Model violations constitute the major limitation in inferring accurate phylogenies. Characterizing properties of the data that are not being correctly handled by current models is therefore of prime importance. One of the properties of protein evolution is the variation of the relative rate of substitutions across sites and over time, the latter is the phenomenon called heterotachy. Its effect on phylogenetic inference has recently obtained considerable attention, which led to the development of new models of sequence evolution. However, thus far focus has been on the quantitative heterogeneity of the evolutionary process, thereby overlooking more qualitative variations.We studied the importance of variation of the site-specific amino-acid substitution process over time and its possible impact on phylogenetic inference. We used the CAT model to define an infinite mixture of substitution processes characterized by equilibrium frequencies over the twenty amino acids, a useful proxy for qualitatively estimating the evolutionary process. Using two large datasets, we show that qualitative changes in site-specific substitution properties over time occurred significantly. To test whether this unaccounted qualitative variation can lead to an erroneous phylogenetic tree, we analyzed a concatenation of mitochondrial proteins in which Cnidaria and Porifera were erroneously grouped. The progressive removal of the sites with the most heterogeneous CAT profiles across clades led to the recovery of the monophyly of Eumetazoa (Cnidaria+Bilateria), suggesting that this heterogeneity can negatively influence phylogenetic inference.The time-heterogeneity of the amino-acid replacement process is therefore an important evolutionary aspect that should be incorporated in future models of sequence change. With the expansion of genome projects, phylogenomics - the use of numerous genes to infer phylogenetic trees - is becoming a common way to resolve controversial relationships e.g. -5). Sinc. Sinc5])a priori biological assumptions and takes advantage of the Dirichlet process prior [substitution profiles, or simply profiles. The number of profiles is often several hundreds, showing that previous models lack flexibility in handling heterogeneity of the substitution process across sites and, for large datasets, the CAT model has a better fit to the data than standard models based on substitution matrices  [More recently, probabilistic models have been developed to take into account heterogeneity of the qualitative aspect of amino-acid replacements along the alignment, by assigning sites to different classes of substitutional processes -25. Of pss prior  to contr or GTR) ,27-30 an or GTR) ,31-34. D or GTR) .The models that assume different evolutionary processes across sites consider that they are homogeneous over time. However, except for a few constant positions for which the evolutionary constraints are uniformly strong, the functional constraints of most positions are likely to have changed over their evolutionary history ,36. IndeIn this study, we will extend to the principle of heterotachy to the heterogeneity of the substitution process over time. We call homopecilly  the hypothesis of an identical substitution process over time at a given site. Since functional constraints acting on proteins change over time, we however expect that not only the rate but also the amino acid substitution process may vary. In particular, the subset of acceptable amino acids or the exchangeability matrix at a given site may change throughout evolutionary time. We will therefore test the hypothesis of homopecilly by evaluating whether the nature of the substitution process varies significantly over time at a given site. Briefly, the substitution process will be characterized by the set of stationary frequencies of amino acids, as estimated by the CAT model . SeveralTo globally estimate the presence of heteropecilly, the Frequency of Different Profiles (FDP), the frequency of positions that are stably affiliated to two different profiles in a pair of taxonomic groups, is computed Figure . For eacn), to estimate the heteropecilly for all sites . A PIPn value of 0 indicates that the site is described by different CAT profiles in at least two groups, whereas a value close to 1 indicates that the site is always affiliated to the same profiles. The distribution of -ln(PIPn) for real and simulated datasets is displayed in figure n) in real data, whereas the number of sites that show a medium value of -ln(PIPn) is higher for the simulated data; results are highly significant . Moreover, since the PIPn criterion is highly correlated with evolutionary rate (see below), the lower evolutionary rate in nuclear genes, relative to mitochondrial genes, decreases the power of the PIPn test, making heteropecilly less marked in Figure The significance of the FDP statistics is limited by the fact that only 15-49% of the sites are considered. To increase the number of sites stably affiliated, it would be necessary to increase the number of substitutions, hence the number of species in predefined monophyletic groups. However, if heteropecilly is frequent, this will have the effect of increasing the probability that a site changed evolutionary properties, and hence cannot be stably affiliated to a single profile. To eschew this dilemma, we devised another criterion, the Probability of Identical Profile over n clades . This result is expected. A slowly evolving position is under strong functional pressure that limits not only the number of substitutions, but also the diversity of acceptable amino acids, thus reducing the probability of being affiliated to different profiles in different clades. Moreover, the statistical power is reduced. In contrast, a fast-evolving position has more opportunities to explore different types of selective constraints, and therefore accepts substitutions in different ways over time; this leads to a small value of PIPn. It is important to note that Tables n far from 0. In contrast, a small PIPn indicates that negative selection in a given clade is strong (i.e. with only a few acceptable amino acids), but that this selection pattern changes over time; for instance, a position might accept only Asp and Glu in one clade, and only Asp and Asn in another.We first evaluated whether heteropecilly is related to the evolutionary rate . For instance, 80% of mitochondrial positions with a PIPn of 0 are very heterotachous (p < 1%), whereas only 65% of all positions are heterotachous at that level. Nevertheless, heterotachy and heteropecilly appear anti-correlated: the proportion of heteropecillous sites is greater when sites are less heterotachous for the nuclear dataset, whereas proportion of heteropecillous sites increases with heterotachy for the mitochondrial dataset. Since the species number (hence the number of substitutions) is reduced and some missing data are present in the nuclear alignment, estimation of heterotachy and of heteropecilly is less accurate than in the mitochondrial alignment. More importantly, the relationship with heterotachy is not only less marked than with the evolutionary rate, but it is in fact mainly a consequence of the correlation between heterotachy and evolutionary rate : when only the fast evolving positions (i.e. with more than 20 substitutions) are considered, heteropecilly is almost unrelated to heterotachy, especially for the mitochondrial dataset . Further studies are therefore needed to determine whether a change of rate over time is independent, or not, of the fact that a site may be affiliated to different amino acid profiles over time. The absence of a strong correlation between heteropecilly and heterotachy makes sense because the two heterogeneities do not apply on the same criteria: heterotachy is mainly due to loss or gain of functional constraints (i.e. variable strength of constraints), whereas heteropecilly is rather due to variation in the nature of functional constraints, not in their strength.A relationship between heteropecilly and rate heterogeneity over time (heterotachy) is possible, since both heterogeneities are due to changes in functional constraints. Accordingly, Tables 2 test of homogeneity rejected at p = 3 × 10-262 and 9 × 10-189 for nuc80 and mt336 datasets, respectively). If we make the assumption that a change in substitution profile reflects a variation in functional constraints, the correlation between the PIPn criterion and the PHS score suggests that, when functional constraints change over time, the new spectrum of acceptable amino acids becomes biochemically different from the previous one. Nevertheless, changes from one profile to another are much easier to detect with our protocol when no acceptable amino acids are common to both than when at least one amino acid remains in the set of acceptable residues. In the first case, sites will surely be affiliated to different profiles in different clades, even if the signal is weak, whereas in the second case the sites will be likely affiliated to several, overlapping, profiles showing closer hydrophobic scores. The use of larger datasets (in terms of species number) is required to address this issue.We analyzed the correlation between heteropecilly and change in hydropathy, using the standard deviation of the site-wise Profile Hydrophobic Score (PHS) index, which measures the diversity of hydropathy a site displays in various clades. Tables Finally, we estimated whether changes between profiles showing similar physico-chemical properties  are more frequent than changes between profiles with different properties. Only sites that are stably affiliated in two different clades are considered. About half of sites  are affiliated to profiles with different biochemical properties. This suggests that heteropecilly is driven not only by different fine-grained functional constraints, but also by important functional changes. Analyses at the codon level  are neve4  and trees are inferred using the GTR+Γ4 Figure  and the 4 model . Changes in the evolutionary process are therefore relatively rare since sites remain affiliated to the same profile over hundred millions of years. The same observation has been made for evolutionary rates, leading to local molecular clock  or auto-ags profile is more frequent in Platyhelminthes and less frequent in Arthropoda). This unequal distribution of profiles across clades could be studied separately within sub-groups of profiles according to their physico-chemical properties. Three sub-groups  show a large variation, whereas other sub-groups  are more homogeneous. Interestingly, fast evolving Platyhelminthes are the most divergent group, and in the vast majority of cases do not have the same bias as other Lophotrochozoa (Mollusca and Annelida). For instance, for the small and uncharged amino acid sub-group, they are associated preferentially with ags or as profiles, whereas mollusks and annelids show an affiliation preference for sT or G profiles. This bias in affiliation frequency across clades generates homoplasy that is difficult to handle, and could explain why Platyhelminthes are so difficult to position . The mt336 dataset yields similar results . ImportSince the amino acid composition is influenced by the genomic nucleotide composition , heteropIn summary, the time heterogeneity of the amino acid evolutionary process (heteropecilly) is a general phenomenon in animal evolution, present in both nuclear and mitochondrial coding genomes. Although the rate of change of the substitution process is sufficiently low to allow the recovery of a phylogenetic signal in the recoded sequences, homoplasy is present as suggested by the different rate of evolution across the tree Figure , and by The observations presented so far demonstrate that the assumption of homopecilly, i.e. no change of the substitution process over time, is violated, potentially leading to tree reconstruction artifacts. As a case study, we chose the relationships between Porifera, Cnidaria and Bilateria (Protostomia+Deuterostomia), which are difficult to resolve with mitochondrial genomes . Since s4 model groups together Cnidaria and Porifera with a posterior probability of 0.70. We then progressively removed heteropecillous positions according to their increasing PIPn value; that is, we first removed positions that most likely violate the assumption of homogeneity over time of the CAT model. For the five sub-datasets analyzed with the CAT+Γ4 model, three kinds of topologies are observed ; (iii) with the smallest subsets, Eumetazoa and Porifera are both monophyletic. With the removal of sites with heterogeneous profile affiliations across clades, support for the monophyly of Eumetazoa  witn criterion, the number of sites having the same profile in Porifera and Cnidaria decreases much more rapidly than the number of sites having the same profile in Cnidaria and Bilateria. One can reasonably argue that sites with the same profile in Porifera and Cnidaria generate a spurious signal that is erroneously interpreted by the CAT+Γ4 model as synapomorphies for Porifera+Cnidaria, since this model assumes that profiles are identical over the whole tree.This result suggests that sites showing a substitutional heterogeneity of profiles over time interfere with the phylogenetic signal and may eventually result in an erroneous topology. We computed the number of sites affiliated to the same profile in Cnidaria and Porifera (and to a different one in Bilateria) and in Cnidaria and Bilateria (and to a different one in Porifera). Choanoflagellates are not considered because only two species are available and an accurate profile affiliation to sites is not possible. Figure 4 model than for site-homogeneous models , the GTR+Γ4 or mtREV+Γ4 models are also used. Results are completely different: the removal of heteropecillous positions does not affect phylogenetic inferences conducted with GTR+Γ4 or mtREV+Γ4 models, for which high support for Cnidaria + Porifera is always observed . This is probably due to the large number of parameters of the latter model and the limited amount of positions, since, with the larger nuclear dataset, the CAT+Γ4 model has a better fit than the two models based on exchange matrices . Importantly, after removal of most heteropecillous sites, the CAT+Γ4 model appears to best fit the data (GTR vs. CAT: -45.2 ± 47.0). This indicates that heteropecilly constitutes a serious violation of the CAT model, because the best fit is obtained despite the limited number of sites (1240).This result is not unexpected because, while heteropecilly constitutes a model violation for the CAT model, its effect on the site-homogeneous GTR model is less clear. To understand the different behavior of these two models, one has to distinguish two model violations, heterogeneity of the substitution process across sites and over time. The first violation is known to seriously exacerbate LBA artifacts, because the amount of homoplasy is underestimated . It is nNumerous heterogeneities of the evolutionary process have been discovered. Most have a clear negative impact on phylogenetic inference when not adequately handled: heterogeneity of rate across lineages , of subsn criterion and the substitution number might suggest a neutral explanation (e.g. change in mutation pressure) of the variation in substitutional profile over time. Since the PIPn criterion is also correlated with a change in hydropathy, this neutral explanation could be insufficient. These changes in the site-specific substitution process could be related to functional shifts, such as adaptation of organisms to new environments (e.g. higher growth temperature) or of the protein to a new cellular environment (e.g. new interactome). To answer these questions, it would be particularly relevant to study paralogous genes in which functional shifts are well characterized.What are the main reasons for these shifts in profile affiliation? The correlation between the PIPThree large datasets have been used: (i) 13 proteins encoded in mitochondria from 336 metazoan species divided into 15 clades , the posterior probability of affiliation of the profile k to site i for clade c. An affiliation was considered stable if k exists such that pik(c)>0.75.To compare the profile affiliation in different monophyletic groups, phylobayes was re-run with the set of common profiles for each clade separately . Under these conditions, only the profile affiliations, branch lengths and site-specific rates were free parameters. This allowed to compute pTwo criteria have been defined to test the homogeneity of the evolutionary process over time. Homogeneity implies that a given site is affiliated to the same profile in all clades, apart from stochastic fluctuations. For pairwise clade comparison, the Frequency of Different Profiles (FDP) is a global criterion over all the positions for which a profile is stably allocated in the two alignments. The FDP criterion is defined by:dif is the number of positions with two different profiles in the two clades, and nid is the number of positions with two identical profiles. For a threshold of 75% of stability across the MCMC, only 28% and 11% of sites are on average stably affiliated, for the nuc80 dataset and the mt336 dataset respectively. This statistic cannot be extended for comparing all clades simultaneously, since only 1% of the sites are always stably affiliated for the 15 clades of the later dataset. Moreover, the FDP criterion does not give information at the site level.where nn) is calculated site by site without any affiliation stability conditions. It is defined for a given site i by:For the simultaneous comparison of n clades, the Probability of Identical Profiles  can be compared and shows a PIPn value close to zero. For instance, the site can belong to various categories containing hydrophobic profiles in one clade and to various categories containing charged amino acid profiles in other clades. For computational reasons, we have limited the phylobayes runs to 1,100 cycles. This choice increases the number of sites with a PIPn value equal to 0: a low frequency of affiliation for a given profile (e.g. 10-5) would artificially be estimated at 0 in the posterior distribution. The more cycles performed, the less sites show a zero PIPn , except for sites with a PIPn value of zero. Because of this latter constraint, results are presented by binning sites into four classes of equal size plus one class for PIPn = 0  and simulated 10 new sequence alignments according to the parameter values of each point, in particular the profiles  under the CAT+Γails see ,31). Usin values were due to unstable profile affiliations related to an insufficient number of taxa, we randomly removed half and three quarter of the species in each clade of the large mitochondrial dataset and recomputed PIPn. As expected, the less species considered, the less profile affiliations were stable (data not shown), because the phylogenetic signal became insufficient. However, this instability led to a sharp decrease of PIPn values equal to 0  Three additional sets of profiles were used in the case of mt336 alignment: 45 profiles defined using a different threshold on the UPGMA tree, the 25 stable profiles obtained from the analysis of the complete alignment, and the 20 profiles obtained by Le et al. [n  The use of different stability thresholds yielded virtually identical results in the FDP analysis . A simple recoding approach might capture this putative phylogenetic signal. For reasons of compatibility with available inference tools, each profile is encoded as a one-letter amino acid, therefore only the twenty most frequent profiles have been conserved for this analysis. More precisely, a new sequence is created for each clade according to the following rule: the site is encoded as an amino acid when profile affiliation is stable, and by a question mark otherwise. Under these conditions, the percent of un-encoded sites in the alignments is 59% and 54% for the mt336 and the nuc80 dataset, respectively. It is difficult to know which model of sequence evolution should be used on this artificial alignment. Since we do not know n. At each step, we removed ~10% of the positions and stopped when 1,039 positions remained in order to keep a sufficient amount of phylogenetic signal. The five steps corresponded to the exclusion of sites with PIPn = 0, and -ln(PIPn) higher than 12, 8, 6, and 4.5, respectively. Phylogenetic trees were inferred from these reduced dataset with the CAT+Γ4 model using phylobayes. The reduced datasets were also analyzed with GTR+Γ4 and mtREV+Γ4 models using RAxML [The mt68 dataset was used to evaluate the potential misleading effect of the detected model violations on phylogenetic inference. More precisely, we made the hypothesis that the observed grouping of Cnidaria and Porifera to the exclusion of Bilateria was due to a long branch attraction artifact. We followed the same approach as for heterotachous positions ,72, by rng RAxML , the rob4 model. Subsequently, heterotachous positions were identified by the test of Lopez et al. [n values over sites was computed.To compare the qualitative heterogeneity studied here (heteropecilly) with the quantitative rate heterogeneity (heterotachy) over time, we looked for heterotachous positions. The number of substitutions per position and per clade was calculated by phylobayes under the CAT+Γz et al.   according to the properties of the two amino acids with the highest equilibrium frequencies in the profile. Only sites stably affiliated (threshold = 75%) to two different profiles in clade pairwise comparison were considered. The numbers of sites for which the two profiles were in the same physico-chemical group were counted over all pairwise comparisons.j in the profile:Finally, we looked for a correlation between heteropecilly and variations in biochemical constraints over time. To do that, we computed a site-specific criterion of hydrophobic variation. For each profile k, a Hydrophobic Score (HS) was computed by summing the hydrophobicity of the twenty amino acids according to Kyte and Doolittle  weightedj) is the hydrophobicity of the amino acid aj and . Then, for each clade c and site i, the sitewise Profile Hydrophobic Score (PHS) was calculated by weighting the HS score of each profile k with its affiliation frequency:where h across all clades was calculated.BR made all the experiments, and wrote the first draft of the manuscript. HP conceived and supervised the study. All authors contributed to the analysis of the results and to the writing of the paper. They read and approved the final manuscript.Supplementary figures.Click here for fileSupplementary material.Click here for file


It has been discovered recently in experiments that the dendritic integration of excitatory glutamatergic inputs and inhibitory GABAergic inputs in hippocampus CA1 pyramidal neurons obeys a simple arithmetic rule as  A single neuron may receive and integrate thousands of excitatory and inhibitory synaptic inputs from its dendritic tree. Through spatial and temporal integration of these synaptic inputs, neurons in the cortex process information efficiently and produce output signals known as spike trains. In order to understand how the brain works, it is important to understand the rules that govern dendritic integration. However these rules remain to be fully elucidated. For the integration of multiple excitatory inputs, cable theory In contrast to theoretical and experimental results for the integration rule of multiple excitatory inputs as mentioned above, we know even less about the integration rule when both excitatory and inhibitory inputs are presented together. In order to describe dynamics of neuronal circuitry within the brain, it is important to understand how excitatory and inhibitory inputs are integrated. For example, the interactions of excitatory and inhibitory synaptic currents have been found to play an important role in many sensory systems Recently, a quantitative description of a dendritic integration rule has been uncovered in experimental results from CA1 pyramidal neurons in one of our authors' lab In Ref. soma, we first address the issue of whether we can understand this dendritic integration rule through somatic properties of a single-compartment point-neuron model. Considering the trade-off between biological plausibility and theoretical complexity among those existing neuronal models fixed. Therefore, it suggests that somatic membrane potential dynamics may play a role in the so-called dendritic integration rule. Through our theoretical analysis, we demonstrate that the nonlinear SC term arises from the multiplication of conductance and voltage in the synaptic input of the neuron. We further point out that, in a static two-port analysis, the product between excitatory and inhibitory conductances gives rise to the product between EPSP and IPSP. Using the insight derived from these analyses, finally, we develop a dendritic-integration-rule-based I&F (DIF) model to phenomenologically incorporate the spatial effect of the integration. This phenomenological model can not only incorporate the dendritic integration rule, but also capture experimental observations that have not been addressed by the multi-compartmental model Many spiking neuronal models have been developed to capture spike dynamics of real neurons Discussion, we determine the parameter range and describe some predictions of the DIF model. In Methods, we introduce the conductance-based I&F model and present both analytical and approximate solutions to the I&F-type models. Here, we also recapitulate the static two-port analysis in detail.The paper is organized as follows, we first show both theoretically and numerically that the arithmetic dendritic integration rule can partially be explained by somatic subthreshold membrane potential dynamics of the conductance-based I&F model. Next, using the insight derived from a static two-port analysis, we develop a simple DIF model to phenomenologically parameterize the spatial dependence of the shunting coefficient Methods) to address this question. First, we use the experimental data to determine appropriate parameters to reproduce the same profiles of EPSP and IPSP as measured in the experiment Methods for details). Then, we use a fourth-order Runge-Kutta method to solve the I&F model numerically. We denote the EPSP by It has been demonstrated that the I&F model can capture very well the subthreshold membrane potential dynamics in the soma of a real neuron when its membrane potential is below Methods for details). From Eq. (1), we haveAs shown above, the I&F dynamics of somatic membrane potential can exhibit the dendritic integration rule [Eq. (1)]. However, one may ask why this linear dynamics of somatic subthreshold membrane potential as described by the I&F model can produce such a nonlinear integration rule. Below, we answer this question analytically (see Methods). Substituting these voltage values  into Eq. (2), we can obtain an approximate If we can demonstrate that Methods).For the mean EPSP and the mean IPSP, we can simply take integrals of As is well known, the conductance-based I&F model is used to describe the membrane potential dynamics in the soma without taking into account dendritic structures. From the above analysis, it seems that the subthreshold membrane potential dynamics in the soma is able to explain the dendritic integration rule [Eq. (1)]. However, as can be seen in Methods for details). For the time-independent case, the conductance inputs of both excitation Methods, we have that the product of To incorporate the spatial dependence of the dendritic integration rule, we first motivate the construction of our neuron model by a static two-port analysis First, we discuss how to determine the parametrization of We now turn to the discussion that in the modified I&F model the dendritic integration rule holds for any moment of time, including the time when the EPSP reaches its peak. Solving the modified I&F model numerically using the fourth-order Runge-Kutta method, we have the relationship among its peak  as well Methods for details), then using Eq. (2), we arrive at the shunting coefficient We can further obtain a theoretical expression of the shunting coefficient. Performing Taylor expansion to the solution of integral form of the modified I&F model to obtain the approximations of EPSP, IPSP, and SSP  It has been found in the experiment that SC vanishes when hyperpolarization is induced by somatic current injection Methods, the soma response As verified numerically in (2) It has also been examined how the amplitude of SC is affected by a relative temporal delay between excitatory and inhibitory inputs. In the experiment (3) By changing the driving force for IPSP from −10 to 0 mV, it has been found in the experiment Note that a pyramidal neuron normally receives a large number of excitatory and inhibitory synaptic inputs For a given network of In this work, we have proposed a simple DIF neuron model that dynamically incorporates the spatial dependence of the dendritic integration rule by a phenomenological parametrization. Via analytical and numerical methods, we have shown that the DIF model is capable of capturing many experimental observations. Below, we will further discuss properties of this model as well as predictions of this model.First, we will provide some rationale to the form of the DIF model in Eq. (10). In fact, Eq. (10) can be viewed as a special case of the following equationNext, we determine the range of the parameter We now turn to the prediction of our DIF model, which can be verified in experiments:(1) The asymptotic behaviors of (2) As discussed previously, the intrinsic origin of the product between EPSP and IPSP in the dendritic integration rule comes from the product between the excitatory and inhibitory conductances. From the DIF model, it is easy to derive the nonlinear relation (3) For synaptic inputs, e.g., inputs are through conductances (4) From the expression of the shunting coefficient Finally, we point out that the rise and decay time constants of EPSP depend on the input sites for real neurons For the conductance-based I&F neuron model, its dynamics are governed by Since the I&F model only describes the soma dynamics, In order to be consistent with the setup in the experiment Based on the I&F model, the individual EPSP [For the modified I&F model [Eq. (7)], the individual EPSP (A linear relationship between the synaptic current and the membrane potential has been observed in the experiment Similarly, we can obtain the IPSP at the soma (For simultaneous inputs of excitation and inhibition, the SSP can be expressed asAs pointed out in Refs.


We report on the evaluation and management of a 47-year-old white male found to have primary carcinoid tumor of the ileal segment of his diverting ileovesicostomy thirty-five months after initial creation. Subsequent to presentation with intermittent gross hematuria, CT urogram highlights an 8 mm enhancing lesion near the enterovesical junction of urinary diversion. Office cystoscopy confirms presence of a lesion that was later endoscopically resected and found to be a well-differentiated carcinoid tumor. Evaluation with serum markers, direct visualization utilizing endoscopy, and imaging was without finding of alternate primary or metastatic lesions. The patient ultimately had the proximal ileal portion of his ileovesicostomy excised and the distal portion converted into an ileal conduit. After briefly discussing the carcinoid tumor and the carcinoid syndrome it may cause, we review the literature on the incidence of carcinoid tumors in a population requiring the use of intestine in the urinary tract. Carcinorcinomas .A 47-year-old man, with paraplegia related to a T7 spinal cord injury suffered at the time of a motor vehicle collision nearly 30 years prior, originally presented carrying the diagnosis of neurogenic bladder that had been managed by indwelling foley catheter. At that time, physical exam demonstrated the manifestations of urethral erosion which would later be complicated by development of a necrotic phallus and eventual loss of this appendage by means of partial penectomy. As a means of urinary diversion, he underwent creation of an ileovesicostomy that was later revised due to redundancy of the efferent limb. At the time of revision, a concurrent bladder neck ligation was performed due to persistent urinary incontinence per urethra. Thirty-five-month status after original diverting procedure, a CT urogram was obtained to evaluate complaint of intermittent gross hematuria. This study demonstrated an enhancing 8 mm mass near the enterovesical anastamosis of the ileovesicostomy . Office According to the 2010 National Comprehensive Cancer Network (NCCN) guidelines for neuroendocrine tumors, triple phase CAT scan or MRI of the abdomen or pelvis is the first-line imaging modality for evaluation of a carcinoid tumor . OctreotTreatment of a localized carcinoid in the ileum should involve resection of the affected segment of ileum with associated mesentery. For patients with the carcinoid syndrome, octreotide is considered first line therapy. Depending on the organ system, therapy for metastatic carcinoid may differ. Treatment may include chemotherapy and, if feasible, resection of metastases. Precise treatment for each organ system affected by carcinoid syndrome is beyond the scope of this review. To our knowledge, this is the first case of a carcinoid tumor within an ileovesicostomy described in the urologic literature. A MEDLINE review of “carcinoid tumors” and “urinary diversion” reveals five results, a testament to the rarity of these tumors and among the reports of carcinoid in intestine used in other forms of the urinary tract; there are three cases seen in an ileal conduit –7 and onAmong the cases involving intestine used in urinary diversion, Frese et al. reported on the case of carcinoid in an ileal neobladder . Their pWe report a case of a unique occurrence, carcinoid in intestine used in the urinary tract. More specifically, we show the first case reported in the urologic literature of a carcinoid tumor in a segment of ileum used in a bladder augment. Due to the low incidence of this unique type of tumor in an urologic patient, definitive treatment algorithms are absent. Interestingly, this patient had a CT scan prior to his initial surgery of bladder augment with ileovesicostomy that was free of tumor burden. The question of whether the use of this segment of ileum in bladder augmentation contributed to the patient's carcinoid tumor is an interesting one. However, due to the low incidence of this tumor type, it is not possible to draw conclusions about the cause of the carcinoid tumor at this time.


Stroke is a frequently-occurring disease threatening the human nervous system. As a serious debilitation affecting a large-scale, hierarchical, and vastly complex electrochemical system, stroke remains relatively misunderstood. Rehabilitation mechanisms and means have suffered from this lack of systematic understanding. Here we propose an evolution model to simulate the dynamic actual evolvement process of functional brain networks computationally in an effort to address current shortcomings in the state of the field. According to simulation results, we conclude that the brain networks of patients following acute stroke were characterized by lower small worldness and lower quantity of long-distance connections compared with the healthy condition. Moreover, distance penalization may be used to describe the general mechanism of brain network evolution in the acute period after stroke. Stroke is a common, debilitating disease threatening the human nervous system. Among 731,000 incidents of stroke and 4 million stroke survivors recorded in the United States annually Neuroimaging technology has been widely used to investigate changes in nervous system function after brain injury. Such studies indicate that the functions of the nervous system change greatly in both the acute period and chronic rehabilitation process after stroke Recently, complex network theory has been applied to neuroscience research and has produced meaningful results Network evolution, as a new approach developed in complex network theory, has previously been shown to be an effective method for simulating the dynamic changing process of complex networks. Gross used network evolution principles to explore the formation process of networks based on the network formation mechanism In this paper, we establish a computational experiment platform utilizing brain network evolution to simulate the dynamic actual evolvement process of functional brain networks after stroke. Firstly, using task-based fMRI data, the functional brain networks of controls and patients following acute stroke were characterized by graph theory respectively. By comparing the topological parameters of the brain network between the two groups, common features of topological alteration after stroke were extracted, and the evolution rules and strategies in accordance with healthy persons and patients in the acute period were established. The connection probability and disconnection probability were both considered in the evolution rules to simulate nodal coupling and decoupling in brain network evolvement processes after stroke.Five right-handed patients  with stroke were enrolled from the inpatient services at the Tongji Hospital of Huazhong University of Science and Technology . Five right-handed healthy controls  were also recruited. There were no group-differences in understanding or education background. The fMRI data of all patients were acquired when they were just admitted to hospital. All subjects gave their written informed consent and the study protocol was approved by the Ethics Committee of Tongji Medical College, Huazhong University of Science and Technology.All patients exhibited the following inclusion criteria: 1) first occurrence of ischemic stroke; 2) study participation within two weeks after stroke; 3) motor deficiency with acute unilateral loss of hand strength  with a custom-built head coil. A high resolution T1-weighted SPGR  inversion recovery 3D MRI sequence was performed for each subject with the following parameters .Blood oxygenation level dependent (BOLD) signal was collected with a T2-weighted gradient echo spiral in-out pulse sequence The functional MRI data set was preprocessed using SPM8. First, the dicom data set was converted into a *.img/*.hdr document. Then, slice timing was used to correct for time-domain. Afterwards, all image volumes were realigned to the mean volume. Subjects whose head displacement were more than 2 mm in x,y,z direction or whose head rotation exceeded 1° were excluded  and a set of edges (or connections) indicating the presence of some sort of interaction between the vertices. The adjacency matrix C and a short characteristic path length L. Such near optimal models are designated as “small-world” networks. When the threshold is exceedingly high, some nodes may become disconnected from the graph which poses problems with regards to the computation of C and L. Latora and Marchiori C and characteristic path length L of unweighted networks conceptually correspond to the local and global efficiency of weighted networks, respectively. The efficiency of the path between two nodes is the inverse of the shortest length  trauma cannot be reduced to simple cases and must be integrated as a whole, and 2) situations or events are not repeatable or re-constructible such that discrete experiments are virtually identical. While traditional approaches are not effective for addressing these problems, new concepts and methods developed in complex systems may provide a potential solution Computational experiments method was firstly proposed by Bankes in 1993 to investigate highly complex systems. He implied that it was difficult to construct a deterministic model to accurately simulate a highly complex system consisting of numerous self-adaptive agents. The computational experiments method provided a solution for such problems in the form of a computation platform In our study, the initial phase of the evolution is the brain network of a healthy control, and the evolution ends when the difference between the simulated network and brain networks of patients following stroke is at a minimum. According to this procedure, the simulated evolution can be implemented repeatedly until a brain networks corresponding to patient controls reappear. Multiple evolutions yield multiple brain-like networks, and are limited in the sense that individual brain-like networks do not necessarily correspond with the discrete outcomes inherent in a small patient set.To evaluate simulation accuracy, we quantified the changes which occurred in the topological profile of the patient group relative to the control group. We found that the small worldness of a brain network in the control group is greater than that of one in the patient group , and thacontrols . Only inThe evolution model was used to simulate the evolution process of brain network in the acute period, defined as from pre-stroke to two weeks after stroke. The evolution of each control subject was simulated 20 times to obtain 20 networks, resulting in 100 outcomes.Firstly, we measured the distance distribution (the probability distribution of Euclidean distance between connected pairs of regions) of a set of simulated networks and brain networks derived from experimental fMRI data . The disSecondly, the small worldness and the number of long-distance connection were compared between two groups (patient and control) and the simulated networks . The smaol group . The numetworks) . Figure ol group .Finally, we used an independent fMRI dataset (patients , Fig. 8.In a functional brain network, varying topological properties are due to the ocurrence of differing arrangements of connections between brain regions after onset of stroke, although the number of connections before and after stroke remains the same in both healthy subjects and patients. The arrangement of functional links between different brain sites can affect the level of information processing and signal synchronization, and have a large influence on experimental results.Small worldness is an index of small world structure, reflecting an optimal structure associated with rapid synchronization and information transfer, minimal wiring costs, as well as a balance between local processing and global integration. Our results suggest that small worldness significantly decreases after stroke . This fiWe also found that the number of long-distance connections (r stroke . Stam [8r stroke .Our evolution model emphasizes a property of the brain network: the anatomical distance between nodes. According to our evolution rules, the attributes of all vertices and edges are modifiable, implying that all the regions of cortex are probably impacted after stroke. These evolution rules are consistent with some results of previous studies using models to simulate the dynamic effects of brain injuries. Honey and Sporns implemented two models of oscillatory cortical interactions and found that lesion effects extend beyond the immediate neighbors of the lesioned site, and that the amplitude and dispersal of nonlocal effects are influenced by cluster patterns in the network It has been reported that small world structure is one of the most important features of the human brain, which has been shown to pursue a balance between local processing and global integration with information transfer at a minimal energy cost In our study, the concept of disconnection was emphasized and probabilistic factors were introduced to the simulated evolution process. If connection takes place in the evolution process solely without disconnection, the network density will necessarily increase on account of the increase on edges. Moreover, Gong and Wang demonstrated that the interactions or connections between nodes in a brain network are not invariable, but change dynamically with age The nervous system is a large-scale, hierarchical and self-adapting complex system The networks simulated by the evolution model confirmed our hypothesis that a decrease in small worldness can arise from the reduction of long-distance connections in the networks of patients following stroke . SimulatThe connection distance, the primary parameter of the connection probability function and the disconnection probability function, is a rough measure representing the information transmission distance between brain regions. In practice, various brain regions are connected by nerve fibers which communicate information. In our models, owing to an absence of high-resolution brain structural data, the Euclidean distance was used to estimate the information transmission distance between brain regions. The Euclidean distance was used as property in a recent study on the evolution model to simulate the formation of brain network, and the results are indeed satisfying Brain regions represented by nodes in brain network contained the area of cerebrum, but not the cerebellum. Because the cerebellum receives information from cerebrum to control movement, we considered it outside the focal area. Accordingly, our brain network consists of cerebrum only and reflects the brain activities in the finger task.On the basis of a computational experiment, we have explored a probabilistic model to parsimoniously simulate the evolution process of brain networks in the acute period from pre-stroke to two weeks after stroke. The evolution model has been effectively applied to simulate the evolution of stroke-affected brain networks in our study. In cases where experimental data is limited, dynamic information was obtained by simulation. This paper provides a novel approach toward investigating mechanisms of brain changes under conditions of neural development disorder or brain injury. In the acute period, the action of distance penalization may be used to describe the general mechanism of brain network evolution. Our study, through the use of evolution model, may contribute to a more comprehensive simulation of brain networks to aid in functional evaluation of stroke patients and is broadly applicable to research of stroke recovery processes.


Encounters between human neutrophils and zymosan elicit an initially protrusive cell response that is distinct from the thin lamella embracing antibody-coated targets. Recent experiments have led us to hypothesize that this behavior has its mechanistic roots in the modulation of interactions between membrane and cytoskeleton. To test and refine this hypothesis, we confront our experimental results with predictions of a computer model of leukocyte mechanical behavior, and establish the minimum set of mechanistic variations of this computational framework that reproduces the differences between zymosan and antibody phagocytosis. We confirm that the structural linkages between the cytoskeleton and the membrane patch adherent to a target form the “switchboard” that controls the target specificity of a neutrophil's mechanical response. These linkages are presumably actin-binding protein complexes associating with the cytoplasmic domains of cell-surface receptors that are engaged in adhesion to zymosan and Fc-domains. Recent micropipette experiments have provided a unique live view of “one-on-one” interactions between human neutrophils and their phagocytic targets. Our results revealed surprising differences between two prominent immunological pathways: the response to fungal targets (mimicked using zymosan particles), and antibody-mediated phagocytosis. Whereas antibody-coated targets were “pulled” into the cell in a straightforward manner, zymosan particles were internalized only after an initial outward “push”. We hypothesized that structural interactions between the cytoskeleton and the membrane patch adherent to a target play a pivotal role in the control of this target specificity. To verify and refine this hypothesis, we here compare our experimental results with predictions of suitable adaptations of a previously validated computational model of neutrophil mechanical behavior. By optimizing the model to best match our experiments, we corroborate that the primary mechanistic origin of the target-specific cell behavior indeed lies in the strength of cytoskeletal membrane anchors. Our recent quantitative comparison of the physical responses of human neutrophils to zymosan  into mathematical equations, as explained in the In earlier work, we have developed and extensively validated a finite-element model of the human neutrophil, and applied it successfully to chemotactic and phagocytic mechanics To model phagocytic behavior, we have identified a number of necessary prescriptions to account for adhesion, basic signaling, and the generation of mechanical forces t  by means of five sequential operations:Mathematical equations representing the physics of the above mechanistic concepts have been published previously The mesh boundary is advected according to the flow of the cytoskeletal network, and then mesh nodes are repositioned for optimal resolution while preserving mesh topology, boundaries and interfacial surfaces Mass is advected from the old mesh positions to the new mesh using a general Eulerian-Lagrangian scheme with upwind interpolation Diffusive mass transport and chemical reactions are treated according to a backward Euler (implicit) scheme coupled with a Galerkin finite-element treatment of spatial derivatives and boundary conditions.Constitutive laws are used to compute necessary quantities such as viscosities.Finally the momentum equations and the incompressibility condition together with the applicable boundary conditions are discretized using the Galerkin approach, and the resulting system is solved for the pressure, velocity of the cytoskeletal network, and cytosolic velocity.This computational cycle is repeated until the simulation is complete. Cylindrical symmetry allows the use of a two-dimensional mesh to solve the axisymmetric version of the model equations. Numerical convergence is confirmed by checking that the results are not sensitive to variations of the tolerance of the different iterations performed by the code as well as to variations of the spatial resolution. Calculations are conducted on PC workstations and typically take a few hours per run.Two distinct yet closely related questions arise from the experimental comparison of the phagocytosis of zymosan and antibody-coated beads We have previously established an optimal computational model describing the phagocytic uptake of antibody-coated beads by human neutrophils A qualitatively different set of interaction forces at the cell-target interface,A lower degree of cytoskeletal polymerization at the pseudopod's leading edge during zymosan engulfment, andA significant rise in viscosity within the cell body toward the end of zymosan phagocytosis.We discuss each of these aspects in turn.We have shown previously that a combination of attractive force and lack of protrusion at the membrane-bead interface accounts for two distinctive features of Fcγ-mediated phagocytosis: the absence of significant outward motion of the bead at the onset of engulfment, and the thin lamellar pseudopod embracing the bead How does one interpret these differences in local protrusion? Consider a cell-surface patch in adhesive contact with an external rigid object. If the engaged adhesion receptors are strongly anchored in the cytoskeleton, they tightly couple the latter to the external object. Then, any disjoining force (such as due to de novo actin polymerization) must act against the tensile stress in the molecular structures linking the object to the cytoskeleton. A protrusive deformation will ensue only if the disjoining force exceeds the strength of this link. On the other hand, if an external object adheres only via membrane binding without further internal structural linkage, local disjoining forces will drive protrusion as if the contact patch was a region of free membrane. Based on this reasoning, we conclude that the adhesion of human neutrophils to antibody-coated targets exhibits strong cytoskeletal coupling, whereas in phagocytic adhesion to zymosan the cytoskeletal linkage is weak (but not non-existent).We also see that the completion of engulfment takes longer for zymosan particles than for antibody-coated beads of the same size. This difference in engulfment duration can be accounted for in the simulations of zymosan phagocytosis by a 25% weaker stimulus of polymerization and protrusive force. Finally, the combination of high cortical tension and large initial target-push-out distance should lead to a much faster inward motion of zymosan particles than actually observed. The only remaining parameter that can be adjusted in the simulations to slow down the inward motion of zymosan is the interior viscosity of the cell body. Whereas this viscosity remains constant throughout the simulation of Fcγ-mediated phagocytosis, our model of zymosan phagocytosis implements a five-fold increase of the viscosity that occurs concurrently with the rise of the cortical tension. This change in cytoplasmic viscosity is assumed to take place throughout the cell interior because otherwise, the intracellular region with the lowest viscosity would determine the rate of cell rounding. To match the measurements, this lowest viscosity would have to have the value currently used for the whole cell interior, and the viscosity in the remainder of the cell would be even higher. Physically, the viscosity increase corresponds to a high degree of polymerization and/or cross-linking of cytoskeletal components throughout the cell.This computational study examines the mechanistic underpinnings of distinct physical responses of human neutrophils to zymosan and antibody-coated targets. A direct quantitative comparison of a finite-element model of the neutrophil with recent single-cell/single-target experiments Our computational framework integrates the reactive interpenetrating flow formalism Our overall strategy has been to vet mechanistic scenarios of phagocytic target uptake by postulating and testing biologically plausible cause-effect relationships. Additional assumptions implemented in our simulations include the irreversibility of cell-target adhesion and the time dependence of the cortical tension (as measured). We do not impose any particular aspects of the cell morphology; instead, the time courses of both the shape (including surface area) of our “virtual immune cell” as well as the cytoskeletal density distribution  As a result, protrusion is limited to the cell surface not in contact with the target, leading to a pseudopodial lamella that envelops the target.Worth highlighting in this physical perspective of phagocytosis is the common role of the cortical tension as primary driver of inward target motion. Note that this contrasts with the notion that an actual inward pulling force, presumably generated by molecular motors, should mainly be responsible for drawing the target into a cell. Neither our experiments  In closing, this study not only illuminates fundamental mechanisms driving the target-specific physical immune responses of human neutrophils, it also reinforces that the present computational framework represents a biologically plausible and physically realistic model of “virtual immune cells”. In addition to correctly reproducing distinct cell morphologies observed in a range of experiments, this model also matches the dynamics of cell deformation, such as the overall engulfment times, or the time-dependent target trajectories measured in phagocytosis experiments. As an early model for calculation of a spectrum of autonomous cellular motions at this level of complexity, it is a step toward one of the key goals of computational biology, i.e., achieving true predictive power.Video S1Finite-element computer simulation of phagocytosis of a zymosan particle by a human neutrophil. The zymosan particle is modeled as a rigid sphere . The coloring of the cell interior (legend shown at the left) reflects the relative density of the cytoskeletal actin network. The counter at the upper right gives the elapsed time in seconds.(1.86 MB MOV)Click here for additional data file.Video S2Finite-element computer simulation of phagocytosis of a 3.2 µm (diameter) antibody-coated bead by a human neutrophil. The coloring of the cell interior (legend shown at the left) reflects the relative density of the cytoskeletal actin network. The counter at the upper right gives the elapsed time in seconds.(1.15 MB MOV)Click here for additional data file.


Many types of epileptic seizures are characterized by generalized spike-and-wave discharges. In the past, notable effort has been devoted to understanding seizure dynamics and various hypotheses have been proposed to explain the underlying mechanisms. In this paper, by taking an integrative view of the underlying mechanisms, we demonstrate that epileptic seizures can be generated by many different combinations of synaptic strengths and intrinsic membrane properties. This integrative view has important medical implications: the specific state of a patient characterized by a set of biophysical characteristics ultimately determines the optimal therapeutic treatment. Through the same view, we further demonstrate the potentiation effect of rational polypharmacy in the treatment of epilepsy and provide a new angle to resolve the debate on polypharmacy. Our results underscore the need for personalized medicine and demonstrate that computer modeling and simulation may play an important role in assisting the clinicians in selecting the optimal treatment on an individual basis. Generalized spike-and-wave (SW) patterns of the electroencephalogram (EEG) are typically observed during many types of epileptic seizures, in particular, during absence seizures, which are characterized by clear-cut spike-and-wave EEG oscillations. The mechanisms underlying spike-and-wave patterns are complex and may involve cerebral cortex and thalamus, intrinsic properties of neurons, and various types of synaptic receptors present in the circuit. There has been notable effort devoted to understanding seizure dynamics and various hypotheses have been proposed to explain the underlying mechanisms It is well known in the field of neuroscience that virtually indistinguishable network activities may arise from widely disparate sets of underlying mechanisms The first half of the paper is devoted to understanding the interplay of various mechanisms underlying generalized spike-and-wave epileptic seizures by taking an integrative view. To achieve this goal, we first study the interplay of inhibitory and excitatory receptors on specific synaptic connections and our results demonstrate that: (1) although both GABApathological instance, which corresponds to a particular individual suffering from epilepsy. There has been widespread debate about the effect of polypharmacy for the treatment of epilepsy In the second half of the paper, we study the implications of the integrative view of mechanisms underlying epileptic seizures on the optimal epilepsy treatments. For a given activity of the network, the underlying parameter combinations form a complex parameter set in the high-dimensional parameter space, where each point in the parameter set of spike-and-wave oscillations can be considered as a specific Our results in the second part of the paper show that: (1) the optimal treatment is a function of the state of individual patients as well as the potency of the candidate drugs; (2) the potentiation of rational polypharmacy for drugs with complementary receptors can be explained by the non-linearity of the drug-response characteristics; (3) while monopharmacy is optimal for the majority of patients, rational polypharmacy is required by a small portion of patients represented by pathological instance points located deeply inside the pathological regime in the parameter space. (4) our study foresees the benefits of personalized medicine, a practice in which computer modeling and simulation assist the clinicians in determining the optimal treatment on an individual basis.An illustration of the thalamocortical network, its synaptic connectivity and the basic network model with eight cells are shown in In the first two seconds of the simulation, the network is in the control condition and generates the typical synchronized spindle oscillations at about 10 Hz. Exemplary firing patterns of the cells are shown in Starting from All the values of parameters in the control condition are provided in In the previous demonstration, the transition from spindles to SW is obtained by blocking GABABefore proceeding further, we first classify the typical behaviors of the network into one of the five categories:RT (resting mode): resting state.SP (spindle): 7–15 Hz oscillation; PY cells generate a few spikes per cycle, and the field potential consists of successive positive and negative deflections.DE (delta): 1–4 Hz oscillation; PY cells generate a few spikes per cycle, and the field potential consists of successive positive and negative deflections similar to that of spindles but at lower frequencies.SW (spike-and-wave): 1–4 Hz oscillation; PY cells generate prolonged firing per cycle, and the field potential consists of large-amplitude negative spikes and small-amplitude positive waves.EF (extreme prolonged firing): an extreme case of prolonged firing; due to overwhelming excitation, such prolonged firing will continue forever.The firing activities and field potentials in different modes of the network are shown in In the following sections, RT, SP, DE, SW, and EF will be used to denote the corresponding behaviors as defined above.Gamma-aminobutyric acid(GABA) is the chief inhibitory neurotransmitter in the central nervous systems vertebrates. There are two classes of GABA receptors: GABAThe role of GABAin vivo injections of bicuculline into the thalamus As shown in With the more complete picture in In addition to GABAStudies based on the current model suggest that the generation of epileptic seizures needs the involvement of both cortex and thalamus In addition, recent studies have also suggested the neocortical origin of spike-and-wave field potentials in experimental models of absence seizure While the earlier studies of While suppressing Although both are excitatory, different from AMPAWhile it is generally true that the suppression of This complex interplay between AMPA-mediated excitations demonstrates another path to seizure, which is different from the common notion that the seizure is caused by an increase of the strength of excitatory synapses. Similar results were reported in computational studies Intrinsic membrane currents affect the network-level oscillatory behavior in an important way. In the study of One important intrinsic current to consider is the persistent Another intrinsic current that plays a similar role is the high-threshold calcium current So far, we have demonstrated the effects of two intrinsic currents, which serve as enhancers of neuronal excitability. On the other hand, some other intrinsic currents may play different roles in determining the mode of network oscillation. One such intrinsic current is the M-current Another important intrinsic current is the afterhyperpolarization current The interplays of a number of parameters have been studied pairwise in the previous sections. Those parameters can be divided into three groups: inhibitory synapses, excitatory synapses, and intrinsic ion channels, which have been widely found in many parts of the brain.The roles of synaptic connections with specific presynaptic and postsynaptic neurons have been demonstrated. In addition to studying such specific synaptic connections, it is also important to study the global role played by a given type of synaptic receptor in the whole network. It is interesting to see how network behavior is influenced by changes in the efficacy of all the synapses mediated by the same type of receptor. It has direct implications on the study of drug treatment of epilepsy. For example, if an AMPA antagonist is applied, instead of a specific AMPA-mediated synapse, the strength of all the AMPA-mediated synapses in the network will be decreased.In this section, we use AMPA and GABAThe three scale factors are used as parameters and the corresponding parameter space is depicted in So far, we have only considered analysis with two or three parameters. In this section, we show the interplay of all the synaptic receptors in the network in a twelve-dimensional parameter space. The maximum conductances of the twelve synaptic receptor channels in the network are varied in the range of One million simulations are run and for each simulation all the parameters are randomly generated following a unform distribution within the ranges specified. Spectrum analysis is used after each simulation to obtain the most dominant harmonic component of the time-domain waveform of the field potentials. Generally speaking, the 7–15 Hz oscillations with large magnitudes (green) represent spindle oscillations (SP), the 7–15 Hz oscillations with small magnitudes (blue) represent the resting mode (RT) , the 1–4 Hz oscillations with small magnitudes (green) represent delta oscillations (DE), and the 1–4 Hz oscillations with large magnitudes (red and yellow) represent spike-and-wave activities (SW).Among one million simulations, there are a total of The above results demonstrate that SW activities could arise from a huge number of combinations of underlying parameters and any parameter with values in the full range being tested could be associated with both pathological and physiological regimes. Although some parameters appear to be more critical than others, there is no guarantee that those parameters will always play a leading role in the generation of SW activities. Instead, due to the strong nonlinearity and high complexity of neuron circuits, the underlying mechanisms of SW activities are very complex.Phase flow analysis has been successfully applied to macroscopic (mean field) models, which are typically described by a few differential equations. However, as the biophysical network model in this paper is described by hundreds of differential equations, it is infeasible to demonstrate a complete phase flow in such high dimensional space. Nevertheless, as neural oscillations are of our interest, two state variables are chosen to obtain phase flow in a two-dimensional subspace: one such state variable is the field potential, an indicator of network-level oscillations, and the other state variable is the intracellular calcium concentration in a reticular cell, an indicator of cellular-level subthreshold oscillations.From the resting state, the network may be entrained to oscillation by applying a hyperpolarizing current step to a thalamocortical cell. If the amplitude of the current step is small, the network will display damped oscillation and return to rest in a few cycles. However, if the pulse is large enough, the network will display sustained oscillation. Typically, the sustained oscillation would be either spindle or delta wave depending on the parameter setting of the network. This indicates that there exit a stable equilibrium point corresponding to the resting state and a stable limit cycle corresponding to spindle or spike-and-wave oscillation. To demonstrate the transition from spindle to spike-and-wave, we use the conductance of GABApathological instance, which corresponds to a particular individual suffering from epilepsy. As a result, the integrative view of mechanisms underlying epileptic seizures has direct implications on the optimal treatments of epilepsies.For a given activity of the network, the underlying parameter combinations form a complex parameter set in a high-dimensional parameter space, where each point in the parameter set of SW oscillations can be considered as a specific To discuss the implication on optimal therapeutic treatments, in this section, we first use simulation to show trajectory activities modified by drug intervention, then introduce the dose-response relationship, define a drug optimization problem, and finally analyze results from the optimization.In this section, we show trajectory activities modified by drug intervention. We perform First, we use the conductances of all the GABASecond, we demonstrate the effect of AMPA antagonists with all the conductances of AMPA receptor channels as the target parameters. In the simulation, all the target parameters linearly scale down at each time step from an initial value of Finally, we show the effect of a combination of GABAIn general, the concentration of a drug at the site of binding determines its effect. However, the actual dependency can be complex and is often nonlinear. The relationship between the drug dose and the response often empirically follows the shape of a receptor binding curve, which is described by Hill equation According to the above nonlinear dose-response relationship, if the dose is From equation (1) , for a desired response level The toxicity of a drug is dose related. Furthermore, as the tests of toxicity can not be easily performed on humans, dose of the drug is often adopted as a metric for toxicity and it is important to reduce the dose to avoid adverse effects. To quantitatively investigate the optimal therapeutic treatments, we consider an optimization problem as follows.Given a number of While the optimization problem (3) is general, as a demonstration, we specifically consider drugs with one of the three complementary mechanisms of action: NaP antagonist, GABASince the working of each drug can be complex, we model the response of a drug by the resulted change of the corresponding scale factorThe parameter landscape shown in The potency of each drug is expected to have a significant influence on the choice of the optimal therapeutic treatment. To more clearly see this, we use the persistent sodium NaP antagonist to demonstrate. As the potency of a drug is often measured by its The resulting optimal drug combinations are shown in In treatability. This is the best illustrated by the results where In addition to the issue of drug efficiency discussed above, it is also worthy noting a related aspect, The nonlinearity of the dose-response relationship also has a large impact on the choice of the optimal treatments. Many dose-response curves follow the shape of a receptor binding curve, where the efficacy of the drug degrades significantly as the dose increases. For instance, the dose required to achieve This partially explains why combining drugs with different mechanisms of action may be more beneficial in efficacy and toxicity than a combination of drugs with similar mechanisms of action, such as two sodium channel drugs More broadly, there has been widespread debate about the effect of polypharmacy for the treatment of epilepsy. As hinted earlier, some people favor the use of multiple drugs with a lower dose for each and believe this is more beneficial than administrating a single high-dose drug. Our foregoing discussion offers one possible explanation for this by attributing it to the nonlinear dose-response characteristics of typical drugs. Other practitioners believe that a full dose of one drug achieves better control of seizures with fewer adverse effects. The results in Nevertheless, with the current model setup, the presented parameter space landscape and optimization results provide additional insights on the issue of polypharmacy. In addition to the nonlinear dose-response relationships, the location of each pathological instance, relative to the boundary of the pathological and physiological regimes, plays an important role in judging the benefit of polypharmacy. Furthermore, the distribution of pathological instances provides a “view” of the entire patient population. Since the distribution of patients is not uniform and more patients are located close to the boundary, one drug may be adequate for the majority of patients. On the other hand, rational polypharmacy may be very beneficial for a small population of patients. These observations are in agreement with typical clinical trials.From the above study, it is clearly seen that the optimal therapeutic treatment varies greatly among patients. Depending on the individual state, optimal monopharmacy or polypharmacy may be the most desirable. Variability is not only in terms of the choice of drugs but also in terms of doses. Low dose may be sufficient for patients whose model parameters are close to the boundary of the pathological and physiological regimes while high dose may be needed for others. It is also possible that, due to toxicity limitation, the epileptic activities of some patients represented by points deeply inside the pathological regime cannot even be controlled by pharmaceutical means. In this case, epilepsy surgery becomes necessary. In addition, although polypharmacy may be very effective for patients deeply inside the pathological regime, the best drug combination and the dose for each selected drug must be carefully chosen. While many road blockers still exist, there is clearly a need towards personalized therapy. To achieve this goal in the future, computer models and simulation may be leveraged to provide computational aids to help clinicians determine the optimal treatments.All the results in this paper are obtained with Matlab 7.1 and the simulation can be downloaded from ModelDB. As shown in Intrinsic currents The cell membrane areas of all cell types and the conductance values of the corresponding intrinsic currents are as follows: for cortical pyramidal cells, The synaptic current The models of AMPA and GABADue to the nonlinear property, the models of GABAThe field potentials (EEG) are simulated based on postsynaptic and intrinsic currents of the two pyramidal cellsGenerally, if there are N pyramidal cells in the model, the field potential should be computed based on N pyramidal cells . In this paper, there are only two PY cells in the eight cell model. The sum of currents from the two PY cells corresponds to the field potential measured in a position with equal distance from each PY cell.


In some pathological conditions like aortic stiffening and calcific aortic stenosis (CAS), the microstructure of the aortic root and the aortic valve leaflets are altered in response to stress resulting in changes in tissue thickness, stiffness, or both. This aortic stiffening and CAS are thought to affect coronary blood flow. The goal of the present paper was to include the flow in the coronary ostia in the previous fluid structure interaction model we have developed and to analyze the effect of diseased tissues (aortic root stiffening and CAS) on coronary perfusion. Results revealed a significant impact on the coronary perfusion due to a moderate increase in the aortic wall stiffness and CAS . A marked drop of coronary peak velocity occurred when the values of leaflet thickness and aortic wall stiffness were above a certain threshold, corresponding to a threefold of their normal value. Consequently, mild and prophylactic treatments such as smoking cessation, exercise, or diet, which have been proven to increase the aortic compliance, may significantly improve the coronary perfusion. In some pathological conditions like aortic stiffening and calcific aortic stenosis, the microstructure of the aortic root and the aortic valve leaflets is altered in response to stress resulting in changes in tissue thickness, stiffness, or both , 2.Aortic stiffening is the consequence of changes in the properties of the arterial wall that accompany aging and arterial hypertension. Increased aortic stiffness is associated with an elevation of systolic blood pressure, a reduction in diastolic blood pressure, and thus a widened pulse pressure . This wiAging of the aortic valve (AV) is characterized by cuspal thickening  and lossAortic stiffening and CAS are thought to affect coronary blood flow , 16. Red In recent years, we have begun to address the critical area of fluid-structure interaction (FSI) and have developed our model of aortic valve including Valsalva sinuses but without coronary arteries . SeveralThe finite element software LS-DYNA  was used to perform all FSI simulations.A generic, anatomically inspired 3D model of the aortic valve was derived from a combination of imaging modalities  and pathological data as previously described by Ranga et al.  and CampThe model was meshed in ANSYS, discretizing the solid components into 10,892 shell elements. These shell elements were used instead of solid brick elements because they can have several integration points allowing bending to be modeled while satisfying the physics of the model. The fluid medium, on the other hand, consisted of 24,500 hexahedral elements. This was found to be an adequate mesh density after doing mesh refinements and mesh independency tests by increasing node numbers up to twice their initial value. After convergence, the percent differences in velocity results using a point-to-point Euclidean norm were less than 2.78%. This meshing was then transformed into the format of an input file including the whole geometry, material properties, boundary conditions, and loads to be analyzed in LS-DYNA. Cardiac tissue is a highly complex material. In the context of large strains, heart tissues can be modeled using nonlinear material properties , 27–29. 3. At high levels of shear rate (>50 s−1), the dynamic viscosity of blood varies between 3 and 4 mPa.s, meaning that in general a simple Newtonian relationship may be used in studies of the larger vessels [−3 and a dynamic viscosity of 3.5 mPa.s. As for blood, its density was set to 1060 Kg/m vessels . In summ There are four sets of boundary conditions in the fluid medium that need to be defined. These boundary conditions are imposed at the aortic root, the ascending aorta, and the two coronary ostia. In order to account for the pulsatility of the flow, the inlet condition at the aortic root is taken to be the difference between the ventricular pressure and the aortic pressure. Therefore, the outlet of the ascending aorta has a free boundary condition, meaning fluid can flow freely, an approach borrowed from previous studies . The res As for the two coronary ostia, it is known that the hydraulic resistance of the coronary vascular bed is largely time dependent and that much of this phenomenon is attributed to the vasocontraction of the coronary vessels . This re In the solid medium, boundary conditions were applied at the aortic ring, the ascending aorta, the coronary ostia, and the leaflets. These boundary conditions constrain the rigid body motion  but are not so limiting as to overrestrict the dynamics of the structure allowing for deformation . To achiThe contact between leaflets was defined using CONTACT_AUTOMATIC_GENERAL in LS-DYNA environment, which is a single surface contact and checks for penetration along the entire length of the free (unshared) shell edges. This is a critical point in the modeling procedure since it prevents the shell elements from penetrating through each other and creating unrealistic leaflet motion. Finally, the coronary ostia were fully constrained in all rotational and translational degrees of freedom to avoid element deformation, which could possibly lead to coronary closure.The simulation of the complete cardiac cycle is performed using a fluid-structure interaction approach. Additionally, for the fluid flow part, the blood velocity is calculated in the context of the ALE formulation of the Navier-Stokes equations, which can be obtained by replacing the convective velocity in the standard Navier-Stokes equations by the relative velocity to the moving mesh. The general form is as follows:ρ is the fluid density, v the velocity vector of the fluid in a fixed coordinate system, t is the time, w the velocity of the fluid medium, and σ the Cauchy stress tensor defined by:p denotes the fluid pressure and τ the viscosity stress tensor.Ωf and an immersed solid medium Ωs. In order to capture the fluid-structure interaction, these two mediums need to be coupled. This coupling is obtained by applying a no slip conditionThe fluid-structure problem presented here consists of a fluid medium νf and νs represent the fluid and the structure velocity, respectively, in the coupling interface. The engineering parameters of interest in the solid medium include the leaflet morphologies, leaflet velocities, and leaflet stresses. Although the solid medium contains the aortic root, sinuses, and ascending aorta, the most accurate clinical data available are related to the leaflets. Looking from the ascending aorta back towards the left ventricle, known as the short-axis view, reveals some key features. An important aspect that can be quantified clinically is the cross-sectional valve opening during the cardiac cycle. The computed leaflet morphologies during the opening and closing phases are presented in P = 40 mmHg) and hypertensive (140/90 mmHg: ΔP = 50 mmHg) conditions and are presented in For a more quantitative assessment, it is also possible to track the velocities at the leaflet tips. Some common aspects of the leaflet dynamic histories that have been clinically quantified by echocardiography studies are the rapid valve opening time (RVOT), rapid valve opening velocity (RVOV), rapid valve closing time (RVCT), rapid valve closing velocity (RVCV), and ejection time (ET). For each of these five parameters, average healthy values have been determined –46. ThesIn the FSI study by Ranga et al. in 2006 , zero co In this section, both the principal and von-Mises stresses are reported and examined both quantitatively and qualitatively. The principal stresses in the leaflets were observed at two instants of the cardiac cycle, one at the beginning of systole and the other one at mid-systole (0.072 seconds into the cardiac cycle). In each of these moments, a preferential direction of these stresses was noticed in a circular arrangement around the attachment edge of the leaflet. Conversely, stress in the inner area, or belly, of the leaflet was more scattered, representing a less structured environment. This particular distribution was also qualitatively similar to previous reports and known stress patterns on the leaflets , 47. The stress levels were also assessed by comparing them to previously reported values under similar conditions. The locations of the elements sampled for comparison of their stress histories are given in The specific values computed for the stress magnitudes at these locations for both models and their percent differences are presented in  Validation in the fluid medium can be accomplished to a certain degree by comparing bulk flow properties of the model to known physiological data and also by searching for known flow patterns such as diastolic recirculation regions, which are known to occur, but are more difficult to quantify. Blood velocities were sampled in the model at three locations: the flow through the valve at the level of the commissures and the sinotubular junction as well as flow through the coronary ostia. For the first two locations, comparisons to clinical data can be made over the entire cardiac cycle regarding both the total flow ejected and the temporal distribution of this flow. For the coronary flow, the shape of the waveform is less precisely known, although certain aspects, such as the total flow and the general shape, have been documented. The computed velocities at the STJ, commissure, left, and right ostia are provided in We also considered the impact of varying the stiffness of the aortic wall elastic modulus from 3.34 MPa to 60 MPa and the thickness of the aortic valve leaflets from 0.05 to 0.1 cm to simulate aortic stiffening and CAS, respectively , 50. In As it can be seen from the figure above, the coronary flow exhibits slight variations up to certain critical values of stiffness and thickness for which a marked drop is observed. Although interesting, this phenomenon warrants to be confirmed with clinical evidence. A model of the aortic valve including flow engaging in the coronary ostia was presented in this paper. An FSI analysis was performed using explicit LS-DYNA to study the aortic stiffening and the dynamics of the valve, and their effect on the coronary flow. The ALE method was used for the FSI analysis of this study. The results from this analysis in terms of leaflet morphologies, leaflet stresses, timing during the opening and closing phases, and velocities at critical points were presented. The leaflet morphologies during the opening and closing phases, shown in For verification, known clinical parameters of rapid valve opening and closing time and velocities were presented in Leaflet stresses were presented in Results obtained from the fluid domain including velocity at STJ or commisures were also in good agreement with previous studies. Another interesting result was obtained from a temporal examination of the velocity plots. Blood flow through commissures and STJ, in a sense, represent the bulk flow of the blood through the aortic valve. A peak velocity of 1.41 m/s occurred at 0.087 s, which is in agreement with previous studies that have reported peak velocities of 1.35 ± 0.35 m/s [Results were also achieved for cases of aortic wall stiffening. These results revealed an impact of aortic wall stiffening on coronary flow. As shown in 2/mmHg in sedentary healthy young subjects to values of about 1.2 to 1.3 mm2/mmHg in middle-aged and older sedentary humans. But in the highly trained middle-aged and older subjects (on a 3-month exercise period), exercise appeared to reduce the decline in compliance with aging by about 50%. Again a short time of regular exercise has a strong effect on the arterial compliance. Finally diet has also a strong effect on arterial compliance. Nestel et al. [These results showed that below a value of aortic wall elastic modulus being equivalent to three times the normal value of aortic wall elastic modulus, the peak coronary velocity remained constant. This observation could be correlated to the beneficial effects of smoking cessation, exercise, and diet on arterial compliance. Oren et al.  revealedl et al.  studied Consequently, the results we obtained associated with those of Oren et al. , Tanaka The increase of aortic valve leaflets thickness (mimicking CAS) led to a decrease in coronary peak velocity. Above a certain threshold, a marked drop in peak velocity occurred. These results were again in agreement with previous studies , 56. In It is known that aortic compliance is reduced as the cardiac tissue becomes aged and pathological . RecentlFor a less compliant aortic wall, the impact of the reduction in elastic recoil would be direct as less energy is stored in the wall during systole. As for the case where the leaflets have thickened, this loss in the potential energy could be linked to the increase in blood velocity through the valves (due to reduction of effective orifice area) and the associated pressure drop. In that context, we believe that the hydraulic resistance and the vessel compliance could compound to produce the observed sudden drop in the perfusion.Several assumptions and simplifications were made in the present study. A linear elastic model was used to mimic aortic root and aortic valve leaflets behavior, which leads to a short computing time compared to nonlinear models. However, in the context of aneurismal diseases, the linear elastic model used for its simplicity and ease of calculations would need to be expanded to nonlinear elastic in order to take into account for the large deformations. In addition, to investigate the aneurysm rupture process, it would be required to generalize the assumption of an isotropic model, which is sufficient for global assessment, to anisotropic model to integrate the vascular microstructures.As for boundary conditions, the inlet boundary condition at the ventricular level is considered to be the pressure difference between the ventricle and aorta. This is an inevitable constraint imposed on the model to avoid introducing instabilities and extensive run-times in an already complex FSI model. This assumption will cause the aortic wall to experience a smaller pressure, specifically during mid-systole. As a result aortic root expansion will be reduced, which could affect the leaflet opening and closing pattern. The percent difference observed for RVCV could also be due to this reduced expansion and loss of distensibility in the sinuses. This assumption might cause the drop observed in the coronary perfusion to have a minor shift across the range of wall stiffness and leaflet thickness studied. Moreover, the leaflets thickness was considered constant on the whole leaflet surface, whereas this one varies along the leaflet. The leaflets are the thinnest in the belly, their load-bearing part. They become thicker towards the line of attachment and the leaflet free edge. The thickest part is the nodule of Arrantius, just below the center of the free edge . FinallyIn this study, we have shown that a moderate increase in aortic stiffness and aortic leaflet thickness (CAS) will lead to a noticeable drop in coronary perfusion. Considering the fact that short-term smoking cessation, regular exercise or diet could cause a mild change in aortic compliance; this study suggests that such preventions and/or prophylactic treatments could significantly improve the coronary perfusion. The thresholding phenomena observed via a drop in the coronary flow, due to varying the stiffness and thickness of the aortic wall and leaflet tissues, are very interesting as it suggests a possible interaction between valvular and coronary diseases but warrants further analysis with exhaustive clinical data. The incorporation of the coronary ostia improved the opening and closing valve dynamics, compared to a model without the coronary arteries. The model is sensitive enough to differentiate between normal and slightly hypertensive conditions showing distinct impact on the valves dynamics.The proposed model that incorporated perfusions in the coronary ostia has the potential to investigate the impact of flow disturbances in the aortic root on the coronary flow and eventually the impact of coronary obstructive diseases on aortic stiffening and aortic valve leaflets dynamics. It would also be possible to examine coronary perfusion variations due to mechanical and geometric modifications of the aortic root using clinical metrics for validation of the approach. Such investigations are not possible with previously described models of the aortic root without any coronary structures.


The blood flow through aortic coarctations can undergo transition to turbulence, as the narrowing causes the velocity to increase. Increased levels of turbulent kinetic energy (TKE) are undesirable, as energy is drawn from the mean flow to the turbulent fluctuations. It has recently been shown that TKE in blood flow can be measured with MRI , and theA 63 year old female with an aortic coarctation was examined in a 1.5T Philips Achieva MRI system before and after balloon dilatation. The catheter intervention resulted in a decrease in pressure drop over the constriction and an increased flow rate. Measurements of the velocity and turbulent kinetic energy in the whole aorta over the complete cardiac cycle were obtained using navigator-gated time-resolved 3D phase-contrast MRI . Blood fTKE is an estimator of the amount of turbulence present in the flow. In the pre-intervention case, both CFD and MRI showed large values of TKE at two locations in the aorta; in the throat of the coarctation and in the aortic arch where a sharp bend of the aorta was present. After intervention, total TKE levels decreased even though the cardiac output increased. This can be explained by the larger cross-sectional area after intervention, effectively reducing local velocity. MRI and CFD results both showed that turbulent flows were present from the aortic arch to the lower descending aorta during systole, and then dissipated during the beginning of diastole. Peak values of TKE occurred during systolic deceleration and not at peak flow rate, as, in general, accelerating flows tend to have a stabilizing effect, while decelerating flows are more prone to break up.The agreement between CFD and MRI results was very good, with both methods predicting transition to turbulence at the same locations in the aorta and with the same TKE magnitudes. As the methods and data used to obtain TKE by MRI and CFD are completely different, these results confirm that MRI-measured TKE is reliable and accurate.Swedish Research Council, the Swedish Heart-Lung Foundation