In this paper, we investigate the time scales of memory maintenance in a calcium-based synaptic plasticity model that has been shown recently to be able to fit different experimental data-sets from hippocampal and neocortical preparations. We find that in the presence of background activity on the order of 1 Hz parameters that fit pyramidal layer 5 neocortical data lead to a very fast decay of synaptic efficacy, with time scales of minutes. We then identify two ways in which this memory time scale can be extended: (i) the extracellular calcium concentration in the experiments used to fit the model are larger than estimated concentrations in vivo. Lowering extracellular calcium concentration to in vivo levels leads to an increase in memory time scales of several orders of magnitude; (ii) adding a bistability mechanism so that each synapse has two stable states at sufficiently low background activity leads to a further boost in memory time scale, since memory decay is no longer described by an exponential decay from an initial state, but by an escape from a potential well. We argue that both features are expected to be present in synapses in vivo. These results are obtained first in a single synapse connecting two independent Poisson neurons, and then in simulations of a large network of excitatory and inhibitory integrate-and-fire neurons. Our results emphasise the need for studying plasticity at physiological extracellular calcium concentration, and highlight the role of synaptic bi- or multistability in the stability of learned synaptic structures.Most models of learning and memory assume that memories are maintained in neuronal circuits by persistent synaptic modifications induced by specific patterns of pre- and postsynaptic activity. For this scenario to be viable, synaptic modifications must survive the ubiquitous ongoing activity present in neural circuits  in vitro preparations. In particular, a model in which plasticity is driven by the postsynaptic calcium concentration was shown to reproduce successfully how synaptic changes depend on spike timing, specific spike patterns, and firing rate. The advantage of calcium-based rules is the possibility of predicting how changes in extracellular concentrations will affect plasticity. This is particularly significant in the view that in vitro studies are typically done at higher concentrations than the ones measured in vivo. Using such a rule, with parameters fitting in vitro data, we explore how long the memory of a particular synaptic change can be maintained in the presence of background neuronal activity, ubiquitously observed in cortex. We find that the memory time scales increase by several orders of magnitude when calcium concentrations are lowered from typical in vitro experiments to in vivo. Furthermore, we find that synaptic bistability further extends the memory time scale, and estimate that synaptic changes in vivo could be stable on the scale of weeks to months.Synaptic plasticity is widely believed to be the main mechanism underlying learning and memory. In recent years, several mathematical plasticity rules have been shown to fit satisfactorily a wide range of experimental data in hippocampal and neocortical  The introduction of bistability in the synaptic plasticity rule further stabilises synaptic changes at low firing rates and extensively prolongs memory time scales when combined with the in vivo extracellular calcium conditions. Finally, we extend our results to a large recurrent network of LIF neurons, where we demonstrate network firing rate stability under synaptic plasticity, decay of an implanted memory for in vitro parameters and long term memory maintenance for in vivo parameters.In the present paper, we study the persistence of synaptic changes, first in a synapse connecting a pair of independent Poisson neurons, and second in a large network of excitatory and inhibitory leaky integrate-and-fire (LIF) neurons. We show that in the absence of bistability, synaptic changes decay exponentially during ongoing activity and that the time constant exhibits a power-law like behaviour with respect to the present firing rate. We demonstrate that the reduced extracellular calcium concentration Memories are thought to be stored in the brain thanks to activity-dependent modifications of synaptic connectivity. According to this hypothesis, memories stored by a particular neural circuit are encoded by the state of all the modifiable synapses of the circuit. Synaptic plasticity allows particular patterns of activity to leave a trace in the connectivity matrix, but this trace is then potentially vulnerable to the ongoing activity that follows. An important question is therefore what controls the time scale of the persistence of a particular synaptic state, in the presence of such ongoing activity. To study this question, we initialize the efficacy of a synapse  at a particular value, and study how this efficacy decays with time in the presence of background activity, using a calcium-based model of synaptic plasticity In the model, the temporal evolution of the synaptic efficacy variable, 1. The dynamics are governed by a potential In this case, This corresponds to a bistable synapse.2. For intermediate calcium concentrations . For the in vitro case, this happens whenever a postsynaptic spike occurs since in vivo parameter set this happens much more rarely because of the smaller calcium amplitudes .The dynamics of the synaptic efficacy in response to calcium transients under the ated in  ,B–E. ForWe now proceed to study the time scales of synaptic decay. We start with the case of a synapse connecting two neurons firing according to uncorrelated Poisson processes, and compare the memory time constants in the flat and double-well potential cases. Simulations were performed using an event-based implementation of the synaptic plasticity model, which updates the synaptic efficacy only upon the occurrence of pre- and postsynaptic spikes . The time constant of this decay is much longer in the case of the in vivo parameter set (B) than in the in vitro parameter set (A). The decay time constant is 2.5 minutes for the in vitro case and approximately 2 hours for in vivo in the presence of 1/s pre- and postsynaptic firing (C).We initialise the synaptic efficacy to function ,A,B. Theeter set ,B than ieter set ,A. The dc firing ,C.The dynamics of the synaptic efficacy  can be dcy,  see , where  A,B the truncated OU theory (blue and red curves), with the simulation mean (green and light blue curves).C). At the same time, the asymptotic value of synaptic efficacy (D). As a result of the smaller in vivo calcium amplitudes, the efficacy decay for the in vivo case is, at all firing rates, much slower than the decay in vitro (C). The asymptotic efficacy value is lower, at small firing rates .Synaptic efficacy decay becomes faster with increasing pre- and postsynaptic firing rates since the calcium trace spends more time above depression and potentiation thresholds ,C. At thhreshold ,D. As a in vitro ,C. The a in vivo ,D.To get a deeper understanding of the dependence of the memory time scale on the firing rates of pre- and postsynaptic neurons, we set C together with the full analytical solution for in vitro parameter set, where a single spike is enough to cross in vivo parameter set, where two spikes are needed to cross the depression threshold.The derived power law behaviour for The implication of this theoretical result is that, at low firing rates, there is a direct relationship between the number of spikes required to clear the lower plasticity threshold and the memory time scale. Note that the full synaptic efficacy model with wing see in vitro and in vivo parameter sets as a function of pre- and postsynaptic firing rates.We now turn to examine the effect of a bistability on memory time scales. The dynamics of the synapse is now described by effective potentialThe effect of background activity on the dynamics of see . In Eq. A, and the effective potentials for 0.1/s and 1/s, indicated by orange and magenta curves in the inset). There is a critical value of the rates at which the high efficacy minimum disappears through a saddle-node bifurcation. Beyond this rate, the synapse is no longer bistable, and synaptic efficacy has one stable state only (A), equivalent to the asymptotic efficacy value for the flat potential (D). Finally, at high firing rates, the ‘bare’ potential becomes negligible, and the effective potential approaches a quadratic potential with a single stable state whose location depends on the rate (green curve in the inset in A). The transition from double-well to single well regimes occurs at different firing rates for the in vitro . In contrast, for the in vivo parameter set, bistability considerably prolongs memory decay times with respect to synapses with flat potential at firing rates below <1.4/s. In the presence of two stable states, the decay of memory occurs only due to synaptic noise fluctuations that push the synaptic efficacy out of the upper well. The influence of the double well potential on the dynamics of the synaptic efficacy traps synapses in the UP state leading to long dwell times before crossing the potential barrier and converging to the low efficacy state (C). The double-well has a prolongation effect on memory duration up to firing rates of about B).For the ly 0.1/s ,B. In cocy state ,C. The dpses see ,B.B; see B for the in vivo case). Both terms in vivo parameter set, up from hours for a synapse with flat potential.For low firing rates, we can accurately predict the increase in the decay time constant in the presence of bistability using Kramers escape rate for the mean first passage time across a potential barrier B; see . In thisWe next study the behaviour of the calcium-based synaptic plasticity model in a recurrent network of spiking neurons. We first examine the steady-state of synaptic efficacy and network activity. We again make use of the event-based implementation of the synaptic plasticity rule (described in The recurrent network consists of 8000 excitatory and 2000 inhibitory leaky integrate-and-fire (LIF) neurons. Each neuron receives an external input which consists of a constant (DC) term and a white noise term. External noise is independent from neuron to neuron. Each neuron also receives synaptic inputs from other neurons in the network. The connection probability between any two neurons is 0.05 and uniform in space and across neuron types. Synapses between excitatory neurons are plastic according to the calcium-based plasticity model , while aA shows how the firing rates observed in the simulations compare with the analytically predicted firing rates. It shows that at sufficiently low rates, the analytical prediction gives a very good estimate of the observed rates; however, for rates above 3Hz the observed rates are significantly lower than the analytical prediction. Likewise, the analytical prediction for the mean EB).The fixed point of the network can be determined analytically by solving a set of three self-consistent equations for the excitatory and inhibitory mean rates as well as for the mean excitatory-to-excitatory (Ecacy see . Two of  neurons . StartinA). This suggests that the underestimation of firing rates and synaptic efficacy emerges from the mapping of firing rates onto synaptic efficacy, and not due to correlations between spike trains of different neurons. We examine this effect in C, where we show asymptotic mean synaptic efficacy results under three different conditions. First, we simulated a population of disconnected, independent LIF neurons, receiving stochastic independent inputs with the same mean and variance as in the ‘real’ network simulation (magenta dots). By definition, this simulation led to uncorrelated spike trains. In this simulation, fake synaptic connections between neurons obeyed the plasticity rule, but had no effect on the dynamics of the neurons. Second, we simulated a connected recurrent network with constant synaptic weights. As in the first case, we simulated ‘fake’ synaptic connections that obeyed the standard plasticity rule, but these fake synapses had no effect on the dynamics (blue dots). Third, we simulated a standard recurrent network in which synaptic weights are plastic according to the plasticity rule (green dots). All three simulations show indistinguishable results, and in all three cases the average  synaptic efficacies are consistently smaller compared to the analytical shot noise prediction . This suggests that correlations have a negligible effect on mean efficacies and firing rates, and that the differences between simulations and theory are due to differences in spiking statistics between the LIF model and a Poisson process.What is the source of the difference between theory and simulations in predicting the steady network state? When synapses are fixed in the network at the efficacies predicted by the corresponding firing rate, the analytically predicted network firing rates provide a good approximation of the observed activity . A reset potential close to threshold  and in turn overestimates the average synaptic efficacy . Conversely, more depolarised reset potentials lead to an under-representation of short ISIs with regard to Poisson firing and consequently to an underestimation of the average synaptic efficacy . We use an intermediate value of To investigate further how the spiking statistics of the LIF model and in particular the interspike-interval (ISI) distribution causes the differences seen in To conclude this section, the calcium-based synaptic plasticity rule does not affect the stability of the asynchronous irregular state in a large recurrent network of LIF neurons. Since LIF neurons in the network exhibit ISI distributions which deviate from those of Poisson neurons, the accuracy of our calculation of the average synaptic efficacy which is based on Poisson firing decreases with increasing firing rates up to a certain point. At high firing rate, calcium remains above the plasticity thresholds most of the time and the fraction of time spent above the thresholds converges to one, irrespective of the underlying neuron model.in vitro and the in vivo parameter set. We initialise all excitatory-to-excitatory synaptic weights at their theoretically predicted asymptotic weights, except for a randomly selected subset of 5% which are set to a weight of 1. With the in vitro parameter set, the potentiated synapses decay relatively quickly to their asymptotic value (B). The time course of the average decay can be described by a single exponential function and the decay time constant is well approximated by the time constant, C). This means that the average dynamics of synaptic decay in the network is equivalent to synapses driven by independent pre- and postsynaptic Poisson neurons firing at the same rate as the excitatory neurons in the network (compare to B). The addition of the double-well potential does not change the decay time constant for the in vitro parameter set, as for a single synapse driven by independent pre- and postsynaptic Poisson firing . The lack of short ISIs in LIFs compared to independent Poisson neurons leads to a small increase in observed decay times in the network as compared with the OU theory (see C).Finally, we examine the decay of a memory trace in a network for the ic value ,B. The tcess see ,C. This eory see ,C.in vivo parameter set with the double-well potential, we observe that the potentiated synapses get locked in the UP state for the duration of the network simulation with an excitatory neuron firing rate of 1/s (C). None of the synapses in the potentiated subset crosses the unstable fixed point and converges to the DOWN state during a network simulation of 120 min, neither does the reverse transition occur. We expect that the escape from the UP state will be predicted by Kramers escape rate ). On the other hand, changing other parameters of the model (such as the time constants and the potentiation and depression rates) have much milder effects, in the flat potential regime, since the time scale depends algebraically on such parameters, rather than exponentially. In the absence of further data, we have assumed a linear relationship between the external calcium concentration and the calcium influx to explore the Previous studies have investigated memory maintenance in networks of neurons connected by synapses endowed with standard spike-timing dependent plasticity rules et al. (2005) studied the stability of the up state in a model of the bistable calcium/calmodulin-dependent protein kinase II system with respect to stochastic fluctuations induced by protein turnover in vivo neuronal activity, not protein turnover, will be the limiting factor of memory life-times.Several studies have shown that synaptic bi- or multi-stability can emerge from a number of mechanisms such as positive feedback loops in extensive protein signaling cascades In vivo, memory in synaptic connectivity structures will be affected both by ongoing background activity, but also by changes in network activity induced by external stimuli. How ongoing presentations of external inputs affect memories of past stimuli has been the subject of several studies in recent years e.g. , in simpDistributions of synaptic weights have been examined in a number of studies in vitro to in vivo conditions, as we have explained here. Scaling laws derived here can be expected to hold also in those other models: at low rates, the time scales of memory decay are expected to be inversely proportional to the rates to a power equal to the number of spikes needed to provoke plasticity. This power should be equal to 2 for standard STDP rules, triplet rules A large number of distinct learning rules that capture quantitatively both spike-timing and firing rate effects have been proposed recently in vitro plasticity data where these neuromodulators were present at very low concentrations, if at all. Hence, we believe that these neuromodulators are likely to enhance plasticity during behaviourally relevant epochs, but that the memory time scales discussed here are likely not to be affected if neuromodulators are not present at high levels during background activity.In this work, we have made the hypothesis that synaptic weights are altered during background activity, and that one can treat background activity as being essentially uncorrelated with the synaptic connectivity structure. Memory time scales could in principle be further extended by two factors. A first mechanism would be to gate plasticity by specific neuromodulator(s) that are present only during stimulus presentation. This idea is consistent with a growing body of experimental data showing how plasticity is modulated by dopamine A second mechanism that would extend memory time scales would be a scenario in which background activity is in fact strongly correlated with the connectivity structure, and wanders stochastically between network states that are strongly correlated with the states of the network during stimuli presentation. This idea is consistent with a growing experimental literature in vivo could have a strong impact on plasticity. A first prediction of calcium-based rules is that plasticity seen in standard protocols should be greatly reduced  at physiological calcium concentrations. While to our knowledge no study has explicitly compared plasticity results at different extracellular calcium concentration, comparisons between different studies using different extracellular concentrations seem to be consistent with this prediction. In hippocampal slices, a standard low frequency STDP protocol produces LTD for all time differences with 2 mM extracellular calcium We showed here that the low extracellular calcium concentrations We provided here an event-based update scheme of plastic synapses which greatly accelerates simulations and should strongly facilitate future studies of the dynamics of recurrent networks with plastic calcium-based synapses. On the theoretical front, it would be interesting to extend the theory to non-Poissonian renewal processes in vitro might translate to the living organism.Our investigations show that realistic external calcium concentration and multi-stability of synapses might stabilise memory traces against the potentially deleterious effect of ongoing background activity. These results call for studies of synaptic plasticity induction and maintenance in more realistic conditions and ideally in the intact animal. They provide a glimpse of how plasticity results obtained The temporal dynamics of the synaptic efficacy in the calcium-based model are given in c. The calcium dynamics are modelled using instantaneous increases of size D, between the presynaptic spike and the occurrence of the corresponding calcium transient accounts for the slow rise time of the NMDAR-mediated calcium influx.Changes in in vitro parameter set is obtained by fitting the calcium-based plasticity model to plasticity data obtained in cortical slices  of the calcium concentration can be calculated if pre- and postsynaptic neurons fire as independent Poisson processes at rate The probability density function In the simple case Fitting the calcium-based model to cortical plasticity data yields  see . In thisi.e.Performing a diffusion approximation of the synaptic efficacy G. The time constant, The bounds at In the case of a double-well potential, the diffusion approximation turns effective potential, U and two quadratic terms proportional to the potentiation and depression rates, respectively  andD  neurons, 8,000 of which are excitatory (E) neurons and 2,000 of which are inhibitory (I). Any two neurons have a spatially uniform probability of connection of 0.05. Autapses are specifically disallowed. Synapses between E neurons are plastic and their weight dynamics are described by the calcium-based plasticity model . All othi of population j, and presynaptic spikes of neuron j in population j in population i after a delay The membrane potential of neuron For all connections involving inhibition  for the synaptic weights assuming a 1/s pre- and post-synaptic Poisson firing process. We then use a reverse lookup of the associated cumulative distribution function (CDF) to determine the random initial values for the synaptic efficacies.In order to initialise the simulations close to their steady-state, with the In a network of excitatory and inhibitory LIF neurons receiving white noise inputs, the mean firing rates of excitatory and inhibitory neurons are given by Note that in


Analyses of viral genetic linkage can provide insight into HIV transmission dynamics and the impact of prevention interventions. For example, such analyses have the potential to determine whether recently-infected individuals have acquired viruses circulating within or outside a given community. In addition, they have the potential to identify characteristics of chronically infected individuals that make their viruses likely to cluster with others circulating within a community. Such clustering can be related to the potential of such individuals to contribute to the spread of the virus, either directly through transmission to their partners or indirectly through further spread of HIV from those partners. Assessment of the extent to which individual  viruses are clustered within a community will be biased if only a subset of subjects are observed, especially if that subset is not representative of the entire HIV infected population. To address this concern, we develop a multiple imputation framework in which missing sequences are imputed based on a model for the diversification of viral genomes. The imputation method decreases the bias in clustering that arises from informative missingness. Data from a household survey conducted in a village in Botswana are used to illustrate these methods. We demonstrate that the multiple imputation approach reduces bias in the overall proportion of clustering due to the presence of missing observations. Targeting HIV prevention interventions to high-risk groups  can be aIn this paper, we consider data collected from a household survey in a village in Botswana that was done in conjunction with a pilot study of combination HIV prevention. Nonresponse is a major concern in these types of studies; contributing factors include work patterns, such as that of migrant workers and other highly mobile individuals, temporary absence of the individuals, and migration . BecauseWe investigate viral linkage though examination of clustering, which is a measure of relatedness among viruses sampled from different people. One metric of interest is the overall proportion of clustering in the community, i.e., the proportion of prevalent HIV cases that are phylogenetically linked to other residents in the same community. In this study our definition of clustering is based on the pairwise distance between viral sequences; we define two individuals to be linked when this distance is below a specified threshold. Test statistics can help determine whether certain demographic groups are more likely to be clustered, which aids in understanding HIV transmission patterns—especially if sampled viral sequences include new infections. Linkage analyses can also reveal the overall proportion of clustering in the dataset, which provides information about the extent to which individuals are being infected by strains circulating inside their community or by strains outside of the community. Information regarding whether HIV transmissions are mainly occurring within or between communities can help reveal virus transmission dynamics, as well as identify subgroups of the population that are driving the epidemic , 26–30. As mentioned above, a major problem arises in linkage analyses when the sample of viral sequences is incomplete; this situation may occur because intended subjects cannot be found or refuse participation. Bias arises even if observations are missing completely at random. Because viral linkage is based on the clustering of pairs of individuals, random missing links in the viral transmission chain will cause underestimation in the proportion of clustering. Since observing a link requires the presence of both linked sequences, removal of a subject removes all links to that subject. Hence, the number of missing links between sequences can increase more rapidly than does the number of missing subjects. Therefore, unbiased estimation of the true proportion of sequences that cluster requires information about both the total population size (the number of missing subjects plus the number of observed sequences), and characteristics that impact the probability that a sequence is missing.When observations are informatively missing , additional sources of bias are introduced. The fact that the presence of linkage depends on each sequence in the database creates a challenge for proper handling of missing data. Adjustment for missing data can be at the test statistic level  or at thThe data we consider arises from a pilot study that provided information to aid in the design of a combination prevention cluster-randomized trial in Botswana . The treDij represents the pairwise distance between individuals i and j, and N is the total number of individuals in the dataset. If Dij is less than the threshold, then individuals i and j are considered to be clustered. Moreover, if Dij is less than the threshold for at least one individual j, where i ≠ j, then individual i is considered to cluster. We represent this by introducing an indicator variable, Ii, for individual i such that:An estimate of the overall proportion of clustering, or the proportion of sequences that link to at least one other sequence, was calculated using the pairwise distance matrix of translated amino acid residues from phylogenetic analysis, which quantifies the degree of similarity between any two sequences. Several methods exist for calculating the distance matrix. These include Jukes-Cantor , DayhoffWe consider two thresholds for illustration of the sequence imputation method: 0.10 and 0.15. These thresholds were chosen based on the distribution of the V1C5 pairwise distances of the translated amino acids. Our methods apply for any threshold; appropriate choice of a clustering threshold is an active research area and can be affected by many factors, such as sampling density .Our sequence imputation approach follows the multiple imputation statistical paradigm for dealing with informative missing data , 25. Mulm imputed-complete datasets have corresponding m estimated statistics  and variance-covariance matrices . The repeated-imputation estimate is Qm is Tm = Um + (m + 1)/mBm, where Following the notation of Rubin 1996, the ribed in . A colle(1) For each missing sequence, determine the demographic group, of which there are four: young males, young females, older males or older females. (2) Use a table of weighted probabilities to select the demographic group with which the subject whose sequences is missing is clustered. The weighted probabilities are the probabilities, calculated using observed sequences, that a sequence in one demographic group has its nearest neighbor in another demographic group. These probabilities are defined by the distribution of minimum distances, which is the minimum number of absolute amino acid changes from one sequence to the next. (3) Randomly select a viral sequence from this demographic group. (4) From the distribution of minimum distances in the observed data between the demographic groups of a subject with a missing sequence and the randomly selected sequence, select a distance, n, at random. This distance is the number of absolute amino acid changes between two sequences. (5) Select n sites from the viral genome of the sequence in (3) to modify. Site selection is weighted by the variability of each site, based on the marginal frequency of the most common amino acid at each site. Marginal frequencies for each amino acid site were computed using the Biopython package, which was also used for alignment parsing [(6) Impute the amino acids for each of the n positions based on assumption that these amino acids are multi-nomially distributed. (7) Add the imputed sequence back into the pool of sequences that can be imputed from.The following algorithm illustrates the sequence imputation mechanism, which is illustrated in  parsing . (6) Impm =  subjects were made. We refer to the sample of N = 371 sequences as the observed data set; the observed data with m deletions that yield N = 371 − m sequences as the incomplete-observed data; and the incomplete-observed dataset plus the imputed values as the imputed-complete data.A simulation study demonstrated the ability of the model to reduce the biases arising from informative missing data. The study was based on incomplete datasets that were created by deleting sequences from the available data, and then using the multiple imputation procedure to estimate rates of clustering for the entire observed database of 371 sequences. Deletions of m was large. The proportion of subjects who cluster with others is naturally larger with a higher threshold (0.15 instead of 0.10).m = 50, 100, 200 sequences from the observed dataset and calculate the mean proportion of clustering for the thresholds of 0.10 and 0.15. The variance was calculated as described in the Methods section. The table also provides the coverage percentages for the 95% confidence intervals on estimates from deletion and imputation. The confidence intervals were obtained by bootstrapping standard errors. For each incomplete-observed dataset, in which m sequences had been deleted, ten imputed-complete datasets were constructed to calculate the imputed-complete estimates and standard errors. This process was repeated over 100 different subset deletions (incomplete datasets with m deletions) in order to calculate coverage. Coverage was defined as the proportion of times that 100 repetitions over 100 different subset deletions yielded a 95% confidence interval that included the clustering value obtained from the complete data. As the amount of missing data increases, the performance of the multiple imputation estimates and the coverage worsens, but the bias is always considerably decreased and coverage improved compared to the results for the incomplete-observed data.m = 100 sequences were deleted, ten imputed-complete datasets were constructed to calculate the imputed-complete estimates and standard errors. This process was repeated over 1000 different subset deletions (incomplete datasets with m = 100 deletions) in order to calculate coverage. The results demonstrate that serious violation of assumptions regarding the nature of the missingness process greatly impact results. As expected, clustering estimates from the imputed-complete dataset under proportional deletions are much smaller than the analogous estimates under inversely proportional deletions.We investigate the performance of the sequence imputation method for two scenarios for sampling data missing not at random (MNAR) in We applied our methods to adjust for the fact that the observed Mochudi pilot dataset is an incomplete, biased sample of the population of interest. The focus of estimation is the true proportion of the clustering in the entire population targeted by the Mochudi pilot study. To improve estimation, we impute missing sequences to create an imputed-population dataset. Although we do not have exact information on the number of missing observations, we do have information about the age-gender structure for Botswana as a whole as well as information about HIV-1 prevalence by age and gender in Mochudi. While we cannot be certain that the age-gender structure for Mochudi resembles that of Botswana as a whole, the former is likely to be much closer to the structure for the country than is the observed sample from Mochudi, given its notable under-representation of males. The 2013 CIA World Factbook provides an age-gender breakdown for Botswana , which wTo assess clustering and viral linkage in the presence of missing data, we propose an approach that combines a traditional missing data framework with a model for viral diversification after transmission. In the setting we consider, our sequence imputation method corrects for biases in viral genetic linkage analyses in the presence of informatively missing data. The performance of the multiple imputation approach appears to depend on the proportion of data that are missing. We implemented simulation studies in which our procedures are used to make inferences on the incomplete-observed dataset, and compared the results with those from the complete-observed dataset.In our simulation study, the proposed method performed well when the proportion missing is less than 30%, but underestimated the proportion of sequences that are clustered when the proportion missing is over 50%. One possible reason for this bias is in the distribution of minimum pairwise distances, from which we randomly select the number of amino acid changes to impute from the selected sequence. Bias arises from the fact that this distribution is based on observed distances from an incomplete sample. The distribution of minimum distances is increasingly shifted to the right with greater number of deletions because of the smaller number of links in the incomplete data. To investigate this issue, we conducted a sensitivity analysis as follows: we used the distribution of minimum distances from the full observed dataset rather than from the incomplete dataset in the sequence imputation approach. This approach, however, did not significantly reduce the bias. Next, we investigated the sensitivity to use of a kernel density estimator for estimating the distribution of minimum distances, compared to using the ad-hoc method. The results in gp120 region; we assumed independence, but other choices are possible. A second assumption is that the clustered sequences have similar processes of diversification as those of the sequences of the larger population from which these clustered sequences are sampled. In addition, we assume that sequences are missing at random given observed characteristics on the missing sequences (e.g. age and sex of the hosts).To impute sequences requires a number of assumptions. One regards the covariation between amino acid positions of the In this paper, we do not provide detailed guidance on choice of clustering threshold. The sequence imputation method is applicable to a diverse range of distance matrix definitions, and we present a simple distance matrix definition for ease of illustration. In practice, thresholds will be specific both to the distance matrix definition and the study objective. For example, in assessing whether two individuals are likely to be fairly closely connected in the same transmission chain, it might be preferable to use a lower threshold. By contrast, assessing whether two individuals are infected by strains circulating within a given community or by strains circulating only outside of the community, one might prefer a higher threshold. We recommend investigation at a range of thresholds as shown above, although we selected two thresholds to demonstrate coverage.In the simulated imputed-population dataset, in which we apply our method to adjust for the bias and incompleteness of the observed Mochudi pilot dataset, our estimates of clustering have limitations that arise from the sampling of the pilot study population in Mochudi . We soleIn summary, viral genetic linkage analyses has been shown to be useful in making inferences about transmission patterns, but analyses can yield biased results unless the impact of incomplete sampling of populations of interest is properly taken into account.S1 TableClus stands for clustering; Obs for observed data; In-Obs for ncomplete-observed data; Impute-Com for imputed-complete data; Cov stands for coverage.Clustering assessed at the 0.10 threshold, with m = 100 deletions. Coverage is calculated as described in (PDF)Click here for additional data file.S2 TableClus stands for clustering; Obs for observed data; In-Obs for ncomplete-observed data; Impute-Com for imputed-complete data; Cov stands for coverage.Clustering assessed at the 0.10 threshold, with m = 100 deletions. Coverage is calculated as described in (PDF)Click here for additional data file.


The traffic in the road network is progressively increasing at a greater extent. Good knowledge of network traffic can minimize congestions using information pertaining to road network obtained with the aid of communal callers, pavement detectors, and so on. Using these methods, low featured information is generated with respect to the user in the road network. Although the existing schemes obtain urban traffic information, they fail to calculate the energy drain rate of nodes and to locate equilibrium between the overhead and quality of the routing protocol that renders a great challenge. Thus, an energy-efficient cluster-based vehicle detection in road network using the intention numeration method (CVDRN-IN) is developed. Initially, sensor nodes that detect a vehicle are grouped into separate clusters. Further, we approximate the strength of the node drain rate for a cluster using polynomial regression function. In addition, the total node energy is estimated by taking the integral over the area. Finally, enhanced data aggregation is performed to reduce the amount of data transmission using digital signature tree. The experimental performance is evaluated with Dodgers loop sensor data set from UCI repository and the performance evaluation outperforms existing work on energy consumption, clustering efficiency, and node drain rate. WSN is emerging as an increasingly used application that might competently examine, monitor, and control physical world via a huge number of small, low-priced sensor nodes. Most of the existing research on movement monitoring focuses on dealing with a single vehicle, where vehicle numeration is not needed.The positioning and the location of numerous vehicles provide tracking of vehicles. For more data congregation with the least amount of restricted resources, sensor nodes should be processed to significantly collect the data by constructing restricted choices . But theSeveral research areas on data aggregation focused on homomorphic encryption mechanisms to hide communication during aggregation. However, the homomorphic schemes were not satisfied for multiapplication environments. Therefore, in , a new cCertain applications including stock exchange, portfolio maintenance for financial decision making, and monitoring sensor nodes make extensive use of dynamic data. For applications involving dynamic data, the data obtained from one or more sources are aggregated to obtain the result. At the same time a low-cost, scalable method was presented in  that incAs WSNs are deployed in hostile environments, sensitive information has to be transmitted. The paper presented in  identifiA possible approach to securitize the routing procedure using existing traffic segmentation also called DRINA  utilizedIn the context of improving the energy efficiency in a road network, intention numeration should provide certain characteristics like reducing the energy consumption, reducing overhead by increasing packet delivery ratio, and improving the clustering efficiency by designing cluster-based vehicle detection with minimum node drain rate. In this paper, we solve the problem of cluster efficiency and how to minimize energy consumption using the intention numeration method. We proposed a cluster-based vehicle detection in road network using intention numeration method which emphasizes sensor nodes that detect vehicle and is grouped according to a node energy adaptive clustering. Compared to the existing vehicle detection, CVDRN-IN uses polynomial regression function to obtain the strength of the node drain rate. We also construct a digital signature tree using enhanced data aggregation to reduce the amount of data transmitted. Extensive performance evaluated using the Dodgers loop sensor data set provides better results on energy consumption, clustering efficiency, and node drain rate.to design node energy adaptive clustering, to detect a vehicle and form separate clusters accordingly;to reduce the amount of data transmission using digital signature tree;to present cluster-based vehicle detection in road traffic network using the intention numeration method.The major contributions of this paper are as follows:The rest of the paper is organized as follows. One of the key technologies involved in the intelligent transportation systems is the identification of a moving vehicle. Traffic surveillance is now being more significant. The work in  presenteMoving vehicle identification is a significant part of the traffic surveillance scheme. The author in  providedThe author in  presenteIn traffic intelligent transportation system, classification of vehicles acts as the most demanding task to obtain the traffic vehicles movement. In , a novelComplex moving vehicle detection is one of the significant means of eradicating the occurrence of accidents. In , a traffIn-network data aggregation is a highly significant communication mechanism to minimize the bandwidth requirements in vehicular ad hoc networks (VANETs). The work in  portrayeDuring the design considerations of WSN, compromised sensor nodes give data falsification during both data aggregation and data forwarding. Certain researchers consider false data injections during data forwarding. However, in  a protocFor vehicle categorization, analysis of presentation of three common categorizations based on two processing methods with the empirical data was presented in . In 2],,2], an iIn this section a cluster-based vehicle detection in road network using enhanced data aggregation with intention numeration method is presented. Then a system model is designed using enhanced data aggregation with intention numeration followed by the three phases involved in CVDRN-IN.Sensors in WSN can be organized to sense the information flow, rapidity, and occupancy by examining the signal around them. In road network, fully charged battery powered sensor nodes are arbitrarily placed in an area with a fixed source and sink nodes. An intention numeration method based on node energy (IN-node energy) distinguishes between power computation, elevated accuracy, and node energy capacity requirement.Intention numeration is to count the number of intentions  nodes in wireless sensor network with dimension equal to n where the sensor nodes are placed in a random manner. Each intended node is considered to be a point source of signal, for example, power computation, elevated accuracy, and node energy capacity, whose strength (or amplitude) attenuates with all queue's distance.The architecture diagram of the proposed cluster-based vehicle detection in road network is shown in The process of enhanced data aggregation with the intention numeration method for detecting the movement of the vehicle for a high traffic road network is illustrated in The first phase in CVDRN-IN clusters the sensor nodes based on vehicle identification. The second phase chooses the cluster head by implementing polynomial regression technique. The third and final phase performs enhanced data aggregation using Merkle hash tree by estimating the size of the network and reduces the large amount of transmission.d). The vehicle recognition system for CVDRN-IN includes four sets as follows:sensor to notice the vehicle's signals produced by vehicles,processor to progress the obtained data from sensor nodes,communication unit to transport the user obtained data to the BS for processing,energy source.In this section, the system model is presented by including certain notations and notions. Vehicles turn up to the traffic light junction (TLI) consistent with the definite arbitrary allocation and disappear after some time. For easy allocation, let us assume that each region of the TLI is represented as M/M/1 queue. All queues' distance end to end for all dynamic directions is set to zero. The distances among any pair of the junctions are determined and are equal to a predefined base distance , that is, the starting time, and the end_point (e), that is, ending time. The movement of vehicles for a specified route path, that is, from s to e, is denoted byR measured from the starting point s to the ending point e in a traffic road network.The next step is to calculate the subsequent location of the moving vehicle and keep viewing the moving vehicles. Since the sensor nodes reveal the uniqueness of clustering process, the clustering mechanism is utilized to figure out the hierarchical formation of the sensor networks. The route path of a moving vehicle VO is formed by specifying the start_point  represents the node drain rate of the nth cluster with Fi(E) denoting the ith node energy level of the former state and Ci(E) denoting the ith node energy level of the present state. In a similar manner, the time interval is represented as CurT and PreT being the current and the previous time interval, respectively.For each cluster in the road network, the node drain rate is estimated based on the sensor nodes holding the vehicle information. For each cluster, the node drain rate is estimated asUsing , the nodIf several nodes in the cluster have the same number of node drain rate strengths, then it is obviously difficult to select the cluster head for better movement. So, polynomial models are utilized to approximate the node drain level of each node in the cluster and choose the cluster head accordingly.S = {S1, S2,…, Sn} with the vehicle information as VO = {VO1, VO2,…, VOn}. The basic assumption to be followed using polynomial regression in CVDRN-IN is that a data set of n paired  pairs is expressed asConsider a set of sensor nodes p to decrease the remaining R at every data point expressed inThe equation in  is measun inside the cluster Cn. With this matrix representation, the vehicle is assigned with appropriate sensor nodes in appropriate cluster. For each cluster, the node draining rate is evaluated and processed with the area of the cluster size. Once the cluster head is determined, the total energy capacity E(Cn) is evaluated based on the area of the cluster Area(Cn) in the road network:D denotes the cluster C. By identifying the area for the cluster Area(Cn), the total energy capacity is evaluated asThe polynomial regression representation for selecting the cluster head is expressed in terms of matrix as follows:With these values, the energy capacity is determined and processed based on the number of sensor nodes on the road network and determines the vehicle movement categories.The third phase in CVDRN-IN is performing enhanced data aggregation using digital signature. The digital signature-based enhanced data aggregation (DSEDA) model consists of three parts, namely, key generation, enhanced data aggregation, and confirmation.The first part involved in digital signature-based enhanced data aggregation is the key generation that generates a private key for each cluster, and each sensor node belonging to the specific cluster has a share of the private key. Each sensor node senses the movement of the vehicle (MV) and then encrypts it using its share of the cluster's private key.KP denotes the private key shared between the sensor node S and the base station. The encryption of the sensed movement of vehicle MV based on sensor node P is evaluated as follows:Let us assume that P and node Q) which is given as follows:The second part involved in DSEDA ensures that base station does not accept invalid aggregation results from the cluster head. The digital signature-based enhanced data aggregation is performed on the encryption of the sensed movement of vehicle MV received from the corresponding sensor node . The first key is shared with the aggregator and the second key is shared with the base station. The sensor node sends these data to the cluster head, which aggregates the nodes MVs and measures their average.Based on the movement of the vehicle, the sensor node sends its ID, data packet, and two message authentication codes. This message authentication code includes the sensor node ID, with the vehicle information and the message authentication code MACThe cluster head then broadcasts the nodes based on the movement of the vehicle to the specified sensor nodes belonging to a cluster. It then evaluates their MVs with the measure of average. If the result of the measure of average is less than a constant factor, the sensor node generates a digital signature on the measure of average using its share of the cluster's private key and then sends it to the cluster head. The cluster head then combines these digital signatures into a full-fledged signature and sends it in addition to the measure of the average value to the base station.The third part involved in DSEDA is the verification phase where the base station interacts with sensor nodes and aggregators in order to verify the aggregation results. When the results of digital signature-based data aggregation reach the base station, the base station exposes the symmetric keys shared with every node. Every cluster head now verifies whether the packet data and message authentication code stored in its sensor node are matched or not. If the cluster head detects the message authentication code to be inconsistent with that of its sensor node, it sends out an alarm signal to the base station along with the message authentication code evaluated using the sensor node's temporary key.With these values, the energy capacity is determined and processed based on the number of sensor nodes in the road network. Based on these values, the energy capacity is identified and determines the vehicle movement categories.http://its.berkeley.edu/publications/UCB/2007/CWP/UCB-ITS-CWP-2007-7.pdf. The characteristics of the data set and attributes in Dodgers loop sensor data set are multivariate and integer categorical. The total number of instances is 50400 and the number of attributes is 3.In this section, an experimental evaluation is done to estimate the performance of the proposed cluster-based vehicle detection in road network using enhanced data aggregation with intention numeration method. The experimental evaluation is done with the Dodgers loop sensor data set extracted from the UCI repository. These loop sensor measurements were received from the Freeway Performance Measurement System (PeMS), These Dodgers loop sensor data were composed for Glendale on a slope for the 101 North Freeway in Los Angeles. The performance of the proposed cluster-based vehicle detection CVDRN-IN in road network using enhanced data aggregation with intention numeration methodis compared with the existing adaptive traffic segmentation  method wThe node energy consumption is measured based on the number of sensor nodes or the number of cars measured in the previous five minutes using Dodgers loop sensor data in the network area. The value of the proposed CVDRN-IN is compared with the existing adaptive traffic segmentation  method. W/L score obtained through the Dodger data set. Based on each ratio of W/L score, the clustering efficiency also gets improved. Compared to the existing adaptive traffic segmentation [entation  method, entation  method.Finally, it is being observed that the proposed CVDRN-IN in road network using enhanced data aggregation with intention numeration method identified the movement of vehicle and collects the information about the direction in which it moves based on clustering. The adaptive node clustering clustered the sensor nodes based on the vehicle information collection. A polynomial regression function is presented to identify the cluster head among the set of sensor nodes in the network. Finally, enhanced data aggregation is achieved using the message authentication code based on the movement of vehicles.In this work, the intention numeration method based on node energy (IN-node energy) is developed for the identification of vehicles. At first, the sensor nodes in the road network are fixed in an appropriate area. It detects the movement of vehicles and performs the clustering as separate clusters and then computes the number of vehicles covered by every cluster. After the formation of clusters and the vehicle analysis, a polynomial regression function is presented to form the cluster head. A polynomial regression function is then applied to determine the node drain rate strength over the formed cluster. Then the total node energy capacity is estimated by taking the integral of the function over the area. Finally, a conceptual framework is provided for enhanced data aggregation using digital signature model to minimize the amount of data transmitted and avoid redundancy. Experimental evaluation is performed with Dodger's loop data set extracted from UCI repository to estimate the performance of the vehicle movement in the road network. Performance evaluation shows that the proposed CVDRN-IN method provides 10–12% increase in vehicle detection rate in road network.


Percutaneous coronary intervention (PCI) is a minimally invasive surgery procedure that is widely used in the treatment of coronary artery disease. This procedure requires interventional cardiologists to have high proficiency and therefore demands an extensive training period in order to ensure successful surgical outcome. In this paper, a realistic and real-time interactive simulator for training PCI procedure is presented. A set of new approaches for core simulation components is devised and integrated into the simulator. Trainees can interact with the virtual simulation environment with real instruments and essential maneuvers encountered in real PCI procedure. Although presently targeted at PCI, our simulator could be easily extended to mimic the necessities of any vascular interventional radiology procedures by updating vascular anatomy. Preliminary validation of the proposed physical model of instruments is conducted on vascular phantom to demonstrate its performance and effectiveness. Coronary artery disease (CAD) is the most common type of heart disease and is one of the leading causes of death worldwide. This disease is caused by plaque buildup inside the walls of the coronary arteries, which narrows or blocks the blood vessels and reduces the flow of oxygen-rich blood to the heart. Percutaneous coronary intervention (PCI), which is also known as coronary angioplasty, is a minimally invasive surgery procedure widely used to open the narrowed or blocked arteries to improve or restore blood flow to the heart muscle.During PCI, interventional cardiologists percutaneously insert long and thin flexible devices (such as guide wire and catheter) into patient's blood vessel from a tiny incision often made in the femoral artery or radial artery and manipulate the devices through blood vessel network under the guidance of X-ray imaging from outside the body. Once reaching the sites of coronary artery narrowing or blockage, a balloon deployed at the leading tip of the catheter is inflated to compress the plaque against the artery wall. Usually, a stent  is placed at the area of blockage, acting as a scaffold to keep the artery open permanently.Performing a PCI procedure is very difficult due to several factors. (1) The vessel network is of high complexity with a great variety of sizes and anatomical configurations, and the characteristics of vascular lesions vary significantly between individuals. (2) The devices such as guide wire are inherent high flexibility . (3) The devices inside the vasculatures are invisible to cardiologists' eyes and the vessels are seen on the X-ray images only when contrast dye is injected to the patient's vessels; most important, due to the morality and safety reasons (overexposure to X-rays can result in leukemia and cancer), X-ray imaging is only performed when really necessary, for example, at some critical treatment phases or positions such as bifurcations, to help make decisions for subsequent device manipulations or to confirm the diseased location and situation. As a result, most of the time, the cardiologists are blind to moving the devices while heavily relying on their sense of touch feeling of the devices at one proximal end in their hands. (4) The procedure involves some risks  and complications can occur even when the most experienced and skilled cardiologist performs the procedure.Considering the above issues, interventional cardiologists need a great deal of training to acquire necessary skills such as good hand-eye coordination of instruments, guide wires and catheters, and accurate interpretation of complex three-dimensional (3D) anatomy and pathological conditions from two-dimensional 2D) images to ensure safe and health outcomes. Traditionally, this medical training is obtained through a one-on-one interaction between the skilled cardiologist mentor and the trainee using live patients as teaching materials. However, such “see one, do one, teach one” apprenticeship training model is a high-cost, unstructured, time-consuming, and resource-intensive process with no objective assessment of proficiency , 2. MostD images Interactive computer-based virtual environment provides promising solutions to overcome many limitations of the traditional training models. In a virtual environment of replicating patient anatomy and the effects of virtual devices and by interacting with sensory inputs or real medical devices, trainees can understand the 3D relationships among anatomical structures and develop other required knowledge and skills at anytime and anywhere without exposing themselves to invasive environment. In addition, trainees can learn to manage intraoperative accidents such as artery rupture with making mistakes without putting patients at risk. Beyond the training purpose, experienced cardiologist can rehearse the PCI procedure on patient-specific image data to evaluate technical feasibility and to foresee any potential challenges that may occur in actual surgical operation. Furthermore, virtual simulator could also serve as an important component of objective certification of skills and continuing medical education to learn novel surgical techniques in a risk-free environment.However, developing a high-fidelity and real-time immersive virtual environment is a particularly challenging task. Several companies and research groups devoted many efforts to virtual vascular interventional radiology simulators in the past years –9. NeuroIn addition to the above-mentioned systems, a good deal of efforts have been put towards modeling of instruments especially guide wire –19. AldeIn this paper, a computer-based real-time and realistic simulation environment for PCI training is presented. It consists of a high-quality surface modeling and a robust centerline extraction for vascular structures. In addition, a realistic physic-based elastic rod model of virtual instruments is proposed. The rod model is discretized into different resolutions that are dynamically adaptive to the diameter and curvature of the vessel and thus can behave well even under highly complex vascular circumstances. At the collision response stage, a force correction strategy is proposed to dynamically adjust the elastic force between the guide wire or catheter and the vessel wall, being able to avoid frequent collision detections to save a great deal of time. Additionally, various rendering techniques based on modern graphics processing units (GPUs) are developed in our virtual system to achieve a real-time and realistic visualization including X-ray effect. Most importantly, our system is designed in such a way that real PCI instruments including guide wires and catheters can be used to simulate the requirements of the catheterization laboratory. Based on the above components, the presented simulation environment allows core skills training of PCI such as hand-eye coordination of catheter/guide wire insertion and navigation by pulling, pushing and twisting, contrast dye injection, C-arm manipulations, and so on.The rest of this paper is organized as follows: details of our simulator are described in In this section, we firstly give a brief architecture overview of the presented PCI simulation system. Secondly, a high-quality geometric modeling method for vascular structures is introduced. Thirdly, a centerline extraction method for vasculatures is presented. Fourthly, a proposed physic-based instrument modeling is described. Fifthly, we introduce the graphic rendering techniques used in our simulation. Finally, short descriptions are given to the hardware part of the simulation system.The presented simulation environment not only offers trainees a realistic visual feedback similar to what an interventional cardiologist could see on the fluoroscope monitor but also provides a haptic apparatus that trainees could efficiently interact with the simulation in a natural way as done in real catheterization procedures. The architecture and the relations among different components of our simulation system and the user are shown in For our development, Microsoft Visual Studio 2010 is used as the main programming platform and the Microsoft Foundation Class library and Windows API are applied to build the graphical user interface (GUI) of the software component. All the algorithms in subsequent sections are implemented in C++, while the graphic programming is based on the OpenGL graphic library and GLSL shading language.Point cloud extraction and adaptive upsampling: the input of this stage is a 3D volume of segmented vessel image data, and the output is a 3D point set with high densities, as shown in  k-nearest neighboring points. Second is making all the directions of the vectors consistent via normal propagation under the help of minimum spanning tree, as illustrated in Normal vector field construction: this stage has two substages. First is calculating the normal vector of each point based on covariance analysis of the point'sIndicator function construction: the function aims at implicitly describing the underlying 3D point set, which is achieved by solving a Poisson equation constructed from the normal vector field.Curvature-dependent polygonization: this stage also contains two parts, mesh expanding and gap stitching. In the former part, an initial mesh composed of six triangles surrounding a given point, whose edge lengths are adaptively determined according to the local curvature radius of the point, is firstly constructed and is subsequently expanded by gradually growing triangles from its boundary edges. The latter part is to fill the gaps yielded in the mesh generation. The gap is sewed by triangulating the polygon formed from the boundary edge of the gap.Anatomical modeling is the first step toward the development of a simulation environment. A high-quality modeling makes it possible to achieve a realistic virtual scenario. In medical visualization, surface modeling of anatomical structures usually resorts to the marching cube technique . HoweverCenterline or curve skeleton, a means of compactly representing the topology of 3D objects, is useful in many medical applications. In , centerlWL and WH are the diagonal weight matrices balancing contraction and attraction constrains; the ith diagonal element of WL(WH) is represented by WL,i. L is the n × n Laplacian matrix with cotangent weights. The iterative contraction process works as follows, where t is the iterative number:Vt+1 through solving WLt+1 = sLWLt and Ait and Ai0 are the current and original one-ring neighborhood, respectively, and sL is a speed-up coefficient of the contraction matrix,updating Lt with the newly solved vertex position Vt+1.constructing the new Laplacian matrix The mesh contraction procedure based on  is a gloWL0, WH0, and sL is set as suggested in [The initialization of ested in . The iteAfter obtaining the contracted mesh, we extract the skeleton on the point domain in the subsequent two steps, in contrast to the  on the mpi a function f(pi) is defined as follows:λi   is the ith largest eigenvalue of the 3 × 3 covariance matrix for pi. Then, if f(pi) is smaller than a user-specified threshold ψf, the point pi is a joint point, and a branch point otherwise. It is noted here that the ψf should be parameterized a little larger to ensure that all joint points are identified. In our work, ψf is empirically initialized as 0.8, achieving better results for a considerable diversity of vasculatures.The identification between the joint points and the branch points is essential for centerline extraction from vascular point set. Here, PCA is employed to assist the determination. Given a point The joint clustering procedure  is then Skeleton grows from seed, which is obtained by computing the joint cluster's center and searching the nearest branch point to the center in each branch. The skeleton growing will stop when there are no more points ahead in the growing direction or two growing directions meet each other. After the skeleton procedure, a complete curve skeleton is generated. Then the skeleton is optimized by performing cubic B-spline fitting.φi on every joint point, this model could represent any types of guide wires with different intrinsic shapes and deforming configurations.Similar to the geometric modeling of anatomical structures, physical modeling of interventional instruments is also an essential element in the development of a simulation environment with high realism. In the current development of our simulation system, the instrument models only include catheter and guide wire. These two models use the same modeling approach. Therefore, for brevity of description, hereafter in this section, we use guide wire to describe the proposed physical modeling approach. In this work, the guide wire is represented as a chain of rigid rods which tend to bend or twist rather than stretch. They are linked by adjacent joint points where material characteristics could be integrated. As indicated in nd denote the times of discretization. It is calculated as follows:dv denotes the diameter of vessel and rc is the radius of curvature. φm is the maximum bias angle of adjacent rods. It is clearly observed that nd is closely related to the diameter and curvature of the vessel. When a guide wire advances through a high-curvature or small-diameter vascular region, nd would be positive and each rod splits into 2nd smaller ones to avoid vascular penetration and visual artifacts caused by low resolution modeling. On the contrary, when the guide wire reaches a low-curvature and large-diameter area, the calculated nd is negative and 1/2nd rods merge as one to decrease the number of joint points whose positions need to be calculated afterwards. To decrease computational cost, nd is calculated in preprocessing stage instead of being calculated in real-time simulation and corresponding trigger points for splitting/merging are planted in certain area for further discretization/merging.To achieve a more robust and realistic simulation in vascular circumstance with high geometrical complexity, we propose an adaptive discretizing algorithm to dynamically discretize or merge the rods. Let In our approach, the updated position of the joints is calculated based on the principle of minimum potential energy which indicates that when the total potential energy of a system reaches minimum, its equilibrium state is achieved. The guidewire-vessel system's potential energy is defined as follows:Etotal is the sum of two parts: the bending energy of the guidewire Eg and the elastic energy of the vessel wall Ev which are both generated by the deformation. In this work we define the bending energy as follows:θi denotes the angle between adjacent rods of point xi, while φi represents the intrinsic bias angle of xi, as illustrated in Here, Ev is defined askv denotes the elastic coefficient of the vessel wall. di is the depth of the vessel wall's deformation by collision.The energy of the vessel wall Etotal reach its minimum. In each iteration, the external elastic force applied to the guide wire's joint point needs to be calculated for the subsequent computation. In previous methods [To obtain the guide wire's equilibrium position, it is needed to iteratively calculate those joint points' displacements which make  methods , 14, colη is the feedback coefficient, representing the scale of the force's reduction induced by the displacement αi. Fi is the external force in the previous iteration while Fi′ is the newly updated force. With this force correction strategy, the collision detection is needed to be performed only once, which means a great relief of computational burden. With proper setting of the feedback coefficient, not only could the external force be corrected efficiently but also the joint points could approach their equilibrium positions in less iteration.In this work, we propose a force correction algorithm to accelerate the convergence of the iteration. Instead of conducting collision detection at each iteration, we apply the outcome of the previous iteration to correct the elastic force which is in return used as the input of the next iteration based on the following equation:In our virtual simulation environment, the graphic rendering is heavily relying on modern GPU, which makes the interactive simulation achieve a real-time visualization. In modern GPU, data could be accessed in any stage of the latest programmable pipeline yet it is hardly possible in old, deprecated fixed rendering pipeline. This provides great flexibility to process the geometry data on GPU, taking full advantage of its high performance computing.I is the grayscale of the target pixel. σ is the attenuation coefficient of different objects. u is the thickness of the object in the corresponding pixel.To simulate the X-ray imaging, we calculate the linear thickness of the vascular model by fetching the transformed geometry data in the perfragment processing stage with the help of floating-point texture attached multiple render target technique. Based on the following equation which approximates the attenuation of the X-ray imaging, we could get the grayscale of every final pixel on the screen:Utilizing the programmability of modern GPU, the Blinn-Phong shading model is implemented in the fragment shader to achieve more realistic and fine visual effect. It means that lighting calculation is postponed to the perfragment processing stage instead of being done in the pervertex processing stage as in the old fixed pipeline. Besides, some other advanced rendering techniques are also employed in our rendering engine to enhance the realism of the simulation environment and to accelerate the interactive rendering speed. For example, geometry data of the anatomical models is transferred to GPU memory, stencil buffer-based shadow volume algorithm is applied to generate high-quality shadows of certain models, and screen space ambient occlusion technique is explored to achieve more realistic endoscopic effect.The interface of our hardware component is specially designed in such a way that trainees could use real guide wires and catheters to simulate the requirements of the PCI procedure. We believe that such a user-friendly design will shorten the time to get familiar with instrumental manipulation. The hardware component involves a haptic controller as well as a motion tracker. The tracker is responsible for measuring the translation (pushing and pulling) and rotation (twisting) of both catheter and guide wire and thus comprises two modules: rotation detection and translation detection. The rotation module includes encoder raster, encoder disc, and dummy revolving hollow rod which is connected to the encoder disc. When manipulating the hollow rod, the rotation will be detected by the encoder grating, and the signal is simultaneously transmitted to the controller to control instrument model rotating in the vascular model. For the translation module, it includes encoder, passive wheel, pressing wheel, and pressure adjusting hand wheel. The translation measurements are synchronously sent to the instrument model in the simulation to compute updated physical behaviors. Mechanically, the guidewire is sandwiched between the pressing wheel and passive wheel connected by the encoder. The pressure adjusting hand wheel is connected to the pressing wheel to adjust clamp force and to adapt to different diameters of the guidewire.The virtual simulation system we have developed is shown in Hand-Eye Coordination of Instrumental Manipulation. The simulation environment allows the trainee to manipulate the real catheter and guide wire with one or both hands. As encountered in clinical PCI procedure, two instruments could be maneuvered at the same time in our simulator, with a guide wire inside a catheter, as illustrated in In addition, our simulator is capable of accepting typical types of guidewire with diameters of 0.254 mm to 0.965 mm and catheter with diameters of 1.33 mm to 2 mm, both with lengths ranging from 60 cm to 260 cm. Therefore, trainees could acquire their knowledge and experience on how to select types of both guide wire and catheter at certain PCI phases or according to the situations of vascular lesion.When contrast dye is injected, the fluoroscopic view can demonstrate vessel  to the same position on the real phantom as well as the reconstructed model. The same operations are preformed several times to guarantee that the guidewire configuration could be reproduced in the physical experimental setup. Meanwhile, corresponding pictures on different stages are taken to make comparisons. Time Performance. Timing performance experiments with guide wire represented by different numbers of nodes are carried out  need different surgical strategies, different manipulation techniques, and different types of instruments. Rich diversity in cases will not lead to boredom for trainees. Furthermore, a vascular editing tool will be developed, with which trainees can change the geometry and characteristic of the vasculature such as changing the diameter of the vessel to mimic a blockage or narrowing or changing the diseased location. We believe that such tool will greatly help to cover enough diseased cases and help trainees to get familiar with the requirements of various cases. The system will be beneficial to senior cardiologists when developing new intravascular devices as well as surgical procedures.Currently, our prototype has been validated in terms of the physical modeling of instruments. However, upon the completion of several additional components that are ongoing development, it will undergo face and content validity from our hospital collaborators and then a comprehensive assessment and validation study including concurrent and predictive validity.As the ultimate goal of the presented system is not limited to providing interventional radiologists training and learning environment with high realism, high immersion, and user friendliness but also offering an accurate pretreatment planning tool for interventional radiologists in preparation for catheterization procedures with patient-specific image data, we will explore the integration of an automatic vascular segmentation or a semiautomatic approach with minimum extra tasks into the current prototype.


The analysis of heart rate variability (HRV) has been performed on long-term electrocardiography (ECG) recordings (12~24 hours) and short-term recordings (2~5 minutes), which may not capture momentary change of HRV. In this study, we present a new method to analyze the momentary HRV (mHRV). The ECG recordings were segmented into a series of overlapped HRV analysis windows with a window length of 5 minutes and different time increments. The performance of the proposed method in delineating the dynamics of momentary HRV measurement was evaluated with four commonly used time courses of HRV measures on both synthetic time series and real ECG recordings from human subjects and dogs. Our results showed that a smaller time increment could capture more dynamical information on transient changes. Considering a too short increment such as 10 s would cause the indented time courses of the four measures, a 1-min time increment (4-min overlapping) was suggested in the analysis of mHRV in the study. ECG recordings from human subjects and dogs were used to further assess the effectiveness of the proposed method. The pilot study demonstrated that the proposed analysis of mHRV could provide more accurate assessment of the dynamical changes in cardiac activity than the conventional measures of HRV (without time overlapping). The proposed method may provide an efficient means in delineating the dynamics of momentary HRV and it would be worthy performing more investigations. Heart rate variability (HRV), the variation of the period between consecutive heart beats over time is the result of complex regulation mechanism through which the autonomic nervous system (ANS) rules heart rate and keeps cardiovascular parameters within physiological ranges . HRV anaTraditionally, almost all analysis methods of HRV carry out over long-term ECG recording (12~24 hours) and short-term ECG recording 2~5 minutes) . Due to  minutes The present study aims at proposing a new method to explore temporal changes in heart rate by performing the HRV analysis in a series of consecutive overlapped windowed short segment of ECG recordings. Different from the traditional method that perform computation on discrete segmented recording along with much detail information lost, the overlapped analysis window would introduce much little new data each time with a short period of time increment, which means the time interval between two adjacent measurements is very short, and then the dynamical information would be reflected by the analysis in detail. In addition, the time courses of the measures computed from each analysis window are graphically plotted for continuously monitoring of autonomic nervous function, so that the dynamical interactive cardiac autonomic regulation now can be investigated in real time.To evaluate the performance of the newly proposed method in delineating the dynamics of mHRV measurement, synthetic time signals and real RR interval series of both human and dog ECG in different physiological status of ANS were applied in the present study.Several synthetic time signals have been primarily used to assess the performance of the proposed method in evaluating transient changes in heart rate. The most representative one was produced based on the following formula to approximately simulate a significant drift in the frequency location of the respiratory sinus arrhythmia of a RR series during a modulated breathing . The lenA group of human RR interval data archived in the MIT-BIH database  was usedDog ECG data  was alsoThe dog experiments were approved by the Animal Care Committee (ACC) at Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences. The ECG data of human were adopted from the MIT-BIH Database which is opened and free-used. The Database was cited according to the requirements of the MIT-BIH Database, so it is unnecessary for us to get an ethic approval for using the ECG data.The QRS complexes in each ECG recording window were determined with a QRS detection algorithm that was adapted from one presented in . In ordeTwo commonly used statistical time-domain measures of HRV, standard deviation of the normal-to-normal intervals (SDNN) and square root of the mean squared differences of successive intervals (RMSSD) were adopted in the present study. Intuitively, the SDNN, as the square root of the variance of heart rate time series, reflects the cyclic components responsible for the variability in the RR interval sequence because the variance is equivalent to the total power of the spectrum, and the RMSSD reflects the high-frequency variation components in heart rate .LFmin, LFmax) = , and the HF power spectrum, designated as SPHF, was calculated at a frequency band of  = .For frequency-domain HRV, three main spectral components are distinguished in a spectrum calculated from short term recordings: very low frequency (VLF: < = 0.04Hz), low frequency (LF: 0.04–0.15Hz), and high frequency (HF: 0.15–0.4Hz) components. The frequency bands of LF and HF are commonly used in HRV analysis since the physiological explanation of the VLF component is much less defined , 6. The T is the number of ECG segments.For a long-time ECG recording, all the measures were calculated from each RR interval sequence, respectively, resulting in four measure sequences of HRV: , where SDNN(t), RMSSD(t), SPLF(t) and SPHF(t) are the four measures computed from each segment of a RR interval sequence that derived from the long-time ECG recording by a sliding window, and The HRV analysis was performed on RR intervals extracted from a series of windowed ECG recordings. As 5-min recordings are the standard for short-term analysis of HRV , the lenThe four time-domain and frequency-domain measurements were derived from each analysis window of the 20-min time series. The time courses of all the four measurements of the synthetic time series were computed for each of the six cases of time increments and graphically illustrated in Figs For each of the three cases of human RR-interval series, the HRV analysis was performed on a time window with a length of five minutes and increments of one and five minutes, respectively. The time courses of the four different measures were computed from each of the analysis windows and normalized with the maximum value of each measure.For the first case of the human RR-interval series, the four time courses of HRV analysis were shown in The time courses of the measure SPLF for the HRV analysis of the second and third cases of human RR-interval series are shown in Figs HRV analysis has been widely accepted as the mean of determining cardiac autonomic nervous function. The HRV is measured commonly with both time-domain and frequency-domain methods –3, 6–12.http://www.cardios.com.br/noticias_detalhes.asp?idNoticia=275&IdSecao=26&IdTipoNoticia=7). However, we did not get any materials and published literatures about the feasibility and performance of the proposed method in capturing the momentary changes in autonomic systems after fully searching. Thus it would be necessary to systematically investigate and report the effectiveness of the proposed HRV analysis method in delineating the dynamics of mHRV measurement before using it as a new technique.In the present study, our goal was to perform HRV analysis based on a short-time ECG recording for continuously monitoring the temporal dynamics in heart rate. Using a smaller window for HRV analysis, the sensitivity of transient changes in detection should be higher, which has the advantage of preventing trends, transient events, biological disturbances, and so on. On the other hand, the time series for HRV analysis should be long enough to have an appropriate number of periodic events. Thus we proposed to segment the ECG recordings into a series of overlapped analysis windows and then to get the RR-interval series from each analysis window for HRV analysis. The overlapped analysis window in the proposed method had a same length of 5 minutes, which was commonly used in traditional HRV analysis, but had a time overlapped. The analysis results of the synthetic time signals suggested that a smaller time increment could capture more dynamical information on transient changes in the synthetic signal than a bigger time increment Figs –4. WhileTo evaluate the performance of the proposed algorithms for measuring temporal dynamics in non-stationary RR-interval time series, human and dog ECG data were used to perform the time-domain and frequency-domain analysis. For a long-time ECG recording, the measures of HRV of each segment recording were obtained and the corresponding time courses, which reflect the trend of HRV measures over ECG recording time and likely provide the diagnostic values rather than individual data point that may be due to normal physiological fluctuations, were graphically plotted. This allows observing the dynamical evolution of heart rate. Note that it should be possible to further increase the temporal resolution by reducing the time increment. However, if the time increment is too short, the new information involved in a HRV analysis window would be less, which may lead to the indented measures of HRV. In addition, a small time increment would increase computational burdens in real-time monitoring of dynamical information of HRV. Therefore, a suitable time increment would be properly chosen according to a particular application of the proposed method.The necessity and performance of the proposed method of short time increment have been primarily evaluated by synthetic time series. In the representative example as shown in Figs As one of possible tool of monitoring human autonomic regulation of cardiac function, the HRV dynamics has been investigated. In order to assess the performance of the proposed measures of HRV by separating data into a series of analysis windows with an increment of 1 minute, RR interval record sets acquired from healthy young adults during meditation state associated with slow breathing and non-meditation state (archived in MIT-BIT database) were used to implement the HRV analysis. The results as shown in Figs We have proposed a continuously monitoring system to explore temporal dynamics in heart rate by the HRV analysis using sliding window with short time increment. Using simulated non-stationary time series and real RR-interval series of human and animal ECG, we have demonstrated that the proposed measures of HRV in time-domain and time-frequency domain are able to provide more useful and detailed information in some cases when the nature of physiological modulation in heart rate changes from one short-time recording to another or heart rate has a short-time fluctuation caused by pathological intervention, as compared with the traditional measures of HRV. These pilot results obtained in the present study suggest that it would be worthy performing more investigations before the proposed method may become an important alternative tool of monitoring human autonomic regulation of cardiac function.S1 Data(TXT)Click here for additional data file.