutualism as an increase in the population of the mutualistic strain, i.e., the ensemble-mean frequency of each mutualistic strain should be >0.04 after the invasion. Figure i, Bj), where . The ensemble-mean frequency that results when Sp. AM interacts with Sp. BP is shown in Fig. bA = 0.15 , the parasitic strains never successfully invade mutualistic populations. A mutually mutualistic relationship between the two species will therefore always be robust, although such an association can only become established infrequently. This scenario is unrealistic because the mortality rates of both mutualists fall below 0.0 if the exploitation rate is higher than 0.1.I then simulated the case where both species behave as parasites at the beginning and mutualists invade on both lattices. For simplicity, model parameters were symmetrical between species, i.e., Online resource 2 (DOCX 347 kb)Below is the link to the electronic supplementary material.


Many everyday actions are implicit gambles because imprecisions in our visuomotor systems place probabilities on our success or failure. Choosing optimal action strategies involves weighting the costs and gains of potential outcomes by their corresponding probabilities, and requires stable representations of one's own imprecisions. How this ability is acquired during development in childhood when visuomotor skills change drastically is unknown. In a rewarded rapid reaching task, 6‐ to 11‐year‐old children followed ‘risk‐seeking’ strategies leading to overly high point‐loss. Adults' performance, in contrast, was close to optimal. Children's errors were not explained by distorted estimates of value or probability, but may reflect different action selection criteria or immature integration of value and probability information while planning movements. These findings provide a starting point for understanding children's risk‐taking in everyday visuomotor situations when suboptimal choices can be dangerous. Moreover, children's risky visuomotor decisions mirror those reported for non‐motor gambles, raising the possibility that common processes underlie development across decision‐making domains. Comparing participants' choices in a rewarded rapid reaching task with those that would be optimal for maximizing reward, we found that unlike adults, children aged 6 to 11 years followed ‘risk‐seeking’ strategies leading to loss of points.Children's errors were not explained by distorted estimates of value or probability, but may reflect changes in action‐selection criteria or protracted development of the ability to integrate value and probability information when planning movements.The finding that the developing system favours risky visuomotor choices forms a first step towards understanding how children deal with risk in everyday activities, when suboptimal visuomotor choices can have dangerous consequences.Children's risky visuomotor decisions mirror those reported for non‐motor gambles, raising the possibility that common processes underlie development across decision‐making domains.Whether crossing a busy road, throwing a ball into a basket, or reaching for one cup without knocking another over, humans continuously make risky visuomotor decisions. The best action strategies maximize the probabilities of desirable outcomes while minimizing those of negative ones. For example, we would like to get across the road promptly, but without being hit by a car. Identifying efficient trade‐offs between potential risks and rewards in everyday behaviour can be highly adaptive. Solving this problem is complex, however. It involves correctly judging one's own capabilities – for example, the probability of a reach missing its target – and combining this estimate with information about costs and gains in the environment. Nevertheless, laboratory tasks measuring adults' performance have often found them to be ideal in this respect, maximizing their gains on rewarded tasks by taking into account their own visuomotor capabilities  in the sensorimotor system. Like an optimal gambler, an optimal action planner should choose the lottery or action strategy with the largest expected gain.Visuomotor risk stems from the uncertainty inherent to perception and motor control. For example, a paper ball thrown at a basket may land anywhere along a bivariate probability distribution around the aiming‐point due to noise in location estimates of the arm, hand, ball and basket, and in the neural signals that activate muscles for motor execution  decisions across different conditions in a visuomotor task require precise online estimation of different outcome probabilities (e.g. the chance of missing), and the correct weighting of outcome rewards by these estimates to trade off potential gains and losses. Research on sensory cue integration suggests that it is only at around age 8–10 years that children learn to take their own perceptual uncertainty into account to optimize their perceptual decisions , 18 8‐ and 9‐year‐olds , 15 10‐ and 11‐year‐olds , and 15 adults . All but three were right‐handed. During training, subjects learned to limit their time‐outs (failures to reach the screen on time) to 5% of the trials or less . Those who timed‐out more frequently during the main task could be trading off speed for accuracy, potentially leaving more time to make online reach adjustments towards the target. This would confound measures of visuomotor strategy selection with movement corrections after the decision process. Therefore, additional subjects with >5% ‘time‐out’ errors (see Procedure) were excluded from the analyses . Some time‐outs were likely caused by occasional lapses in attention rather than trading off speed for accuracy (this would not affect aiming strategy). Because sustained attention develops with age, this probably contributes to higher exclusion rates in younger groups. All participants had normal or corrected‐to‐normal vision and no known neurological or psychological disorders.Participants were children aged 6 to 11 years and adults: 15 6‐ and 7‐year‐olds , at 26 cm distance for adults, 20 cm for children. A wireless numeric keypad was mounted on the table, centred before the monitor 6 cm from the participant's trunk  radius. Target circles were unfilled, while penalty circles were filled with a darker shade of their yellow, blue or grey outline colour . Training trials were identical to the experimental trials described below, except that target hits did not count towards the final score, and the (grey) penalty circle was irrelevant.Each training trial started with a central fixation cross. Participants pressed the ‘Enter’ key with the index finger of their dominant hand to trigger presentation of the blue frame , and their explicit knowledge of their own visuomotor ability (hit probability task).There were 10 blocks of 20 trials, a total of 50 per condition. Penalties and payoffs were explained before the first and sixth block when penalty rules changed. Before each block, participants were asked to repeat these back to ensure that all remembered the current outcome values. Running scores were displayed graphically in a chart on the screen .they would prefer to lose . For example: would you prefer to lose 5 points once (5 × 1), or to lose 1 point four times (1 × 4)? The task was described in terms of losses to best match the penalty situation in the main experiment. To make the problem concrete, subjects received 10 stickers or snacks and were informed that one of their answers, randomly drawn at the end of the task, would determine how many they would have to give back. For each age group and comparison value, we counted how often the constant sum was chosen over the variable sum. We used the standard psychophysical method of fitting a cumulative Gaussian distribution through the resulting proportions (using the Psignifit toolbox for Matlab), and determining the Point of Subjective Equality (PSE); see Figure x‐axis at which the comparison and standard are chosen with equal (0.5) probability, and therefore measures the point at which they are, on average, judged to be equal. Deviations of the PSE from the correct value of 5 (1 × 5) thus provide information about systematic under‐ or overestimations of the value of losing 5 points relative to the value of losing 1 point multiple times.All subjects took part in a two‐alternative forced choice task with 35 trials. On each trial they chose between a pair of values (7 repetitions of 5 pairs). Each pair consisted of the standard value of ‘5 points × 1’, and a comparison in which ‘1 point’ was multiplied with the values 3 to 7 . For each pair, subjects were asked to select the value In a hit probability task, subjects were presented with five circle sizes in a display such as the one used in the experiment. In 10 blocks, all circles were presented in random order . The circles were presented in isolation , and their locations were jittered as in the experiment. Circle sizes were scaled individually for each subject based on their own visuomotor variance measured during the main task. The five circle sizes seen by each subject corresponded to hit probabilities of 0.1, 0.3, 0.5, 0.7, and 0.9. On each trial, subjects judged ‘how many times out of 10’ they would successfully hit the circle, from the same position and with the same time constraint as in the main experiment. This provided their estimated probability of hitting (e.g. ‘5 out of 10’ = 0.5). Judged probabilities were averaged over 10 repetitions . Mean judged probabilities were averaged across all subjects in an age group, and compared with the true probabilities (95% error bars).mean X, mean Y), horizontal and vertical variance (varX and varY), and total score were computed for each subject and condition using the remaining data.On each trial, reaction time (target onset to screen touch), touched horizontal (X) and vertical (Y) screen position, and score were recorded. ‘Time‐out’ trials were excluded from the analysis . Variance estimates for each subject were therefore obtained by pooling data across conditions. The expected consequences of aiming towards any given location on the screen were modelled as depending on a bivariate Gaussian distribution described by each participant's own X and Y variance. The gain expected from pointing at any location is given by a weighted sum of all the possible outcomes, in which each outcome  is multiplied by the probability of a reach landing in a location with this outcome. For each participant and condition, we computed the ‘gain landscape’ describing the gain expected from aiming for each pixel in a 200 × 200 grid around the target centre  of this landscape  = 30.7, p < .01) and in accordance with age‐related shortening of individual time‐limits  = 13.6, p < .01; see Table F = 5.77, p = .002; Y: F = 3.58, p = .019), with significantly larger variances than adults only for 6‐ to 7‐year‐old children for both X and Y  for all conditions. Accordingly, the height of subjects' aiming‐points did not vary by condition  = 1.62, p = .19; Condition × Age: F = 1.43, p = .18). Aiming‐points did, however, vary significantly with Age  = 3.58, p = .019); see Table 0 (adults: t(14) = −1.44, 6–7: t(14) = −0.33), both p‐values > .1), 8‐ and 9‐year‐olds and 10‐ and 11‐year‐olds tended to aim slightly below this point (10–11: t(14) = −8.4, p < .001; 8–9: t(17) = −2.6, p = .02).The Y‐coordinate with the highest predicted score fell at the centre of the stimulus configuration  = 63.51, p < .001) found a slope of 0.97 and intercept of 0.01  = 20.45, p < .001; Offset: F = 22.7, p < .001; interaction not significant, F = 2.52, p = .134). Moreover, adults shifted by the correct distance to maximize their expected gain given their own visuomotor precision; an ANOVA comparing actual and optimal aiming‐points across the four conditions showed that adults' mean X‐coordinates were statistically indistinguishable from their gain‐maximizing X‐coordinates  = 0.024, p = .88; actual‐optimal × condition interaction: F = 0.058, p = .91).To test whether adults were able to find their own gain‐maximizing coordinate by weighting outcome values by their probabilities, we compared their actual and predicted optimal aiming‐points Figure . A lineaWith age, movement end‐points shifted closer towards the gain‐maximizing X‐coordinates, and regression slopes for optimal vs. actual points Figure  clearly F = 54.38, p < .001; Actual‐Optimal × Age interaction: F = 6.68, p = .001). Distances between actual and optimal aiming‐points also varied with condition; they were larger in those conditions for which the gain‐maximizing coordinate required a larger shift from the target centre; see Figure F = 5.9, p = .01; this effect did not depend on age: F = 0.78, p = .54). Follow‐up ANOVAs revealed that even by ages 10 and 11 years, children's mean X‐coordinates still significantly undershot the predicted gain‐maximizing location  = 29.28, p < .001; 8–9 years: F = 18.23, p = .001; 6–7 years: F = 44.15, p < .001). Thus, even in relatively late childhood, movement strategies were suboptimal, and carried unnecessarily high risks of touching the penalty.A three‐way Actual‐Optimal × Condition × Age ANOVA confirmed that distances between actual and optimal aiming‐points become smaller with age from childhood to adulthood  = 7.68, p = .02; 8–9 years: F = 23.61, p < .01; 6–7 years: F = 5.15, p = .04; for Offset, 10–11 years: F = 5.53, p = .03; 8–9 years: F = 6.87, p = .02; 6–7 years: F = 5.63, p = .03); no interaction in any group, largest F = 0.20, p = .63. The deviation between the optimal and actual aiming‐point in childhood did not significantly depend on whether the low or high penalty was presented first  = 3.49, p = .069, ‘far 1’: F = 0.79, p = .38, ‘near 5’: F = 0.001, p = .97 ‘far 5’: F = 0.19, p = .67). It is therefore unlikely that these sub‐optimal aiming strategies were due to rule switching difficulties when penalties changed halfway through the task.While children up to age 10 and 11 years systematically mis‐localized the gain‐maximizing coordinate, some sensitivity to gain landscape changes across conditions was already evident by 6 and 7 years. As Figure t‐tests of slope versus 0: All p‐values > .05, with Sidak‐correction for 252 comparisons; except for one 10‐ to 11‐year‐old in the ‘near 1’ condition). So, in line with previous findings . The data points plot distances between participants' actual and gain‐maximizing X‐coordinates against their obtained rewards . Obtained and model‐predicted scores are likely to differ somewhat due to noise, since movement end‐points are ‘sampled’ probabilistically from a subject's visuomotor distribution. However, most data points fall within the range of the predicted curves, revealing a correspondence between model predictions and task performance.Subjects were not explicitly instructed to aim for gain‐maximizing coordinates, but only to score as many points as possible. A crucial question, therefore, is whether children's deviations from gain‐maximizing X‐coordinates did indeed result in reduced scores. Otherwise, children might have had little reason to choose closer‐to‐optimal strategies. Solid curves in Figure mg in Table p = .35 and .01, respectively), but not than 6‐ and 7‐year‐olds (p = .42). Therefore, any differences in score between the oldest and youngest groups will be mainly due to a different directional bias in movement selection .Expected gain curves are asymmetrical, with lower predicted scores for movement end‐points undershooting the gain‐maximizing coordinate (left of the peak) than for those shifting too far (right of the peak) by the same distance. In childhood (three bottom rows), many end‐points fall left of the peak , at X‐coordinates with relatively lower predicted scores. Obtained scores are accordingly lower. In contrast, adult movement end‐points  = 5.07, p = .003), but this effect was modulated by condition  = 2.91, p = .03). Follow‐up ANOVAs showed that scores only significantly differed by age in the ‘near 5’ condition with the steepest gain landscape; ‘near 5’ condition: F = 3.78, p = .015, all other conditions: largest F < 1.44, p = .24). In the ‘near 5’ condition, all three child groups scored significantly below their optimal predictions (10–11 years: t(14) = −4.20, p = .01 8–9 years: t(17) = −2.56, p = .02, 6–7 years: t(14) = −3.20, p = .006). Adults showed a non‐significant trend towards a sub‐optimal mean score in this condition (t(14) = −1.89, p = .08).To test whether age groups differed significantly in their abilities to maximize gain, scores were expressed as percentages of the predicted maximum score Figure  and compwhy children aimed so ‘dangerously’ close to the penalty area (a risk‐seeking strategy).In sum, these findings clearly show that children aged 6 to 11 years chose reaching strategies with an overly high risk of hitting the penalty circle, and that this had detrimental effects on the rewards they obtained. For example, 6‐ and 7‐year‐olds won less than 50% of their potential points in the most challenging condition . However, this summary measure of numerical distance distortion did not predict subjects' visuomotor strategies: the correlation of RMSE with absolute deviation between Xmean and Xopt was not significant for any single condition, or for the mean of all conditions , and hence did not explain performance on the reaching task.Young children often show nonlinearities in their understanding of number, typically underestimating larger values ; see Supplemental Methods for details. Cumulative Gaussians were fitted to proportions of trials on which participants preferred to lose the variable multiple  over losing 5 points; Figure varX, this would lead them to underestimate the shift from penalty required to maximize their winnings. To test whether probability distortions explained children's tendency to undershoot the gain‐maximizing coordinate, understanding of own visuomotor precision was measured after the main experiment. Participants gave verbal estimates of how many times out of 10 they could hit target circles of different sizes with the same setup and time limit as in the reaching task; see Supplemental Methods for details. In Figure et al., Forming stable representations of developing visuomotor skills might be challenging; if younger subjects distorted outcome probabilities by underestimating their own pointing variance To advance understanding of when and how optimal visuomotor decision‐making develops in childhood, 6‐ to 11‐year‐olds and adults were asked to rapidly reach towards targets to win as many points as possible, whilst avoiding touching an overlapping penalty area. Because time was limited, movement end‐points were imprecise, placing probabilities on missing or hitting the target and penalty. The implicit task was to locate the aiming‐point giving the highest expected score by accounting for this imprecision. By quizzing subjects about the point rules between blocks, we ensured that all could remember these throughout the experiment. To maximize their expected winnings, subjects should shift their aiming‐points further from the penalty area when penalties were greater and closer to the target. The precise amount of shift required to optimize performance depended on each participant's own visuomotor precision.and on participants' own visuomotor precision, did not develop until much later. Unlike adults, even the oldest (10‐ and 11‐year‐old) group of children still differed significantly from optimal. Children of all ages displayed a group‐level tendency to place movement end‐points too close to the penalty circle to maximize their scores  only comprised 25% of the trials. Did children stick with risk‐seeking strategies because they were not sufficiently motivated to optimize their scores? This is not supported by the data; ANOVAs revealed that children were sufficiently motivated to change their aiming strategy across conditions – except that they systematically placed their new aiming‐points too close to the penalty area. Further analyses revealed that this was not due to difficulties with switching between penalty rules or slower learning of where in the display most points could be won at younger ages. The patterns of children's errors could reflect specific distortions in estimates of outcome values or probabilities . However, control tasks measuring value representation and understanding of own visuomotor precision Figure A–C proviet al., et al., This leaves us with two interesting explanations. Firstly, sub‐optimal reaching might result from incorrect computation of the optimal strategy by weighting of outcome values by probabilities. Immature weighted averaging would be in line with recent developmental studies showing that abilities to average multiple sensory estimates to make optimal perceptual decisions are still developing until the 8th–11th year of life (Gori Alternatively, children might be able to compute the gain‐maximizing strategy, but not employ this information to optimize performance. Instead, they might pursue goals other than maximizing gain, such as striving for variation in the results of their reaches or fulfilling a desire to hit the target as often as possible, irrespective of overall winnings. Both could lead to avoidance of more conservative strategies with higher score expectations (for similar explanations of risk‐taking in rhesus monkeys, see Hayden, Heilbronner, Nair & Platt, To better understand the underlying representations and mechanisms, future studies should compare how the expected gain of an embodied gamble is represented in the developing brain. In adults, for example, increasing the expected value of a ‘classic’ gamble yields parametric activation increases in brain regions associated with reward and decision‐making, such as the ventral striatum and orbitofrontal cortex (e.g. Peters & Büchel, This work significantly extends findings from other decision‐making domains. It was recently proposed that classical and visuomotor decision‐making rely on different neural mechanisms because adults show near‐optimal performance in the visuomotor domain but display well‐known value and probability distortions when making equivalent choices in a gambling task (Wu, Delgado & Maloney, In sum, we found a clear, age‐related shift towards more optimal visuomotor decision‐making across childhood and adulthood, with overly risk‐seeking action selection between ages 6 and 11 years. Choosing actions with overly high risks of negative results in real‐life visuomotor tasks can clearly be dangerous, and could be a factor significantly contributing to higher accident rates in childhood Kingma, .Data S1. Supplementary Methods.Click here for additional data file.


Mild cognitive impairment (MCI) is a heterogeneous cognitive status that can be a prodromal stage of Alzheimer’s disease (AD). It is particularly relevant to focus on prodromal stages of AD such as MCI, because patho-physiological abnormalities of AD start years before the dementia stage. Medial temporal lobe (MTL) atrophy resulting from AD lesions and cerebrovascular lesions  are often revealed concurrently on magnetic resonance imaging (MRI) in MCI subjects. Personality changes have been reported to be associated with MCI status and early AD. More specifically, an increase in neuroticism and a decrease in conscientiousness have been reported, suggesting that higher and lower scores, respectively, in neuroticism and conscientiousness are associated with an increased risk of developing the disease. However, personality changes have not been studied concomitantly with pathological structural brain alterations detected on MRI in patients suffering from MCI. Therefore, the objective of the present study was to assess the relationship between MTL atrophy, WML, lacunar strokes, and personality traits in such patients. The severity of WML was strongly associated with lower levels of conscientiousness and higher levels of neuroticism. Conversely, no association was detected between personality traits and the presence of lacunar strokes or MTL atrophy. Altogether, these results strongly suggest that personality changes occurring in a MCI population, at high risk of AD, are associated with WML, which can induce executive dysfunctions, rather than with MTL atrophy. Mild cognitive impairment (MCI) is a heterogeneous cognitive status, which can be a prodromal stage of Alzheimer’s disease (AD)  performed within a year and diagnosed as MCI according to the European AD Consortium , a validated and reliable tool to assess global cognitive function  were highlighted by the use of bold in tables.Data were analyzed using JMP Pro  and R . Significant associations or differences  stated having experienced migraine, 31 were smokers (34.4%), 10 were above the at risk consummation of alcohol (11%), 44 had hypertension (48.9), 8 had diabetes (8.9%), 28 had high cholesterol levels (31.1%), 11 had coronary heart disease (12.2), 4 had chronic heart failure (4.4%), and 5 had atrial fibrillation (5.6%).p < 0.05) and extraversion (p < 0.001). A positive correlation was also observed between conscientiousness and extraversion (p < 0.05). However, no correlation was observed between conscientiousness and neuroticism.Correlations among personality traits are reported in Table F = 4.07; p < 0.05) and tended to have higher levels of neuroticism (p = 0.07). Openness to experience and agreeableness were associated with higher education level  = 4.36; p < 0.05; F = 3.46; p < 0.05, respectively). Alcohol consumption was associated with lower extraversion  = 8.75; p < 0.01) and higher neuroticism  = 4.09; p < 0.05). Migraine episodes and smoking were associated with lower agreeableness  = 8.70; p < 0.01; F = 4.06; p < 0.05, respectively). Hypertension was associated with lower openness to experience and extraversion  = 9.87; p < 0.01; F = 10.63; p < 0.05, respectively). Finally, a trend between hypercholesterolemia and neuroticism was observed but it did not reach the significant level (p = 0.06).Table F = 3.24; p < 0.05). In contrast, higher stages of subcortical or periventricular WML were associated with higher scores in neuroticism  = 3.95; p < 0.05 and F = 6.07; p < 0.01, respectively). Lower scores in conscientiousness were associated with subcortical  = 3.67; p < 0.05) but not with periventricular WML  = 2.66; p = 0.08). Finally, no other association was found between WML and the other personality traits .Table p < 0.01) but not with periventricular WML (p = 0.10) or MTL atrophy (p = 0.13). Similarly, levels of neuroticism were only associated with subcortical WML (p < 0.01).In the mixed model adjusted for age, sex, and education level Table , lower sp < 0.01) but not with periventricular WML (p = 0.27) or MTL atrophy (p = 0.15). Higher scores of neuroticism were associated with higher stages of subcortical WML (p < 0.05) and periventricular WML (p < 0.05).In the mixed model adjusted for age, sex, and education level including MTL atrophy and subcortical and periventricular WML simultaneously Table , lower sp = 0.001 and p = 0.29, respectively) and between neuroticism and subcortical WML . Second, because women tended to have higher scores in neuroticism, mixed models were run with BFI gender specific z-scores. It did not modify the relationship between neuroticism and moderate and severe periventricular WML  and between neuroticism and light, moderate, or severe subcortical WML . Finally, because migraine has been associated with scores in neuroticism, mixed models were adjusted for migraine. It did not modify the relationship between neuroticism and moderate and severe periventricular WML (p = 0.03), whereas it decreased the association between neuroticism and subcortical WML (p = 0.06).Sensitivity analyses were performed to take into account supplemental variables in addition to the variables already in the fully adjusted model. First, because alcohol consumption was associated with the score in neuroticism and a trend was observed between hypercholesterolemia and neuroticism, mixed models were adjusted for alcohol consumption and hypercholesterolemia. It did not modify the relationship between neuroticism and moderate and severe periventricular WML . As mentioned in Section “Methods,” the different MCI subtypes [i.e., amnestic versus non-amnestic and single versus multiple domain (Petersen, The study has several strengths. It is the first study examining associations between personality traits and the different kind of MRI abnormalities in MCI subjects, revealing new information about the relation between these personality traits and the MRI abnormalities. Also, the multiple adjustments with several confounders limited the effect of unknown factors.In an MCI population, we reported associations between personality traits and WML but not with the presence of lacunar stroke and MTL atrophy. These results suggest that personality changes observed in a MCI population, at high risk of AD, are initially associated with WML, which can induce executive dysfunctions, rather than with MTL atrophy. This study emphasizes the need of a longitudinal study to determine if personality traits are associated with conversion to AD with regards to brain structural changes.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


The aim of this study was to examine whether young adults in nonmarital romantic relationships experience better mental health and lower levels of mental health problems compared to single young adults. In addition, the current study also tested the hypothesis that perceived social support mediates the association between relationship status (single vs. partnered) and mental health, and mental health problems. Five hundred fifty three participants  aged 20–30 completed the Polish versions of General Health Questionnaire-28, Mental Health Continuum–Short Form, Social and Emotional Loneliness Scale for Adults–Short Form, and Multidimensional Scale of Perceived Social Support. Results indicated that single individuals reported lower emotional well-being than partnered individuals. No differences emerged between single and partnered individuals in regard to social and psychological well-being, as well in total well-being. Results also revealed no differences between single and partnered individuals in regard to somatic symptoms, anxiety and insomnia, social dysfunction, severe depression, and total mental health problems. Mediational analyses indicated the perceived social support mediates the association between partner status and mental health problems. The engagement in a stable intimate relationship is one of the most prominent social roles in late adolescence and young adulthood , and externalizing problems such as substance use and abuse  . This is to our knowledge the first study in Poland on relationship status, perceived social support, and mental health in young adults who are just entering into young adulthood. The aims of this study are twofold. First, we address the question of whether there are differences in mental health and mental health problems between young adults who are single and who are in nomarital romantic relationships. Based on previous research , while non-student participants with a higher education level constituted 51.20 % of the total sample (n = 283). The age of participants ranged from 20 to 30 years old . Women represented 60.60 % of the sample (n = 335) and men represented 39.40 % of the sample (n = 218). Participants resided in a large Polish city with a population exceeding 500,000. All the respondents were heterosexual, never married, and had no children, but declared that they wanted to have a lifetime partner in the future. Two hundred and seven participants (37.43 %) reported being single at the time of the assessment, while 346 participants (62.57 %) had a nonmarital romantic partner. Being single was defined as “not in a committed relationship for at least 6 or more months, but wanting to become committed in the near future (within the next year or so)”, and being in a nonmarital romantic relationship was defined as “in a nonmarital romantic relationship for at least 6 or more months, and wanting to be committed in the near future (within the next year or so)” . Of these, 135 participants were removed because they were married, widowed, divorced, separated, older than 40 years old or because of incomplete data, yielding a final sample of 553 participants. The university students constituted 48.80 % of the total sample . In the current study the bimodal scoring procedure  was applied. Using the conventional bimodal GHQ scoring method, there is a range of 0–28 with a score above a threshold of 4 indicative of psychiatric disorder. In the present study the internal consistency for the subscales was α = .75, α = .80, α = .77, α = .79, and α = .89 for Somatic symptoms, Anxiety, Social dysfunction, Severe depression, and for the Total scale, respectively. to 5 (every day). The MHC-SF also provides a categorical diagnosis of mental health, namely a diagnosis of flourishing is made if someone feels 1 of the 3 hedonic well-being symptoms “every day” or “almost every day” and feels 6 of the 11 positive functioning symptoms “every day” or “almost every day” in the past month. Languishing is the diagnosis when someone feels 1 of the 3 hedonic well-being symptoms “never” or “once or twice” and feels 6 of the 11 positive functioning symptoms “never” or “once or twice” in the past month. Individuals who are neither “languishing” nor “flourishing” are then coded as “moderately mentally healthy.” The short form of the MHC has shown excellent internal consistency (>.80) and discriminant validity in adolescents and adults in the U.S., in the Netherlands, and in South Africa. In the present study the internal consistency for the subscales was high: α = .87 for Emotional well-being, α = .80 for Social well-being, α = .81 for Psychological well-being, and α = .89 for Total mental health. to 7 (very strongly agree). Higher scores on each of the subscales indicate higher levels of perceived support, and a sum of the three scales yields a global satisfaction with perceived support score. Zimet et al.  = 7.98, p < .001, η2 = .04.We first examined the hypothesis that individuals in committed relationships would experience better mental health  than single young adults. In order to examine possible mean differences between single individuals and individuals in nonmarital romantic relationships in regard to mental health, a one-way multivariate analysis of variance was used. The analysis resulted in a significant multivariate effect of relationship status on mental health, Wilks’s Λ = .96, d = .24 which is close to what Cohen  = 1.42, ns, η2 = .01 . A one-way multivariate analysis of variance resulted in a non-significant multivariate effect of relationship on mental health problems, Wilks’s Λ = .99, χ2 = 44.14, df = 15, p < .001, χ2/df ratio = 2.43, NFI = .96, CFI = .98, RMSEA = .06, 90 % c.i. = .04–.08. Next we analyzed the structural model depicted in Fig. Structural equation modeling in AMOS 20.0 was used to test whether perceived social support mediated the association between relationship status and mental health (hypothesis three). For this analysis, partner status  was the exogenous variable, perceived social support score was treated as the mediating variable, and mental health was the dependent variable. Perceived social support was treated as a latent variable indicated by amount of support available from friends, family, and a significant other. Similarly, mental health was represented as a latent variable, indicated by anxiety and depression from the GHQ and by psychological well-being and emotional well-being from the MHC-SF scale. Prior to evaluating the fit of the structural model, a measurement model was analyzed in which correlations were specified between all possible pairs of observed or latent variables in the model. The initial results indicated that the fit of the model could be improved by specifying an additional correlation between the anxiety and depression error terms of the mental health latent variable, and between the partner status observed variable and the error terms associated with friend and significant other social support. With these correlations specified, the model provided a good fit to the sample data, Because we were interested in comparing the direct effect of partner status on mental health problems to the corresponding indirect effect, through perceived social support, we specified both the direct and indirect effects in the model. The significance of the indirect effect was estimated with a bias-corrected bootstrapping procedure based on 2000 bootstrap samples to estimate standard errors and confidence intervals around the indirect effect.χ2 = 43.11, df = 15, p < .001, χ2/df ratio = 2.87, NFI = .96, CFI = .98, RMSEA = .06, 90 % c.i. = .04–.08. In this model, the path from partner status to perceived social support was significant  indicating that people in nonmarital romantic relationshipsThe results of this analysis suggested that this model provided a good fit to the sample data, β = −.55, p < .001, reflecting the fact that perceived social support was negatively associated with anxiety and depression and positively associated with psychological and emotional well-being. As predicted, there was a statistically significant indirect effect of partner status on mental health problems, through perceived social support, β = .08, p < .05. In contrast, the direct effect of partner status on mental health problems, controlling for perceived social support, was not statistically significant, β = .06, ns. This indicates the perceived social support mediates the association between partner status and mental health problems.reported greater overall social support than people who did not have a partner. Similarly, there was a significant association between perceived social support and the mental health latent variable, B = .091, p = .037) was virtually unchanged from the indirect effect in the original model . Therefore, the indirect effect of partner status on mental health, through social support, is not simply a consequent of lower significant other support among those without a romantic partner.To determine whether the indirect effect of partner status on mental health, through social support, was influenced by inclusion of the significant other social support scale, we re-estimated this indirect effect, after deleting that scale from the social support latent variable. The indirect effect without the significant other social support factor  than single young adults. This hypothesis was not supported as our analyses revealed no differences between single individuals and individuals in nonmarital romantic relationships in regard to mental health problems. This pattern of results contradicts prior findings indicating that in general commitment in romantic relationships is associated with benefits for people’s mental health and sense of well-being  = 10.64, p < .001. However, when removing this variable from the structural model depicted in Fig. M = 16.94) than partnered individuals did (M = 17.72), t(551) = 2.00, p < .05, suggests that their social support deficits are somewhat pervasive and not constrained exclusively to the domain of significant other relationships.It should also be noted that among the three types of perceived social support  the most prominent difference between the single and partnered participants was on the significant other dimension, understandably. Means for single and partnered participants were 16.84 and 20.60, respectively, social selection hypothesis indicates that better-adjusted, healthier individuals become and remain married (Horn et al. The present results should be considered in light of several limitations. First, the cross-sectional data do not allow for inferences about the direction of associations between relationship status and mental health. Although prior research provides support for the linkage between relationship status and mental health, the This results of this study question whether single young adults are at risk for greater mental health problems than counterparts in nonmarital romantic relationships. At this point in the lifespan, being single may not have the stigma that it once did in the past, and it is possible that many young adults remain single voluntarily while they pursue educational and career goals. This may explain why the mental health problems and psychological well-being were generally comparable between single individuals and individuals in nonmarital romantic relationships. At the same time, these results clearly illustrate that even though relationship status does not have a direct effect on mental health, it does have an indirect effect. Individuals in nonmarital romantic relationships enjoy greater social support, and that social support, in turn, is associated with greater psychological well-being and fewer symptoms of mental health problems.


We aimed to assess the feasibility of 3 dimensional (3D) respiratory and ECG gated, gadolinium enhanced magnetic resonance angiography (MRA) on a 3 Tesla (3 T) scanner for imaging pulmonary veins (PV) and left atrium (LA). The impact of heart rate (HR) and rhythm irregularity associated with atrial fibrillation (AF) on image and segmentation qualities were also assessed.101 consecutive patients underwent respiratory and ECG gated (ventricular end systolic window) MRA for pre AF ablation imaging. Image quality (assessed by PV delineation) was scored as 1 = not visualized, 2 = poor, 3 = good and 4 = excellent. Segmentation quality was scored on a similar 4 point scale. Signal to noise ratios (SNRs) were calculated for the LA, LA appendage (LAA), and PV. Contrast to noise ratios (CNRs) were calculated between myocardium and LA, LAA and PV, respectively. Associations between HR/rhythm and quality metrics were assessed.35 of 101 (34.7%) patients were in AF at time of MRA. 100 (99%) patients had diagnostic studies, and 91 (90.1%) were of good or excellent quality. Overall, mean ± standard deviation (SD) image quality score was 3.40 ± 0.69. Inter observer agreement for image quality scores was substantial, : 0.46, 0.90). Neither HR adjusting for rhythm  nor rhythm adjusting for HR  demonstrated association with image quality. Similarly, SNRs and CNRs were largely independent of HR after adjusting for rhythm. Segmentation quality scores were good or excellent for 77.3% of patients: mean ± SD score = 2.91 ± 0.63, and scores did not significantly differ by baseline rhythm (p = 0.78).3D respiratory and ECG gated, gadolinium enhanced MRA of the PVs and LA on a 3 T system is feasible during ventricular end systole, achieving high image quality and high quality image segmentation when imported into electroanatomic mapping systems. Quality is independent of HR and heart rhythm for this free breathing, radiation free, alternative strategy to current MRA or CT based approaches, for pre AF ablation imaging of PVs and LA. Catheter ablation of atrial fibrillation (AF) is considered appropriate treatment for symptomatic AF, refractory or intolerant to at least one antiarrhythmic medication, and may be considered as first line treatment for certain patients . The ratCT angiography (CTA) of the PVs and LA offers high spatial resolution and fast acquisition times. However, CTA requires the use of iodinated contrast agents and radiation exposure, which increases overall radiation exposure when added to fluoroscopy related exposure during catheter ablation. Therefore, for patients with no contraindication, CMR is increasingly preferred for pre ablation PV and LA imaging. There is no significant difference in registration accuracy during image integration into electroanatomic mapping systems with contrast enhanced CT imaging versus gadolinium enhanced CMR ,11. CMR end-systole, the phase of the cardiac cycle least sensitive to increases in heart rate ). A similar method using a ROI within the largest PV and within the LAA was used to calculate CNRPV/myocardium and CNRLAA/myocardium, respectively.A ROI with an area of at least 1.0 cmMRA datasets were imported into an electroanatomic mapping system . Using CartoMerge semi automated image integration software, a technician with over 10 years of experience, blinded to other results, segmented the LA and PVs. Segmentation quality was then assessed according to a 4 point score, similar to that used by Wagner et al. : 1- poorComplications related to catheter ablation of AF were defined as per consensus guidelines  and recoContinuous, normally distributed data are presented as mean ± SD. Continuous, non-normal data are presented as median with interquartile range (IQR). Categorical data are presented as percentages. Data are presented for entire patient cohort, patients in normal sinus rhythm (NSR) and patients in AF at the time of imaging. Continuous variables and binary variables are compared between NSR and AF patient cohorts using a two tailed Student’s t test and Fisher’s exact test, respectively. The Mantel Haenszel Chi Square test is used to test for group comparisons of image quality and segmentation quality scores. The image quality scores of readers 1 and 2 are compared using a paired t test, dichotomized as poor  or good , and inter observer agreement for dichotomized quality scores between readers is determined by calculating the kappa statistic.The crude relationship between dichotomized consensus image quality (score ≥3 good versus score ≤2 poor) and heart rhythm is presented as an unadjusted odds ratio (OR), with associated 95% confidence intervals (CI). To adjust for the effect of HR at the time of CMR, a logistic regression model with dichotomized consensus image quality as the dependent variable and HR and heart rhythm at time of CMR as predictor variables is used. Effect modification by HR on the association between heart rhythm and image quality is investigated using the same model with the inclusion of an interaction variable. To assess for non linear associations with HR, HR was tested in four formats: (i) continuous linear relationship, (ii) categorical relationship , (iii) log transformation of HR, and (iv) quadratic relationship. Multiple linear regression models were used to assess the relationship between categorical HR and rhythm with each of the SNRs and CNRs. A p value of <0.05 was considered significant. Analyses were performed using SAS 9.3® .101 patients were included in this study. All patients had a history of persistent or paroxysmal AF. 35 (34.7%) patients were in AF at the time of CMR. Baseline characteristics for entire patient cohort, as well as by AF status at time of imaging are outlined in Table The mean ± SD acquisition time and acceptance rate were 7:51 ± 2:58 minutes and 54.4 ± 11.8%, respectively. The mean ± SD dose of gadobenate dimeglumine delivered was 29.8 ± 8.5 mls, over a mean ± SD infusion duration of 1:39 ± 0:28 minutes. 100 (99%) patients’ studies were considered diagnostic , and 91 (90.1%) were of good or excellent quality. Overall, mean ± SD consensus quality score was 3.40 ± 0.69. Among patients in NSR and AF, there were no significant differences in mean acquisition times, acceptance rates, quality scores, SNRs or CNRs, Table The mean ± SD quality scores for reader 1 and 2 were 3.34 ± 0.70 and 3.31 ± 0.73, respectively ; the overall inter observer agreement for dichotomized quality scores assigned by these readers was substantial , (k = 0.PV and CNRPV/Myocardium which demonstrate a negative association with HR < 55 bpm compared to a reference HR category (55 < HR ≤ 90 bpm), Table LA/myocardium was higher than mean values of both CNRPV/myocardium (p < 0.0001) and CNRLAA/myocardium (p < 0.0001), mean values of CNRPV/myocardium and CNRLAA/myocardium were similar, (p = 0.51).Heart rhythm was not significantly associated with dichotomized consensus image quality . By logistic regression, neither HR adjusting for rhythm  nor rhythm adjusting for HR  demonstrated significant association with dichotomized image quality. Further adjusting for LA diameter, LVEF, and SBP did not significantly alter results. Similarly, models fitted to allow for effect modification or non-linear associations with HR did not yield different results. Multiple linear regression models demonstrated that SNRs and CNRs were largely independent of categorical HR after adjusting for heart rhythm and vice versa; with the exceptions of SNR97 (96%) patients’ MRA datasets were segmented using CartoMerge semiautomated image integration software. Segmentation quality scores were good or excellent for 75 (77.3%) patients, with a mean ± SD score of 2.91 (+/− 0.63). There were no significant differences in segmentation quality scores between NSR and AF patient cohorts, Table 94 of 101 (93.1%) patients included in this study proceeded to catheter ablation of AF. Three complications occurred in 2 (2.1%) patients: right phrenic nerve injury and heart block requiring permanent pacemaker insertion occurred at time of procedure in the same patient, and atrioesophageal fistula presented in another patient 17 days after ablation. Follow up data for recurrent arrhythmia were available for 91 of 94 (96.8%); 76 (83.5%) remained in NSR after median (IQR) follow up of 308  days following ablation. The median (IQR) interval from ablation to recurrence of atrial arrhythmias in 15 patients (16.5%) was 348  days.In our study, we found that free breathing 3D respiratory and ECG gated gadolinium enhanced MRA of the LA and PVs on a 3 T system is both feasible and reproducible, achieving diagnostic images in almost all patients (99%) and good or excellent diagnostic quality images in 90% of patients. Image quality is independent of HR or heart rhythm at the time of imaging. Furthermore, the quality of image segmentation obtained from these 3D MRA datasets using image integration software of an electroanatomic mapping system is high.Fast heart rates and irregular rhythm, common among patients undergoing pre ablation LA and PV imaging, can compromise quality and increase radiation dose of gated CT imaging ,32. HoweAlthough still practical, the overall mean acquisition time for this 3D respiratory and ECG gated MRA sequence of 7:51 ± 2:58 minutes is longer than acquisition times reported for commonly employed contrast enhanced MRA in expiratory breath hold, without ECG gating (5:45 ± 1:53 minutes) . FurtherThe 3D dataset produced by free breathing respiratory and ECG gated MRA offers the potential to obtain a range of important data using a single test prior to catheter ablation of AF:(i) High image quality facilitates PV anatomy delineation.(ii) Using post processing software, the 3D dataset facilitates accurate measurements of PV diameters with orthogonal planes and the double oblique technique.(iii) LA volume can be quantified using 3D chamber reconstruction technique using similar software; LA volumes have been shown to predict AF recurrence post ablation ,36.(iv) (v) High quality PV segmentation using image integration software of an electroanatomic mapping system as shown in this study, facilitating intra procedural image guidance.(vi) The SNRs and CNRs for the LA and LAA were similar in this study. Contrast opacification of the LA and LAA is generally good with this technique. No LA or LAA thrombi were identified within this patient cohort. Further studies to determine if intra atrial or appendage thrombus can be reliably detected using this technique, with comparisons to transesophageal echocardiography, would be interesting.Furthermore, these data can be provided for a wide range of patients as HR, heart rhythm and ability to breath hold do not render patients ineligible for this imaging technique. These data could be further supplemented with an estimation of LV systolic function by acquiring additional images at the time of CMR; LV systolic dysfunction is another predictor of post ablation AF recurrence . SimilarDirect comparison of this 3D respiratory and ECG gated MRA sequence for imaging pulmonary veins to conventional contrast enhanced, breath held, ungated MRA is necessary, and is a major limitation of this study. While this study establishes the feasibility and high quality of 3D respiratory and ECG gated MRA for imaging pulmonary veins, the lack of a direct comparison precludes conclusions regarding superiority of one technique over another. Superiority over breath-held, ungated MRA will need to be investigated in future studies in order to justify longer acquisition times associated with 3D respiratory and ECG gated MRA. In addition, direct comparison to CTA would be informative. Such comparisons should include an assessment of registration errors during image integration into electroanatomic mapping systems. Certain patients, such as those with claustrophobia, may not tolerate longer acquisition times, but patient tolerance may be improved by the free breathing nature of this respiratory gated technique. Changes in LA and PV anatomy that occur during breath held imaging techniques may predispose to registration errors during image integration into electroanatomic mapping systems ; whetherPre ablation imaging of the PVs and LA by end systolic 3D respiratory and ECG gated gadolinium enhanced MRA on a 3 T system is a feasible technique that achieves high quality images, reproducible image interpretation, and high quality image segmentation when imported into electroanatomic mapping systems. Image quality is independent of HR and heart rhythm for this free breathing, radiation free strategy. This technique offers an alternative strategy for pre-ablation imaging of PVs and LA to current CMR or CT based approaches, and comparative effectiveness studies are necessary to determine the optimal approach.3D: Three dimensional; 3 T: Three tesla; AF: Atrial fibrillation; CI: Confidence interval; CMR: Cardiovascular magnetic resonance imaging; CNR: Contrast to noise ratio; CT: Computerized tomography; CTA: CT angiography; ECG: Electrocardiogram; FA: Flip angle; FOV: Field of view; HR: Heart rate; LA: Left atrium; LAA: Left atrial appendage; LGE: Late gadolinium enhancement; LVEF: Left ventricular ejection fraction; MR: Magnetic resonance; MRA: Magnetic resonance angiography; MRI: Magnetic resonance imaging; NSR: Normal sinus rhythm; OR: Odds ratio; PV: Pulmonary vein; ROI: Region of interest; SBP: Systolic blood pressure; SD: Standard deviation; SNR: Signal to noise ratio; SSFP: Steady state free precession; TE: Echo time; TR: Repetition time; TI: Inversion time; TSA: Total surface area.The authors declare that they have no competing interests.All authors  made substantial contributions to the conception, design, drafting, and critical revision of the manuscript. All authors read and approved the final manuscript.