Explaining the prediction of deep neural networks makes the networks more understandable and trusted, leading to their use in various mission critical tasks. Recent progress in the learning capability of networks has primarily been due to the enormous number of model parameters, so that it is usually hard to interpret their operations, as opposed to classical white-box models. For this purpose, generating saliency maps is a popular approach to identify the important input features used for the model prediction. Existing explanation methods typically only use the output of the last convolution layer of the model to generate a saliency map, lacking the information included in intermediate layers. Thus, the corresponding explanations are coarse and result in limited accuracy. Although the accuracy can be improved by iteratively developing a saliency map, this is too time-consuming and is thus impractical. To address these problems, we proposed a novel approach to explain the model prediction by developing an attentive surrogate network using the knowledge distillation. The surrogate network aims to generate a fine-grained saliency map corresponding to the model prediction using meaningful regional information presented over all network layers. Experiments demonstrated that the saliency maps are the result of spatially attentive features learned from the distillation. Thus, they are useful for fine-grained classification tasks. Moreover, the proposed method runs at the rate of 24.3 frames per second, which is much faster than the existing methods by orders of magnitude. Recent years have witnessed the evolution of deep learning at an astounding rate. For instance, in the image classification task, residual networks , the winHowever, generating human-understandable explanations of model predictions is critical for the widespread adoption of deep neural networks. For example, a medical decision support system based on deep neural networks should be trustworthy and able to explain its predictions for patients or clinicians in addition to its ability to accurately diagnose the problem. The excellent performance of deep neural networks is attributed to the learning capability of the models that typically comprise several billions of trainable parameters ,5,6,7. SA large body of approaches has been proposed to create visual explanations of the models’ predictions. They provide visual explanation methods that create saliency maps representing the importance of input features for classification tasks ,14,15,16The practical deployment of the explanation methods should satisfy two requirements. First, the methods should run rapidly . Second, the method should generate saliency maps of high fidelity that only highlight truly important regions of the image in a fine-grained way . The advIn this paper, we propose a novel approach that generates a saliency map to explain the prediction of the target network by the corresponding surrogate networks see . A salieWe propose a knowledge distillation method that transforms the black-box target model into the corresponding surrogate network. The proposed knowledge distillation provides enriched information at various levels to be integrated into a saliency map for the model prediction.As a result, the proposed method creates a fine-grained saliency map compared to those of the existing methods. Experiments demonstrate that fusing the multi-level information is beneficial, especially in a fined-grained classification task.The proposed method requires no individual learning for the input once the corresponding surrogate networks are trained using the knowledge distillation. Generating a saliency map is done at the inference speed of the surrogate networks, which is significantly faster than the learning-based methods while providing comparable explanations both quantitatively and qualitatively.In this section, we briefly review recent work on explaining deep neural networks to highlight the advantages of the proposed method.Methods that belong to this category aim to learn the optimal explanation for a given input by gradually improving a randomly initialized saliency map  with random perturbations of the input. Perturbing the input image and measuring the corresponding sensitivity of the model prediction is a popular approach to estimate the importance of the input features. Occlusions or masks (as perturbations) are queried to the image repeatedly to determine the optimal saliency map. In particular, this approach measures the prediction difference between the input image and its perturbation assuming that if the important regions of the input are perturbed, the model output  will degrade, compared to that for the original input. These methods learn the feature importance of an input at the pixel-level  or at thThe method proposed in  uses arbThese methodologies learn to generate a visual explanation by aggregating the model outputs from the perturbations of the input. The resulting saliency maps identify the informative regions representing the object. Furthermore, it is possible to create a fine-grained visual explanation when the perturbation is made at the pixel-level. However, saliency maps generated by those methods are non-deterministic due to the randomized input perturbation. Another disadvantage is that creating a visual explanation in such a way is time-consuming because of numerous inferences for random samples from the input perturbation. For instance, in our experiments, the representative perturbation-based methods  maps of a convolutional neural network (ConvNet) have the regional information. Zeiler and Fergus  proposedA gradient represents the amount of change in the output score of the model corresponding to a small change of each dimension of the input. As a result, the gradient can be viewed as a measure of pixel importance to represent how much the pixel contributes to the model prediction. Simonyan et al.  proposedSelvaraju et al.  generalid-dimensional vector and a target network  with an emphasis on attention. Attention is a method that aims to obtain information on which part a neural network considers important for the prediction; this originated from a machine translation task in the field of natural language processing . RecentlThe student network is based on ResNet-50  and thusIn particular, a set of features ectively . Then thAs explained earlier, the student network provides the explanation network with information on the attentive features that are taken from the three layers at different scales, as shown in Training the explanation network aims to generate a faithful saliency map for a given input in terms of retrieving the class score on the target network. Then, the cost function for training the explanation network in Equation  is givend images ,26,27. Ac is the target class of x. The proposed method is end-to-end trainable by combining Equations (We formulate Equation  by lettiquations  and 3)  LEXP(x) How do saliency maps generated by the proposed method retrieve the class score that is predicted by the target network for a given input?How is the proposed method advantageous over existing explanation methods? In other words, how fast does the proposed method process images? Additionally, are there any downstream tasks that the proposed method performs favorably as compared to the previous methods?We conducted a set of experiments to evaluate the proposed method. The goal of the evaluations was to answer the following questions:Dataset. We used four datasets for the experiments: ImageNet [ImageNet , CUB-200ImageNet , Cars [3ImageNet , and FGVImageNet . ImageNeImplementation Details. We used ResNet-50 that was pretrained on ImageNet as the target network t to 1 in Equation . The student network aims to approximate the output of the target network using attention and was trained with the knowledge distillation to better transfer the inference capability of the target network. The explanation network takes the attentive features learned by the student network as inputs. The goal of the explanation network is to generate a saliency map that faithfully retrieves the original class scores of the target network. The experimental results demonstrated the advantages of the proposed method as follows. First, the fidelity of saliency maps generated by the proposed method is competitive in terms of two quantitative metrics  as compared to the best-performing approaches. In addition, the proposed method is efficient in that it runs much faster than the best method by two orders of magnitude. Lastly, the qualitative evaluation indicates that the proposed method results in fine-grained saliency maps and enables itself to be suitable for fine-grained classification, a useful downstream classification task.


Research using linked routine population-based data collected for non-research purposes has increased in recent years because they are a rich and detailed source of information. The objective of this study is to present an approach to prepare and link data from administrative sources in a middle-income country, to estimate its quality and to identify potential sources of bias by comparing linked and non-linked individuals.We linked two administrative datasets with data covering the period 2001 to 2015, using maternal attributes  from Brazil: live birth information system and the 100 Million Brazilian Cohort  implementing an in house developed linkage tool CIDACS-RL. We then estimated the proportion of highly probably link and examined the characteristics of missed-matches to identify any potential source of bias.A total of 27,699,891 live births were submited to linkage with maternal information recorded in the baseline of the 100 Million Brazilian Cohort dataset of those, 16,447,414 (59.4%) children were found registered in the 100 Million Brazilian Cohort dataset. The proportion of highly probably link ranged from 39.3% in 2001 to 82.1% in 2014. A substantial improvement in the linkage after the introduction of maternal date of birth attribute, in 2011, was observed. Our analyses indicated a slightly higher proportion of missing data among missed matches and a higher proportion of people living in an urban area and self-declared as Caucasian among linked pairs when compared with non-linked sets.We demonstrated that CIDACS-RL is capable of performing high quality linkage even with a limited number of common attributes, using indexation as a blocking strategy in larg e routine databases from a middle-income country. However, residual records occurred more among people under worse living conditions. The results presented in this study reinforce the need of evaluating linkage quality and when necessary to take linkage error into account for the analyses of any generated dataset. Research using routine population-based data collected for social, financial, and clinical purposes has increased in recent years because they are a rich and detailed source of information available at a relatively low cost . Record Record linkage can be conducted using two main methods: deterministic and probabilistic. Deterministic linkage usually uses a unique identifier or a set of several attributes present in all the databases to be linked . ProbabiSome extensions of linkage error in administrative data are expected and inevitable due to the imperfect and transient nature of the attributes. However, even a small amount of linkage error can lead to biased results, diluting real association, or creating spurious ones . MeasureWe aimed to use Brazilian nationwide administrative databases to build CIDACS  birth cohort that will be originated by the link between the live births dataset and the baseline of the 100 Million Brazilian Cohort . The design of CIDACS Birth Cohort follows a life course perspective, using routinely collected data from Brazil. The use of linked high-quality administrative datasets provides a unique opportunity to examine factors that might result in long-term and rare child and maternal outcomes over time, with the additional advantage of using large samples, little loss to follow-up, high level of external validity and a great deal of applicability for policymaking .We expected an overlap between the baseline of the 100 Million Brazilian Cohort and the live birth databases. In this scenario, we were able to measure the linkage error. This study presents an approach to prepare and link data from administrative sources in a middle-income country, estimating the proportion of births for which you were able to identify a link based on a specified threshold and identifying potential sources of bias by comparing link and no-links.In this section, we describe the methods we used to integrate two major nationwide databases, the Live Birth Information System (SINASC) and the baseline of the 100 Million Brazilian Cohort from 2001 to 2015.SINASC (Sistema de Informação Sobre Nascidos Vivos/ Live Birth Information System)The Brazilian Ministry of Health defines live births as the complete expulsion or extraction from the body of the pregnant woman of a product of conception, independent of the duration of pregnancy, who, after the separation, breathes or shows any other signs of life, such as heartbeat, umbilical cord pulsation, or definite movement of voluntary muscles, whether or not the cord is cut and whether or not the placenta is attached. SINASC records live births in Brazil, and this system is updated using the registration of live birth. It is a compulsory document, completed by a health professional who assisted the delivery. This form is divided into eight blocks. I -characteristics of the newborn; II- identification of the place of birth; III- characteristics of the mother; IV- identification of the father; V- characteristics of pregnancy and delivery; VI- characteristics of congenital anomalies: this block should be filled in when congenital anomalies are identified at birth using the ICD-10 code. VII- identification of the professional completing the notification. VIII- registry office identification . Between2)The baseline of the 100 Million Brazilian CohortData completeness is very high, with 97% of Brazilian births registered , and mosThe baseline of the 100 million Brazilian cohort was built using information from the application of families and their family members for social assistance programmes in Brazil through the registration with the Unified Register for Social Programs (CadÚnico). The CadÚnico is the main instrument used by the Brazilian government to assess the inclusion criteria of potential beneficiaries of social programs. To be enrolled in CadÚnico, one person in the family must provide information and required documents of all family members to an interviewer. This person must be at least 16 years old and, preferably, be a woman. The information available in the 100 million cohort is collected for each member of the family in a standardized form that includes individual  and familial  sociodemographic information. The information is renewed periodically as long as the person is a candidate to receive one of the several Brazilian government social protection programs [Data completeness depend on the variable, but name and municipality of residence are available for all individual registered. Once registered, each family receive a unique code.During the data pre-processing phase, first, we searched automatically for invalid names , by comparing the recorded name with a standardized list of possible Brazilian names. All names considered invalid are submitted to a clerical review. In this review, the potential invalid terms are analysed to see if they are valid but were not recognized because they had typos, different spelling, or foreign name, among other reasons, or if in fact; they are invalid . And so, any term that deviates from what is known as “valid” is excluded. We removed punctuation, deleted consecutive spaces; middle initials, prefixes, and suffixes were maintained as recorded to retain the discriminatory power of the name variable.The complexity of the record linkage task is quadratic. We have to find the best match, on database B, for each record in database A, |A| X |B|. ‘To enable the record linkage is efficient when massive datasets are involve, we need to use methods capable of avoiding unnecessary comparisons, whilst keeping the accuracy. The total number of pairwise comparisons between SINASC and CadUnico would otherwise be prohibitively high 44,485,267 x 114,007,705=5,07166e15. To meet these challenges, we use the CIDACS-RL [The CIDACS-RL applies the combination of indexing and searching algorithms implemented in Apache Lucene solution as the blocking strategy to reduce the number of comparisons during the linkage. The indexation strategy allows the CIDACS-RL to search the most similar records from the Indexed baseline of the 100 Million Brazilian Cohort for each record in SINASC and submit them to the pairwise comparisons step, instead of restricting the comparison group as an ordinary blocking step. This search was performed in two ways, (i) using the mothers’ name, municipality, and mothers date of birth records as attributes, from 2011 to 2015 (ii) using mothers name and municipality, from 2001-2010, because the mothers’ date of birth was not registered before 2011. This search strategy uses a mixture of exact, semi fuzzy and fuzzy queries to return the 1000 best candidates from the indexed baseline of the 100 Million Brazilian Cohort. The exact queries return only records with equal attributes in every querying, while the semi-fuzzy and fuzzy approaches permit more flexibility by retrieving candidates where one (semi-fuzzy) or more attributes differ (fuzzy). In cases where the name of the mother was not the same, the Damerau-Levenshtein distance is used as a string comparator to estimate the similarity between comparison pairs, and values above 0.5 are considered .The most discriminant variables available on the live birth database to identify a child are a maternal name, maternal municipality, and maternal age. For those records from 2011 to 2015, the mothers’ date of birth attribute becomes available, and its filling increases gradually across the years. For 2001-2010, where the mothers date of birth is not available, we proceeded with the search using only two attributes  then, we create a new variable by subtracting the date of birth of the child information recorded in SINASC from the date of birth of the mother recorded in baseline of the 100 Million Brazilian Cohort, and this value was compared with the age of the mother registered in SINASC, only the candidates with exacted same value were considered as possible candidates and submitted to the pairwise comparison step. This step was also executed for records from 2011 to 2015 with missing values in the mothers’ date of birth.Figure The similarities between names recorded in SINASC and the 1000 best candidates from the baseline of the 100 Million Brazilian Cohort were compared using the Jaro-Winkler string comparator . The JarCandidate linking records were ordered by the scores achieved; only the comparison pair with the highest score is retained as a potential link. All remaining candidate records are discarded. If two people received the same candidate as a potential link, we retained only the ‘best candidate’ as a comparison pair. We removed this candidate as a possible match for all other comparison pair. Then a sample of 2000 pairs stratified in three categories of linkage score  is evaluated manually, and the records pairs are classified as likely true pairs or likely false pairs. Based on the training dataset of 2000, the receiver operating curve (ROC) is built to choose the best cut off point, and calculating the area under the curves (AUC), balancing between sensitivity and specificity values. Records were therefore classified as links or non-links based on a single threshold. The software R is used to generate accurate results.Since we expected that all births registered in the baseline of the 100 Million Brazilian Cohort overlapped with the births existing at SINASC databases, we were able to identify the number of missed matches (record from the same mother-baby pair that failed to link) of the linkage. We then examined which characteristics were associated with missed matches. We examined race, sex, place of residence, sewage treatment, water supply, garbage collection.The process described above identifies maternal links between the SINASC and the 100 million cohort dataset. After the mother is identified, we searched for the registry of the offspring in the 100 million cohorts using the child date of birth and sex.A total of 27,699,891 live births were submitted to linkage with maternal information recorded in the baseline of the 100 Million Brazilian Cohort dataset from 2001 to 2015. Of those, 16,447,414  children were found registered in the 100 Million Brazilian Cohort dataset. However, the proportion of liked pairs were not similar over the years  has been considered a more problematic task, due to the limited number of shared identifiers within datasets , 22. WhiThis study has several limitations. A weakness of using the CIDACS birth cohort that should be addressed when answering individual research questions, is that it is restricted to people enrolled at CadUnico, which represents some of the poorest of Brazil's population. The main limitation inherent to the linkage process is the low proportion of births for which you were able to identify a link based on a specified threshold in the first years before the introduction of the mother's date of birth. This information is highly valuable because when using our cohort it could be decided to use only those years that have achieved the highest proportion of births for which you were able to identify a link. More important than the proportion of highly probably link of linkage in terms of proportion of links, the linkers have to guarantee that the linkage error did not introduce bias in the final analyses. Although the difference in some living conditions variables and socio-demographic’s characteristics between the linked and non-linked groups were less than 10%, even small amounts of linkage error can result in substantially biased results. For example, in the variable race, almost 25% of indigenous people were not linked; it could make a difference in studies using this population. Therefore, we recommend further studies to evaluate if these small differences can introduce bias and to take this in consideration in any future analyses using our birth cohort.An essential step of the linkage process is to estimate the linkage quality and to identify potential sources of bias that can be introduced in the results of analyses using the linked data. The linkage involving two nationwide large Brazilian databases evaluated here showed proportion of highly probably link for more recent years comparable with previous finds in developed countries , 24. Alt


Despite the longstanding appreciation that how we move, think, and feel has an impact on stomach function, the areas of the cerebral cortex that are the origin of these influences are largely unknown. Here we identify the cortical areas that influence the rat stomach. Output neurons in the rostral insula are the major cortical source of influence over parasympathetic control of the stomach, whereas output neurons in sensorimotor areas of the cortex are the major source of influence over sympathetic control. Thus, cortical areas involved in action, interoception, and emotion differentially influence stomach function. The central nervous system both influences and is influenced by the gastrointestinal system. Most research on this gut–brain connection has focused on how ascending signals from the gut and its microbiome alter brain function. Less attention has focused on how descending signals from the central nervous system alter gut function. Here, we used retrograde transneuronal transport of rabies virus to identify the cortical areas that most directly influence parasympathetic and sympathetic control of the rat stomach. Cortical neurons that influence parasympathetic output to the stomach originated from the rostral insula and portions of medial prefrontal cortex, regions that are associated with interoception and emotional control. In contrast, cortical neurons that influence sympathetic output to the stomach originated overwhelmingly from the primary motor cortex, primary somatosensory cortex, and secondary motor cortex, regions that are linked to skeletomotor control and action. Clearly, the two limbs of autonomic control over the stomach are influenced by distinct cortical networks. The central nervous system both influences and is influenced by the gastrointestinal system. Most research on this gut–brain connection has focused on the ascending pathways that link signals from the gut and its microbiome to alterations in brain function , 2. LessCentral control over stomach function is mediated by the parasympathetic and sympathetic limbs of the autonomic nervous system. In general, parasympathetic output to the stomach tends to increase secretions and enhance the patterns of smooth muscle contractility that are required for processing a meal –7. In co8Given the importance of the central control over stomach function, it is surprising how little is known about the cortical origins of the descending commands that mediate these effects. Here, we used retrograde transneuronal transport of rabies virus (RV) to reveal the chain of interconnected neurons that links the cerebral cortex to parasympathetic and sympathetic control of the rat stomach. This species is of particular interest because of its rapid development of stress-induced stomach ulcers , 14. We We injected RV into the anterior wall of the rat stomach and used retrograde transneuronal transport of the virus to label the cortical neurons that most directly influence this organ. We confined our analysis to cases in which cortical neurons infected with RV were restricted to Layer V, the origin of subcortical outputs from the cerebral cortex. To isolate cortical labeling to parasympathetic or sympathetic circuits, we carefully adjusted survival times and employed bilateral subdiaphragmatic vagotomy in some animals .Transport of RV in parasympathetic circuits labeled first-order neurons in the dorsal motor nucleus of the vagus, second-order neurons in the nucleus of the solitary tract, and third-order neurons in Layer V of the cerebral cortex A, and 3.The overwhelming majority of the cortical neurons that influence parasympathetic control of the stomach were located in two cortical regions: the insula (>81%) and portions of medial prefrontal cortex , primary somatosensory cortex , and secondary motor cortex  to the trunk and trunk/hindlimb representations  and “fight or flight” (involving action). Although these characterizations are an oversimplification, and autonomic regulation is more nuanced and predictive , 19, theThe rostral insula is the major cortical source of descending control over parasympathetic output to the stomach A and 5. Right). This network architecture is comparable to the series of three synaptically connected neurons that link the output from the primary motor cortex to skeletal muscles in the rat (Left). Thus, the rostral insula may serve as a parasympathetic motor cortex with a command structure and function that is comparable to the control of skeletal muscle by the motor cortex.Our results indicate that the rostral insula is linked to the stomach by a series of three synaptically connected neurons , Right.  the rat , Left. TThe rostral insula gathers visceral afferent information, including signals from the stomach , 23, andIn the rat, the descending control over sympathetic output to the stomach is embedded in M1/S1 and M2 B and 5. The viscerotopic shifts in the location of cortical neurons that influence sympathetic output  are simiIt is also noteworthy that the cortical distributions of the output neurons innervating the stomach and kidney display considerable overlap. This arrangement is similar to the overlap observed between the cortical distributions of output neurons innervating synergistic muscles. In both cases, the partially shifted overlap may be the substrate for variable, but integrated, control of the different output systems.There has been a growing awareness of the importance of the gut–brain axis to human health. However, the discussion of this issue has largely focused on how the gut microbiome influences the function of other organ systems , 30–32. 30Helicobacter pylori . Most of the technical procedures, as well as those for handling virus and virus-infected animals, have been described elsewhere  that received RV injections into the anterior stomach wall. We used the N2c strain of RV  and xylazine (4 mg/kg intramuscularly), and all animals received perioperative analgesia with buprenorphine (0.1 mg/kg subcutaneously). The stomach was accessed via an anterior midline incision. The gastrohepatic ligament was cut to allow the liver to be reflected superiorly and expose the full extent of the anterior wall of the stomach. We placed eight injections of RV  into a region of the distal fundus and proximal body of the stomach. Following the injections, we sutured the wound in layers and then returned each animal to an isolation cage specifically designed for housing virus-infected rats.We placed animals on a liquid diet  for 48 h before surgery. To cut the vagus nerve, we retracted the liver to reveal the subdiaphragmatic portion of the esophagus. The anterior vagal trunk was identified and cut just proximal to the gastroesophageal junction. We cut the posterior vagal trunk at a more proximal level. Immediately following the nerve sections, we injected the stomach with RV as described earlier. Because vagal denervation of the stomach leads to gastric stasis and potentially impairs tolerance for solid foods, we provided these animals with a diet composed of a diluted nutrient drink  and DietGel for the entirety of the survival period.n = 4 animals, mean survival time, 89.5 h); to examine sympathetic circuits, the survival time was set to label fourth-order neurons  and the vagus nerve was sectioned . This control group demonstrated infection of third-order neurons in the spinal cord and brainstem, but no labeling in the cerebral cortex. At the end of the survival period, each animal was anesthetized and then perfused with blood washout (phosphate buffer) and fixative  to preserve the nervous system (We varied survival times to restrict labeling to Layer V neurons in the cerebral cortex. To examine parasympathetic circuits, the survival time was set to label third-order neurons (ectioned . A contrs system . FollowiWe used standard immunohistochemical methods to section and react the tissue from these experiments . In brieOur analytic procedures have been described in detail previously . Briefly2 tests to compare the proportions of neurons in various cortical regions that were linked to either the parasympathetic or sympathetic regulation of the rat stomach. All P values were adjusted for multiple comparisons using the Bonferroni method. P values <0.05 were taken as statistically significant.We used χData are available from the corresponding author upon request.


Streptococcus–Veillonella sp. biofilm system as an example for numerical investigations. The presented model describes both the cooperation and competition between these species of bacteria. The coupled partial differential equations are solved by using an integrative finite element numerical strategy. Numerical examples are carried out for studying the evolution and distribution of the bio-components. The results demonstrate that the presented model is capable of describing the symbiotic behavior of the biofilm system. However, homogenized numerical solutions are observed locally. To study the homogenization behavior of the model, numerical investigations regarding on how random initial biomass distribution influences the homogenization process are carried out. We found that a smaller correlation length of the initial biomass distribution leads to faster homogenization of the solution globally, however, shows more fluctuated biomass profiles along the biofilm thickness direction. More realistic scenarios with bacteria in patches are also investigated numerically in this study.We present a multi-dimensional continuum mathematical model for modeling the growth of a symbiotic biofilm system. We take a dual-species namely, the  Competition and cooperation among species of bacteria are normally involved in multi-species biofilm systems  biofilm system. Recently, Tang and Liu  oral biofilm system with a further developed CA model. Three models on the relationship between these two species of bacteria, namely independence for substrates, competition for substrate, and inhibition of one to another, are compared in their study. Individual-based Modeling (IbM) have also been used for studying various multi-species biofilm problems, such as modeling ammonium oxidizer bacteria (AOB) and nitrite oxidizer bacteria (NOB) system  coexisting in the system   biofilm models which involve complex reactions.The model presented in this paper can be used for quantitatively understanding of the This paper is structured as follows. Details of the model will be presented in Sect. Streptococcus–Veillonella biofilm system is illustrated in Fig. S. gordonii and V. PK1910 interact with each other in a mutualistic relationship. Especially, S. gordonii produces lactic acid, which plays a vital role in the chain of the symbiotic bio-chemical process is modeled explicitly. Despite the saliva cannot function as a carbon source for the Veillonella sp., saliva still may provide other nutrients for the growth of both species due to its complex mixture substance property. Therefore, a competition of the saliva between S. gordonii and Veillonella sp. is considered in the model. On the other hand, Veillonella sp. helps to prevent the environment from being too acid, and thus benefits the growth of S. gordonii. We develop the mathematical model based on the following assumptions:A layer of biomass with a finite thickness has been presented as an initial condition. The model does not capture the process in which individual bacteria grow into a biofilm. On the other hand, the growth process after forming an initial layer of biofilm is modeled.Streptococcus sp., and Veillonella sp. are considered in the model. The volume fractions of the bacteria sum to one inside of the biofilm, which implies that the pore space and EPS are not explicitly modeled  during biofilm growth. This is mostly due to the difficulty of enforcing proper potential (or pressure) boundary conditions for the newly generated biofilm-fluid surface. Such a problem may come up when trying to model the merge of different colonies. As illustrated in Fig. mentclass2pt{minimTo build up the model based on the above assumptions, the mass balance of each substrate and component of biomass in the biofilm is considered. Eventually, the mathematical model, which is essentially a free boundary problem, consists of five partial differential equations (PDEs) including four coupled nonlinear time dependent advection–diffusion-reaction (or advection-reaction) equations and a Poisson’s equation.Taking a 2D model as an example, the biofilm is modeled within a computational domain of S. gordonii and Veillonella are modeled as advective movements driven by the production and reduction of biomass inside of the biofilm. Writing the mass balance equations of S. gordonii and Veillonella sp. in terms of their volume fraction S. gordonii and Veillonella bacteria respectively and, g refers to the mass production/reduction rate of the biomass. A no-flow boundary is applied for both Eqs.  is much smaller than the time scale of the biofilm growth S. gordonEquations , 5), ,  and 15a15a togetH and To obtain the dimensionless form of the governing equations, we introduce the following dimensionless variablesSubstituting Eq.  into EqsWe investigate the solution behaviors of the mathematical model in this section. An initially evenly mixed scenario has been investigated in Sect. Two-dimensional simulations are carried out with the modeling parameters listed in Table A wave shape initial biofilm-fluid interface in the dimensionless domain is appliedS. gordonii and Veillonella at early and late times are shown in Fig. Simulation results of biomass distribution of both S. gordonii, Veillonella and total biomass at different times along S. gordonii moves up as a result of winning the competition for nutrients in saliva in the vicinity of the biofilm-fluid interface. Such a phenomenon has also been observed in experimental studies  Will the local homogenization process always happen in this model regardless of the initial biomass distribution? If so, will the initial distribution influence the homogenization process? (2) How will a heterogeneous initial biomass distribution influence the morphology of the biofilm interface as well as the components (including the biomass and the lactic acid) distributions during the growth?In order to answer these questions raised in the previous section, we study the sensitivity of the presented mathematical model to different types of initial biomass distributions. As a matter of fact, the initial distribution of different species of bacteria in a biofilm can be never evenly mixed in nature. As shown in Fig. Veillonella patches are stretched and thus generating plume-like structures during the biofilm formation in all three cases. This indicates that processes happen mainly in the vertical direction, and the horizontal movement is not obvious. By increasing the correlation length of the initial biomass distribution, the size of the plumes increases. This results in that the biomass volume fraction profiles along a vertical line, for instance at Veillonella between the evenly mixed and randomly distributed cases to measure the homogenization processVeillonella, N is the number of the unknowns in the vector and indexes “mixed” refers to the evenly mixed initial condition. The index As shown in Fig. The evolution of Veillonella group bacteria are embedded in Streptococcus group bacteria , are generated by using an implicit superquadric function which is defined by an implicit equation with random parameters  in which the growth of both species of bacteria is limited only by the nutrient . In this case, the lactic acid does not play a role in biofilm growth, and it accumulates in space. One would expect that by applying CM, the biofilm grows faster than using SM due to the absent limitation of the lactic acid. Meanwhile, the species which has a larger maximum growth rate becomes dominant during the growth. As shown in Fig. Streptococcus sp., has been explicitly modeled. We found that the volume fractions of different species of bacteria homogenize at a later time. To understand the solution behaviors, we studied how the initial biomass distribution influences the homogenization process. Random distributions of the biomass volume fractions with different correlation lengths were taken as initial conditions. We compared the simulation results of the case where the bacteria were initially evenly mixed. As would be expected, the biomass homogenized faster associating with an initial state with a smaller correlation length. However, the random distribution cases do not converge to the same concentration distribution as the evenly mixed one, although the same initial mass and morphology of the biofilm surface (flat surface) have been assigned.We have presented a new mathematical model for modeling the growth of symbiotic biofilms in this paper. An intermediate product, namely the lactic acid produced by the For a better understanding of the role of the initial distributions, we investigated scenarios with patch-shape biomass. The simulation results demonstrate that the local growth field can lead to changes in the morphology of the biofilm surface and different bacteria patches’ movements. Moreover, we also observe various homogenization speeds that are induced by the heterogeneity of the symbiotic reactions. To understand the role of the reactions in the homogenization process, we simplified the model by switching off the symbiotic reactions, resulting in a competitive model. The competitive model’s numerical solution does not get homogenized, which demonstrates that the symbiotic reaction is one of the main reasons for spatial homogenizations.It is well-known in microbiology that bacterial biofilms’ biological behaviors are a lot more complicated than a mere competition of “food” in nature. Many efforts have been put in the past decades to understand how different bacteria species interact in a biofilm. The symbiotic relationship between two species of bacteria is one of the most interesting phenomena in microbiology systems.Mathematical modeling has been proved to be a powerful tool for understanding biofilm’s biological behaviors in the past years (Mattei et al. To the best of the authors’ knowledge, this study provides the first comprehensive investigation of the dynamics of a biofilm’s symbiotic reactions using a continuum mathematical model. We modeled the biofilm growth as an advective movement of a reactive potential flow in this study. The model has the advantage of capturing a sharp biofilm interface without introducing additional parameters; however, it suffers limitations on modeling merge of different colonies (see Discussion in Sect. Instead of modeling the colonies’ merge, we are more interested in the reaction model developed for the symbiotic biofilm systems. Even though the simulation results demonstrate that the model can represent the species of bacteria’s symbiotic behaviors, we found that the reactive model can lead to homogenized solutions. The presented model may fail to predict the biological behavior of the symbiotic biofilms after a certain time when the numerical solution becomes over-homogenized. Therefore, it is necessary to investigate what factors influence the homogenization speed in the model. It turned out that the speed of the homogenization depends on the initial biomass distribution.et al. presented experimental evidence of signaling between S. gordonii and V. atypica (Egland et al. Individual bacteria are never resolved in a continuum biofilm model. This might be another potential reason which leads to the over-mixing of the biomass. However, the discretized element based biofilm models can also result in considerable internal mixing, especially for multi-species problems (Tang and Valocchi


The collective behaviour of neural networks depends on the cellular and synaptic properties of the neurons. The phase-response curve (PRC) is an experimentally obtainable measure of cellular properties that quantifies the shift in the next spike time of a neuron as a function of the phase at which stimulus is delivered to that neuron. The neuronal PRCs can be classified as having either purely positive values (type I) or distinct positive and negative regions (type II). Networks of type 1 PRCs tend not to synchronize via mutual excitatory synaptic connections. We study the synchronization properties of identical type I and type II neurons, assuming unidirectional synapses. Performing the linear stability analysis and the numerical simulation of the extended Kuramoto model, we show that feedforward loop motifs favour synchronization of type I excitatory and inhibitory neurons, while feedback loop motifs destroy their synchronization tendency. Moreover, large directed networks, either without feedback motifs or with many of them, have been constructed from the same undirected backbones, and a high synchronization level is observed for directed acyclic graphs with type I neurons. It has been shown that, the synchronizability of type I neurons depends on both the directionality of the network connectivity and the topology of its undirected backbone. The abundance of feedforward motifs enhances the synchronizability of the directed acyclic graphs. Particularly, synchronization plays a key role in the proper functionality of brain neurons. The synchronization of neuronal networks has been associated with many cognitive processes including memory formation7, directed attention9, and the processing of sensory stimuli10.For several decades, there has been a continuing research interest in the synchronization phenomenon due to its widespread application in natural and artificial systems ranging from neural dynamics12.Synchronization patterns mainly depend on the dynamical properties of individual oscillators as well as the underlying structural connectivity. It has been found that brain neurons have different types of intrinsic dynamics that close to threshold, they may be grouped into two excitability classes: Type I and Type II. These two types of neurons are different in terms of the bifurcation structure observed during their transition to firing. Type I oscillations arise via a saddle-node-onto-limit-cycle bifurcation, whereas type II oscillations are initiated by Andronov-Hopf bifurcation. In addition, type I neurons exhibit a continuous frequency-current curve, whereas type II neurons show a discontinuous frequency-current curve13. Different profiles of the neuronal phase response curve arise for different types of neurons in that in type I neurons, any excitatory perturbation causes an acceleration of the next spike, while in type II neurons, perturbations cause acceleration or delay of the next spike depending on the phase at which the perturbation is delivered to that neuron. These qualitatively different responses to stimulation lead to dramatically different synchronization patterns in neural networks. Previous studies have shown that, type I cells exhibit relatively poor propensity for synchronization under excitatory couplings, while type II cells are synchronized better16. Experimental results verify the neurons’ ability to switch between types as well as the coexistence of both cell types in the brain19. For instance, changes in the neocortical synchronization during sleep-wake cycle are often associated with excitability changes in the cortical neurons21.The aforementioned excitability type of a single neuron can be quantified by the phase response curve (PRC) which is an experimentally obtainable measure based on the transient change in the cycle period of the neuron in response to an external stimulus22. According to this formalism, the spread of the eigenvalues of the Laplacian matrix is a synchronizability index. That is, the more compact the eigenvalues, the more likely the synchronous state will be stable. This index works well when comparing synchronizability of chaotic oscillators and identical Kuramoto oscillators. Using the index, it can be shown that complete graphs and directed acyclic graphs with identical node in-degrees are optimal networks provided that they embed an oriented spanning tree24.Regarding the underlying network connectivity, Master Stability Function is a well-known formalism providing estimation of the synchronization stability in the networks of coupled identical oscillators28. Motifs are significantly over represented subgraphs that have been recognized as the building blocks of many real-world networks in various domains29. Therefore, it’s important to understand how the global dynamics are affected by the network motifs. For example, previous studies have shown that feedback loop motifs contribute to two phenomena: responses to noise and dynamical stability31.An entirely different approach to explore the impact of network structure on synchronization is investigating important and dominant topological features of networks known as motifs33. In order to study the dynamics of a large collection of such motifs, we generate two different directed graphs, with the same undirected skeleton, constructed only from FFLs or FBLs. These directed graphs are called directed acyclic graph (DAG) and balanced directed graph (BDG), respectively. Both analytical and simulation results show that type I excitatory and inhibitory neurons are synchronized in directed acyclic networks (i.e. networks without any feedback loops). However, these neurons fail to synchronize in undirected networks. In fact, feedback loops destroy synchronization of the networks with identical type I neurons.In this paper, we investigate the role of network motifs in synchronization of directed neural networks with type I or type II neurons. Among various network motifs, we focus on two distinct categories: (I) feedback loops (FBL) and (II) feedforward loop motifs (FFL). These motifs are commonly highlighted features observed in real-world networks and have attracted a great deal of attention in the literatureAn orientation of an undirected graph is an assignment of a single direction to each of its edges, turning the initial graph into a directed graph. In this paper, using two different algorithms, we built different orientations of a graph such that the number of feedback loops (FBLs) is maximized in one orientation and minimized in the other one. These algorithms are described bellow.34. Therefore, we start with an undirected graph, and try to assign each edge a single direction in such a way that the in-degree and the out-degree of any given node are almost the same. The Eulerian cycle in an undirected graph is a cycle that visits every link exactly once. An undirected graph has an Eulerian cycle if and only if every vertex has an even degree. Eulerian orientation of a graph is an orientation that directs the edges along the Eulerian path such that every vertex has the same number of incoming and outgoing edges. The resulting directed graph is called a balanced directed graph (BDG) and has maximum number of feedback loops. In a network in which some nodes are of odd degree, we can still build an orientation in a way that the resulting directed graph is almost balanced. To this end, a new fake node is added to the undirected graph and any existing node with an odd degree is connected to this new node. Since every undirected graph has an even number of nodes with odd degree, all the nodes in the new undirected graph have even degree and we can build the Eulerian orientation of the new graph. After orienting the graph, the fake node is removed with all its adjacent links. In this manner, the difference between in- and out-degree of each node is at most one and the oriented graph is almost balanced35.It has been shown that, the number of feedback loops increases by enhancing the correlation between the in- and out-degrees of the nodes37. At first, each node is labeled by a residual degree which determines the number of adjacent undirected links. The residual values drop as more adjacent links are assigned directions. Thus, initial and final residual values for each node equal to its degree and zero, respectively. In each iteration of assigning the directions, the node with the smallest residual degree is selected and all of its adjacent undirected links are assigned incoming directions. The residual values are updated afterwards and iterations are repeated until there are no undirected edges left in the network. Since each node will have incoming links only from the previously chosen nodes, the constructed graph will be acyclic. It is probable that this method gives rise to a disconnected DAG which in turn leads to an incomplete synchronization. Therefore, to avoid drawing incorrect conclusions when comparing synchronizability of different graphs, we have considered just connected DAGs in our simulations.Directed acyclic graphs (DAGs) are constructed by extending the residual degree gradient methodIt should be noted that, directed and undirected networks should have the same number of nodes and arcs  to be comparable in terms of their synchronizability. To this end, we double the number of arcs while giving directions to the links of an undirected graph. Therefore, the adjacency matrix of an undirected graph is defined as 15. It can be defined as, 38.The phase response curve (PRC) is an illustrative tool to determine the phase shift of an oscillating neuron in response to a brief current pulse delivered at various phases of the cell cycleNeurons can be modeled using both phase oscillators and conductance-based models. Since phase models are simple enough to be mathematically tractable, the networks of coupled phase oscillators have been widely studied to model biological and physical systems including neuronal networks. On the other hand, the detailed investigation of the neuronal dynamics and systematic parameter variation is possible through the use of conductance-based models. Here, we choose the extended Kuramoto model (simulating dynamics of coupled phase oscillators) and Wang-Buzsáki and Traub neuron model (simulating the dynamics of coupled spiking neurons) to consider different aspects in the synchronization of neuronal networks. In the following, each model is explained with its corresponding synchronization order parameter.40 to analyse the dynamics of directed networks with type I or type II oscillators. This model assumes a network as a collection of We use the extended Kuramoto model41: 41 are summarized in the Table We used Wang-Buzsáki model to analyse the dynamics of the networks with type I inhibitory interneurons. The Wang-Buzsáki neuron model includes the following differential equation42. The equations describing the model is ith neuron is evaluated from ith neuron and We have also used the the Traub pyramidal excitatory type I neuron model43: 44 is another commonly used measure that has been investigated in the supplementary material.There are various measures to quantify the level of synchrony in a large population of neurons within a network. Among the various metrics, we choose the interspike distance synchrony measure, denoted as First, we studied the synchronization stability of the FBLs and FFLs connecting identical type I or type II phase oscillators analytically. For different motifs, we considered the reduced two-dimensional systems of the phase differences . As expected, we found stable (unstable) synchronous states for type II excitatory (inhibitory) FFLs and FBLs. On the other hand, we observed stable asynchronous state for type I excitatory and inhibitory FBLs, and stable synchronous state for type I excitatory and inhibitory FFLs. In fact, both eigenvalues of the Jacobian matrix, for the synchronous state of the type I FFL, are zero. Consequently, this fixed point is globally stable, but not asymptotically. It means that, if one perturbs the system and then leaves the system alone, the time dependence of the perturbation is milder than exponential. The phase portraits of the type I and type II excitatory and inhibitory oscillators situated in different motifs are plotted in the Fig. et al.45). The evolutions of the three Lyapunov exponents for the type I and the type II FBLs and FFLs are demonstrated in the first and the third rows of the Fig. We also numerically investigated the synchronization stability of the type I and II identical excitatory phase oscillators including different motifs  can be transformed into strictly lower triangular form by a permutation matrix. Therefore, as we can see, our orientation algorithm constructs DAGs correctly from different undirected graphs. The Laplacian matrix of directed network is defined as 48. For example, since the eigenvalues of a lower triangular matrix are the same as its diagonal entries, the Laplacian eigenvalues of a DAG are real and equal to the in-degrees of its nodes. Therefore, as we expected DAGs do not have any FBL and their eigenvalues are real. On the other hand, we can see that the variance of the imaginary part of the small-world BDGs is higher than that of the scale-free BDGs. It is because of the fact that clustering coefficient of a small-world network is higher than clustering coefficient of scale-free networks with the same number of nodes and arcs. Therefore, small-world BDGs have higher number of FBLs than scale-free BDGs. In addition, because of the hubs (i.e. large-degree nodes in the undirected graphs), the real parts of the eigenvalues of the scale-free BDGs are more spread out than small-world BDGs. On the other hand, the real parts of the eigenvalues of the scale-free DAGs are compacter than small-world DAGs, because they have narrower in-degree distributions. Note that based on our orientation algorithm the source node would be a hub in a scale-free DAG. Now that we understood the structural differences between our directed networks, in the following we will compare the synchronizability of type I and type II oscillators on these structures. Figure As mentioned, unlike FBLs, FFLs favour synchronization in networks of type I oscillators. However, in real world networks motifs are merged together to form more complex structures. In order to see the effects of FFLs and FBLs in the synchronization of the large networks, we constructed two different directed networks from the same undirected backbone. Balanced Directed Graphs (BDGs) with many FBLs, and Directed Acyclic Graphs (DAGs) without any FBL. The flow of information in the BDGs is similar to their undirected backbone, but the information flow in the DAGs is directed from the source node to the rest of the graph. Therefore, BDGs and DAGs are very different, even if they have the same undirected skeleton.49. According to the plot of the Lyapunov exponents versus the coupling strengths, all the Lyapunov exponets of the type I DAG are small. Therefore, we considered very long time simulation to estimate the Lyapunov exponents of type I DAG. The results confirm that the absolute values of all the exponents are smaller than The synchronizability of the scale-free networks with different link-directionalities has been investigated in the Fig. see Fig. . Thus, tmentclass2pt{minimsee Fig. .Figure 430.In order to better investigate the role of undirected topology of the DAGs on their synchronization, we construct the DAGs from scale-free networks  are purely inhibitory or excitatory, can provide balance networks with incoherent dynamics  and directed acyclic graph (DAG). Precisely, many feedback loops are merged together to construct a BDG and only feedforward loop motifs are combined to make a DAG. Both the linear stability analysis and the numerical simulation confirmed that identical type I neurons connected by DAGs via strictly excitatory or inhibitory synapses are fully synchronized, while they are not synchronized when they are connected by BDGs. We can see that the steady Lyapunov exponents of type I DAGs are zero. This is in agreement with the result we found for the synchronization of feedforward loops. Therefore, studying the dynamics of the motifs can provide an intermediate step to better understand the synchronization of the larger collections. Besides the directionality, we showed that the undirected topology of the graphs also affects the synchronization of directed networks. The DAGs constructed from undirected networks with higher clustering coefficients, have higher number of feedforward motifs and higher synchronizability. In fact, a DAG is more synchronizable when all of its nodes are easily reachable from the source node. The results are also verified using conductance-based Wang-Buzsáki and Traub neuron models. In reality inhibitory and excitatory neurons work together to perform complex tasks. In general, excitatory and inhibitory inputs of a neuron are said to be balanced, and this balance is important for the highly irregular firing observed in the cortexSupplementary Information.


This study sought to quantify a comprehensive set of passive muscle-tendon properties such as slack length, stiffness, and the stress-strain relationship using a combination of ultrasound imaging and a three-dimensional motion capture system in healthy adults. By measuring tendon length, the cross-section areas of the Achilles tendon subcompartments , and the ankle torque simultaneously, the mechanical properties of each individual compartment can be specifically identified. We found that the medial gastrocnemius (GM) and soleus (SOL) aspects of the Achilles tendon have similar mechanical properties in terms of slack angle , moment arm at 0° of ankle angle , and stiffness . However, maximal tendon stress in the GM was significantly less than that in SOL , largely due to the higher passive force observed in the soleus compartment . Moreover, the tendon contributed to more than half of the total muscle-tendon unit lengthening during the passive stretch. This unequal passive stress between the medial gastrocnemius and the soleus tendon might contribute to the asymmetrical loading and deformation of the Achilles tendon during motion reported in the literature. Such information is relevant to understanding the Achilles tendon function and loading profile in pathological populations in the future.The  The main function of human tendons is to transfer the force generated by muscle contraction to the skeleton, but some tendons, e.g., Achilles tendon, exhibit important elastic and time-dependent characteristics that influence the function of the overall muscle-tendon complex . Therefoin vivo. The MTU experiences spring-like properties in a relaxed state [in vivo data on passive mechanical properties of individual tendon compartment, and muscle-tendon interaction of the synergistic ankle plantarflexors, i.e., medial gastrocnemius and soleus, is available in the literature.Analyzing the interactive lengthening behavior of the muscle-tendon unit (MTU) allowed us to make an inference about the muscle's tensile behavior, which was challenging to measure ed state . During ed state  and the ed state ). Moreoved state  and mighed state , 10), whed state  and are ed state . In addied state . It is aed state . Only a ed state , Young Med state , and momed state ). To thein vivo on a subject-specific basis; second, to investigate the passive extensibility of muscle and tendon. These data will provide a normative reference data for muscle-tendon property alternations in clinical populations.The purpose of this study was twofold: first, to quantify passive mechanical properties of medial gastrocnemius and soleus aspect of the Achilles tendon Ten healthy subjects volunteered to participate in the study . All participants were physically active on a recreational basis and reported no recent lower limb musculoskeletal injuries. Written consent was given by all participants, and the study was approved by the regional ethics committee, Karolinska Institutet, Stockholm, Sweden. All procedures complied with the Declaration of Helsinki.The experimental measurement consisted of three parts. First, the subjects were lying in a prone position with their knee flexed at 20° and their foot fixated to a footplate connected to a dynamometer . Only the right foot was tested in the convenience of the experimental setup. The ankle joint was carefully aligned with the rotational axis of the footplate with a laser device. In its initial position, the footplate was positioned perpendicularly to the tibia of the subject, which was defined as 0° ankle rotation. Shoulders, hips, legs, and the tested foot were adequately fixated, while paying special attention to securely strapping the foot to the footplate. The test range of motion (ROM) was decided as 30° plantarflexion and 20° dorsiflexion. Prior to testing, the available ROM of each subject was assessed, and no discomfort was discovered within the test ROM. The ankle of the participant was then passively rotated through the test ROM to familiarize the movement, and a static gravitational correction at the neutral position (ankle at 0°) was applied. For the actual measurement, the ankle was rotated at a constant velocity of 5°/s five consecutive times. All participants were instructed to stay relaxed during the passive ankle rotation. Ankle torque generated during the passive rotations and corresponding ankle angle were recorded by the dynamometer at 3 kHz. An ultrasonography system  with a 38 mm linear transducer (3.5–10 MHz) was used to record muscle-tendon junction (MTJ) excursion of the medial gastrocnemius (MG) and soleus (SOL). The same experienced investigator imaged all the participants. The ultrasound transducer was optimally placed parallel to the tendon in the sagittal plane, and therefore, the ultrasound image plane was therefore aligned with the longitudinal axis of the tendon. To determine the position of the MTJ and the insertion point of the Achilles tendon relative to the global coordinate system, in combination of the ultrasound system, a motion capture system  was utilized. Three reflective markers were placed on the ultrasound transducer, one marker was attached to the skin at the location of Achilles tendon insertion over the calcaneus and two more markers were attached to the IsoMed 2000 footplate appliance  and the lT) of GM and SOL aspects of the Achilles tendon at a specific ankle angle was calculated as the Euclidean distance between the global MTJ position and the insertion point on the calcaneus. The coordinate of the insertion point was then shifted along the longitude axis of the foot by considering the size of the marker [The location of the MTJ was manually digitized  and transformed to the 3D laboratory coordinate system via the use of the three reflective markers mounted on the US probe. Tendon length (e marker .The tendon excursion (TE) method was used to estimate the moment arm, which has been well-detailed documented in literature , 20. Thei = SOL, GM, and GL, FT is the tendon force, Tankle is the measured ankle torque, maT is the moment arm, and AR is the ratio of the muscle cross-section area , and GM. Other deep plantarflexors were not taken into account. The contribution of the individual MTU  to the total ankle torque was assumed to be correlated with the CSA of the individual muscle . The tenσMTJi) as Equation . Tendon stiffness tionship . To excllMTU) of GM and SOL was estimated by scaling a musculoskeletal model using the static standing reference trial to each subject using OpenSim v.3.3 [lMTU during the passive ankle movement was estimated by placing the scaled model in the same joint configuration as the subject. Muscle length lM can then be estimated inThe MTU length . The Mann-Whitney U test was conducted to compare muscle-tendon properties for SOL and GM aspects of the Achilles tendon. A significance level of 0.05 was used for comparison. All statistical analyses were performed using SPSS V25 .In the following, plantarflexion of the foot will be expressed in negative angles and dorsiflexion of the foot will be expressed in positive (+) angles. The fitness between the experimental force-strain relationship and the estimated third-order polynomial function was computed using R2) was 0.97 ± 0.02 for GM and 0.97 ± 0.03 for SOL, respectively.No active sEMG signals were observed during the measurement in either GM, SOL, or TA (Supplementary p = 0.024). Moreover, the slack length of the GM tendon was significantly longer than SOL (p < 0.01).At a very short muscle-tendon length, increases in MTU length were accompanied by a quick increase in tendon length in both the GM and SOL aspects of the Achilles tendon , which ain vivo passive mechanical properties of the individual muscle-tendon unit of medial gastrocnemius and soleus in healthy persons using ultrasound imaging combining with a three-dimensional motion capture system. To our knowledge, this is the first study to describe a comprehensive set of in vivo mechanical parameters of individual subcompartment of the Achilles tendon. We found that the GM and SOL aspects of the Achilles tendon have similar mechanical properties such as slack angle, moment arm, and stiffness. However, the maximal passive tendon force and stress at the MTJ of GM were significantly lower than in SOL. Regarding individual MTUs, the tendon contributed to more than half of the total MTU lengthening.The current study presented the in vivo studies reported that tendons contributed between half and three-quarters of the total compliance of human gastrocnemius and tibialis anterior MTUs [Passive tension generated in the relaxed MTU during lengthening is physiologically important, because it constraints joint movement for human locomotion. In many movement disorders, mechanical properties of muscle, tendon, or both altered, which prevents the joint motion necessary for normal motor function. For instance, shortened and stiffer muscle might compensate for the longer and more compliant Achilles tendon in the spastic population . Howeverior MTUs . Tendon ior MTUs . Similarin vivo. Compared to the active muscle, only a few studies have assessed a relaxed MTU, which can provide important insights into the therapeutic approach for improving joint function in pathological populations.Computational modeling and simulation of the human musculoskeletal system show great promise for improving the diagnosis and treatment of movement disorders . Among oin vivo [Tendinous tissues can be considered as a rope, where the slackness as well as the elongation of the rope influences the muscle fiber length and overall joint movability. In past decades, the ultrasonography-based method was considered a golden standard to assess tendon structural and mechanical properties noninvasively . In a coin vivo . It is nin vivo , 39 and in vivo , 41. Somin vivo  and in ain vivo  reportedin vivo. Most published data have been based on the measurement of the free Achilles tendon or GM aspect of the Achilles tendon. By tracking the MTJ displacement of both SOL and GM, we can estimate the mechanical properties of SOL and GM aspects of the Achilles tendon separately. As expected, most of the parameters are similar; the observed significantly greater slack length of the GM aspect was due to the more proximal MTJ location anatomically. Interestingly, we found significantly higher stress in the SOL aspect of the Achilles tendon than GM, which was mainly due to the higher passive tendon force according to our force distribution scheme. There was no consensus on how the tendon forces developing during the passive movement should be distributed; however, it is well-accepted that the force-generating capacity of the three triceps surae muscles is proportional to their physiological CSAs. Therefore, we used the CSA ratio of the muscles to distribute the total passive tendon force. The reason to use the CSA instead of the physiological CSA was that the pennation angles of these three muscles were found rather similar when muscles are at rest. Although this scheme should be further evaluated, our measurement-based observation supports the hypothesis by Bojsen-Møller and Magnusson [The Achilles tendon transmits the force from the main plantarflexors  through an intricate system of aponeuroses. It has been recently reported that the force-bearing tissues of the Achilles tendon in humans originate from each of the three muscle compartments and can be mechanically separated well into the free tendon and calcaneal bone. But this feature has received limited attention in general, and whether the mechanical properties of the subcompartment of the Achilles tendon differ has not been investigated agnusson  that musThere are several limitations to this study. The origin locations of GM and SOL were not experimentally tracked due to the limitation of the measurement protocol. Therefore, the MTU length was estimated by scaling a musculoskeletal model using reflective markers. Errors might be induced in the scaling process. However, the mean elongation of the MTU was estimated to be 36.46 mm, which was in the range of the reported data . In addiIn conclusion, we have presented a comprehensive set of mechanical property parameters of the GM and SOL perspective of the Achilles tendon in healthy adults. These parameters have important implications in musculoskeletal modeling and provide normative reference data for muscle-tendon property alternations in pathological populations. The unequal stress in the GM and SOL tendon might contribute to the asymmetrical loading and deformation of the Achilles tendon during motion. Such information is relevant for understanding the Achilles tendon function and loading profile in the future.


Myalgic Encephalomyelitis/Chronic Fatigue Syndrome (ME/CFS) is a debilitating disease characterized by persistent fatigue and post-exertion malaise, accompanied by other symptoms , 2. The With the aim to identify putative genetic factors that could explain the pathophysiological mechanisms of ME/CFS, four genome-wide association studies (GWAS) and two targeted-genome association studies (TGAS) were conducted in the past decade –10. In tCurrent GWAS or TGAS of ME/CFS are based on data of the so-called single nucleotide polymorphisms (SNPs) located in specific positions of the human genome. These genetic markers are short nucleotide sequences that differ in a single position from each other. Each possible sequence of a SNP is interpreted as a different allele. In theory, there are up to four alleles of the same SNP given that there are only four possible nucleotides . However, by design, classical genotyping technologies can only assess the two most frequent alleles per SNP. As an alternative to classical GWAS and TGAS, studies using data from next-generation sequencing technologies are able to assess all possible alleles of a given SNP. As far as we know, these alternative studies have been never performed on ME/CFS.In general, several QC checks should be performed in the genetic data before carrying out the association analysis itself. First, it is important to determine all monomorphic SNPs and to report the respective number. These SNPs are non-informative for the subsequent genetic association analysis, because they show the same allele in all study participants. It is also important to calculate the so-called minor allele frequency (MAF) of each SNP. Statistically speaking, the MAF is defined as the frequency of the least frequent allele of a given SNP. In practice, a very low MAF is in the same order of magnitude of the underlying genotyping error rate and, therefore, SNPs under this condition should be excluded from the study. A typical threshold for a very low MAF ranges from 1 to 5%. Less stringent thresholds for the MAF can be used in studies with smaller sample sizes.2 goodness-of-fit test. In this statistical test, p-values below the specified significance level suggest evidence against the HWE. Since the HWE is supposed to be tested in data of each SNP separately, the significance level of each individual test should be adjusted in order to ensure a global significance level for this QC check. Bonferroni or Sidak-Dunn corrections are two popular methods to make such adjustment. Alternatively, one can use procedures based on the control of the false discovery rate, as proposed by Benjamini and Hochberg  should be tested in the observed genotype frequency distribution of each SNP. The HWE is a mathematical expectation for the probability of observing a given genotype under random mating (or panmixia), no selection, no migration, non-overlapping generations, and no genotyping errors. According to the HWE, the frequency of a given genotype is expected to be factorized into the product of the respective allele frequencies. The HWE is usually tested by the popular Pearson's χHochberg . In theoThird, the proportion of heterozygous genotypes  across all SNPs should be calculated for each individual sample. Excessive heterozygosity rate suggests a possible contamination of the respective biological sample, while reduced heterozygosity rate indicates genetic inbreeding. The usual practice is to exclude samples from individuals whose heterozygosity rates are not falling into a “confidence” band. This confidence band is usually defined by the average heterozygosity rate of all the samples plus/minus a given number of times the standard deviation of the heterozygosity rate. The heterozygosity of SNPs located in the X chromosome is also used to confirm the gender of a sample and to detect putative label swaps.e.g., deletion or insertion). A low genotyping rate of a given individual indicates a low quality of the DNA material used for genotyping. Again, researchers must decide what is considered a reasonable genotyping rate for their study. In addition, different exclusion criteria can be applied to the genotyping rates of SNPs and individuals.Fourth, data of SNPs or of individuals with low genotyping rates should be excluded from the analysis. The genotyping rate of a given SNP is the proportion of individuals with fully determined genotypes of that SNP, whereas the genotyping rate of a given individual is the proportion of SNPs with a fully determined genotype of that individual. A low genotyping rate of a given SNP suggests that the genomic site associated with that SNP includes another type of genetic variation  can also be performed in GWAS and TGAS, as reviewed elsewhere  out of 61 patients based on the 1994 Center for Diseases Control Criteria (Besides the partial QC checks, the investigated genetic data on ME/CFS suffer from the curse of not having an objective biomarker for disease diagnosis. Similar problem can be envisioned for other complex diseases lacking a biomarker, such as Fibromyalgia and the Gulf War Syndrome. The absence of a biomarker is likely to introduce a possible misclassification of the true disease status of the recruited patients . To illuCriteria , 18. HowIn summary, given the partial QC checks performed in current GWAS and TGAS, the question of a genetic component in ME/CFS remains open for investigation. To accelerate the discovery of promising disease-gene association, future genetic studies of ME/CFS should set data and methodological standards as high as those followed by the 1,000 Human Genome Project and the UK10K project , 20. DatNS conceptualized this research. AG and NS performed the literature review. EL and LN helped in the interpretation and discussion of all the results. All authors read, revised, and approved the final draft of the manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


To analyze the reliability of semiconductor transistors, changes in the performance of the devices during operation are evaluated. A prominent effect altering the device behavior are the so called bias temperature instabilities (BTI), which emerge as a drift of the device threshold voltage over time. With ongoing miniaturization of the transistors towards a few tens of nanometer small devices the drift of the threshold voltage is observed to proceed in discrete steps. Quite interestingly, each of these steps correspond to charge capture or charge emission event of a certain defect in the atomic structure of the device. This observation paves the way for studying device reliability issues like BTI at the single-defect level. By considering single-defects the physical mechanism of charge trapping can be investigated very detailed. An in-depth understanding of the intricate charge trapping kinetics of the defects is essential for modeling of the device behavior and also for accurate estimation of the device lifetime amongst others. In this article the recent advancements in characterization, analysis and modeling of single-defects are reviewed. The complementary metal-oxide-semiconductor (CMOS) technology is the cornerstone of a vast number of integrated circuits, which are the building blocks of numerous electronic applications. Such circuits typically consist of a large number nMOS and pMOS transistors and their performance and geometry have been successively improved over the last decades. For instance, the width and length of the transistors have been reduced and the gate insulating layers have been thinned. Furthermore new device geometries such as FinFETs ,2,3 and rocesses ,9,10 simrocesses . Howevernsistors ,13.Although a number of defects can become passivated using POA during fabrication, the interaction of high energetic carriers with atoms at the semiconductor/insulator interface during operation can break Si-H bonds and can lead to an electrically active dangling bond . The bonAnother important reliability issue in miniaturized devices is the so called bias temperature instabilities (BTI) ,22,23,24are used . Alternaed [ΔVth . A typicThe inset indicates the number of defects affecting the device behavior. Quite interestingly, although the same physical mechanism are responsible for charge trapping in large-area and miniaturized devices, the picture of the drift of the device current is different for the scaled MOS transistors, see The discrete steps in the current signal were first documented by Ralls et al.  and haveOver the recent years a number of measurement methods have been developed in order to properly characterize the impact of defects on the device behavior. Most of the methods aim at applying a high stress bias for a specific period of time, and afterwards the state of the device is evaluated considering various ways. For instance stress-IV measurements, where IDVG sweeps are measured after a stress cycle has elapsed  have beereleased ,48,49,50released ,52. With10–15 mV ,54. HoweTo perform single defect spectroscopy MSM sequences are typically used. Patterns for MSM characterization of charge trapping in large-area devices and miniaturized transistors are shown in Before the first stress cycle is applied, an IDVG sweep within a narrow gate bias range is typically performed. As mentioned before, the IDVG characteristics serves for the calculation of the imulated , as the An important criterion when applying MSM measurements is the energetic and spatial distribution of the traps which can contribute to the measurement signal. One condition for charge trapping concerns the timing of the MSM sequence and the charge capture and charge emission time of the defects at the respective bias condition and device temperature. The second boundary condition for charge trapping is defined by the stress and recovery bias used for the experiment. These biases determine the so called active energy region (AER) for charge trapping which is shown in In principle, the defects which exhibit a trap level below the Fermi level of the channel can become charged, and the defects with a trap level above the Fermi level remain neutral. Thus the key prerequisite of a defect to change its charge state during an MSM cycle is that its trap level is shifted below the Fermi level of the channel during the stress phase, but lies above the same during the recovery phase. The green area shown in The impact of BTI on the device characteristics is typically expressed in terms of an equivalent shift of the device threshold voltage eristics . In geneeristics . In the terparts , which mro-volts . DespiteSeveral recovery traces recorded at the same stress and biases conditions but at different temperatures are shown in fixed traps, whereas defects exhibiting a bias dependent emission time are typically referred to as switching traps. Thus, providing an accurate model to explain the bias dependence of BTI is pretty challenging, as the field dependence of individual defects is observed to be on one hand negligible and on the other hand very strong. In order to explore a more detailed picture of the many peculiarities of the charge trapping kinetics of defects in miniaturized devices the recent findings employing the TDDS are discussed next.The bias dependence of charge trapping is shown in Most of the characterization techniques proposed to investigate defect distributions and densities at various bias and temperature conditions employing large-area devices. One prominent example is the so called deep level transient spectroscopy (DLTS)  which haThe time-dependent defect spectroscopy (TDDS) makes use of the principle of DLTS, applies it to miniaturized devices and augments it by a statistical analysis. The main prerequisite of TDDS is that the devices are small enough to reveal charge transition events as discrete steps of measurable size in the device current. According to recent reports the step height of the defects is proportional to the effective gate area, that is, η=Aη0 ,64,65,66NT=NT0/A . To apprNT=NT0/A ,67. The NT=NT0/A .The procedure to extract their charge transition kinetics, that is, their respective charge capture and emission times, as well as their steps heights will be discussed next in great detail.To extract the average charge emission time at a certain gate bias the measure-stress-measure (MSM) scheme from If the device is small enough discrete steps, which correspond to charge emission events of defects, can be observed. Afterwards, a step detection algorithm is applied to the measurement data in order to extract the charge transition events ,69, whici being the rank of the data point in the emission time series sorted in ascending order, and For this the probability estimator (1)F=i−0As noted in A the occupancy and In contrast to the direct extraction of the charge emission time from the recovery traces, the charge capture time cannot be determined directly, but can be extracted employing an indirect approach. For charge capture it can be assumed that the longer the stress time is the larger the probability of a defect to get charged becomes, when the same stress bias is considered. Thus, the expectation value of the occupancy, that is, the ratio between the number of recovery traces in which an emission event of the corresponding defect can be observed  followsO(ts)=A and two metastable states (1’ and 2’). In the model the transitions between the defect states are either described by an NMP process for the transitions where a charge exchange takes place, that is, re shown . This dere shown ,88. Furtre shown ,90 or hy centers . The elo centers .In the final section of this paper the different charge trapping behavior of defects which have been observed from single defect investigations and the corresponding configuration of the defect model to explain the trap behavior is discussed.In the following, results from single defect studies performed on nanoscale devices are discussed in detail. The shown charge trapping kinetics has been extracted either by applying TDDS, or from RTN measurements, and is modeled considering the four-state defect model. It can be observed that the model nicely explains the experimental data. In addition to the charge trapping kinetics, the impact of the defects on the device behavior is also an important parameter for device reliability assessment. This can be analyzed by calculating distribution function of step heights of the single charge transition events, which is subject of the second part of this section.switching trap, or (ii) bias-independent, a behavior which is assigned to so called fixed oxide traps. In both cases strong bias dependent charge capture times are observed. Another remarkable observation is that (iii) defects can show a volatile behavior [Extensive studies employing the previously mentioned TDDS have been carried out using utilizing pMOS and nMOS transistors. These investigations reveled many peculiarities visible in the charge trapping kinetics of the defects, which all have to be covered by a uniform model. It has been observed that the charge emission times of traps can be either (i) bias-dependent, which is typically referred to as behavior . More deIn The defect presented in Once the defect model is calibrated to a number of defects the parameters can be extended to explain BTI in large-area devices. For this the trap levels and energy barriers are considered distributed, which enables to calculate a number of defects with different configuration of their PESs. Finally, the superposition of an large ensemble of defects allow explanation of BTI in large-area devices . Based oq, the dielectric constants To estimate the impact of a single defect on the device behavior the charge sheet approximation (CSA), which assumes that the oxide charge is spread over the insulator according to (5)ΔVth=ven ΔVth ,95. Howevaluated ,49,96. Ianalyzed ,96. To eIt can be seen, that the step heights are exponentially distributed and can be described by the respective probability distribution function (PDF)To study the distribution of the step heights the complementary CDF is used, and is evaluated normalized to the number of devicesA remarkable observation here is that the distribution function of the step heights follow a bi-modal exponential distribution. Recent studies  suggest nsulator ,96. In RAnother important finding is that exponentially distributed amplitudes have also been found for RTN signals ,98,99. T devices ,101.The characterization and accurate modeling of the reliability of miniaturized transistors poses a major challenge for measurement instrumentation, defect modeling and device simulation. In order to explain the experimental observation empirical models are often used. However, such models typically omit certain observations, like saturation of the drift of the threshold voltage with increasing stress time. In order to provide a physical description of the measurement data the four-state defect model has been proposed, and is discussed here. The defect model is based on the charge trapping kinetics of single defects which can be observed in miniaturized devices. To extract the trapping behavior the time-dependent defect spectroscopy (TDDS) can be used. From recent TDDS studies it has been observed that defects exhibit bias dependent charge capture times, but certain defects exhibit bias-independent charge emission times while others show bias-dependent charge emission times. Both characteristics can be nicely explained by the defect model. To explain the behavior of large-area devices a number of defects with distributed trap levels and energy barriers for charge transitions have to be calculated, and their superposition enable to describe the devices’ behavior. These simulations can be further used to accurately extract the lifetime of the devices under various operating conditions. Finally, the distribution function of step heights is discussed, and it is shown that the typically use charge sheet approximation significantly underestimates the effective impact of a defect on the device behavior. This is especially important for circuit designers to ensure a high robustness of the applications against charge trapping.