Escherichia coli, Helicobacter pylori and Saccharomyces cerevisiae, and it seems to be a common key feature to all cellular organisms. In concordance with these observations, the cell can be considered a complex metabolic network which mainly integrates a large ensemble of self-organized multienzymatic complexes interconnected by substrate fluxes and regulatory signals, where multiple autonomous oscillatory and quasi-stationary catalytic patterns simultaneously emerge. The network adjusts the internal metabolic activities to the external change by means of flux plasticity and structural plasticity.The experimental observations and numerical studies with dissipative metabolic networks have shown that cellular enzymatic activity self-organizes spontaneously leading to the emergence of a Systemic Metabolic Structure in the cell, characterized by a set of different enzymatic reactions always locked into active states (metabolic core) while the rest of the catalytic processes are only intermittently active. This global metabolic structure was verified for In order to research the systemic mechanisms involved in the regulation of the cellular enzymatic activity we have studied different catalytic activities of a dissipative metabolic network under different external stimuli. The emergent biochemical data have been analysed using statistical mechanic tools, studying some macroscopic properties such as the global information and the energy of the system. We have also obtained an equivalent Hopfield network using a Boltzmann machine. Our main result shows that the dissipative metabolic network can behave as an attractor metabolic network.We have found that the systemic enzymatic activities are governed by attractors with capacity to store functional metabolic patterns which can be correctly recovered from specific input stimuli. The network attractors regulate the catalytic patterns, modify the efficiency in the connection between the multienzymatic complexes, and stably retain these modifications. Here for the first time, we have introduced the general concept of attractor metabolic network, in which this dynamic behavior is observed. Living cells are essentially highly evolved dynamic metabolic structures, in which the more complex known molecules are synthesized and destroyed by means of a sophisticated metabolic network characterized by millions of biochemical reactions, densely integrated, shaping one of the most complex dynamic systems in nature The enzymes are the main molecules of this surprising biochemical reactive network. They are responsible for almost all the biomolecular transformations, which globally considered it is called cellular metabolism.Saccharomyces cerevisiae have shown that at least 83% of all proteins form complexes (containing from two to eighty-three proteins), and their overall enzymatic structure is formed by a modular network of biochemical interactions between multienzyme complexes Intensive studies of protein-protein interactions have shown that the internal cellular medium is an assembly of supra-molecular protein complexes The self-organization Apart from forming complex enzymatic associations, the catalytic dynamics of multienzymatic sets present metabolic transitions between different quasi-stationary and oscillatory molecular patterns From a dynamic point of view, the multienzymatic complexes represent dissipative structures in which oscillatory patterns and functional integrative processes emerge, allowing the reactive coordination between their catalytic parts In concordance with the structural and functional self-organization of enzymes see , the celIn order to research the functionality of the cellular metabolism, the dissipative metabolic networks (DMNs) were created In the DMN, the emergent output activity (the connection pattern) for each metabolic subsystem can be either steady state or oscillatory with an infinite number of distinct activity regimes on-off changing state and inactive state: all these catalytic states are also due to the metabolic synaptic changes. Flux plasticity and structural plasticity have been experimentally observed in the metabolism of several organisms as the main systemic biomolecular mechanisms for the adaptation to external perturbations The DMN adjusts the internal metabolic activities to the external environmental change by means of flux plasticity i.e., changes in the physiological values of the metabolic synapses which lead to a differential catalytic activity of subsystems, and structural plasticity i.e., persistent change in the state of the metabolic subsystems which can be active state, Numerous mathematical studies on metabolic rhythms have contributed to a better understanding of the functionality of the self-organized multienzymatic subsystems (the nodes of the dissipative metabolic networks). Most of these functional biochemical studies have been carried out by means of systems of differential equations e.g., the Krebs cycle In all these studies, it is assumed that each metabolic subsystem forms a unique dynamical system Therefore, a dissipative metabolic network can be considered as a super-complex dynamic structure which integrates a set of different dynamic systems (the metabolic subsystems) forming a dynamical-super-system The first model of a DMN was developed in 1999 Escherichia coli, Helicobacter pylori, and Saccharomyces cerevisiaeAfterward, in 2004 Extensive analyses for DMNs have shown that the Systemic Functional Structure is very robust and stable Recently, it was possible to quantify the bio-molecular information flows in a single metabolic subsystem Understanding the systemic mechanisms involved in the regulation of the cellular enzymatic activities in the complex conditions prevailing inside the cell is a key issue for the contemporary biological thought. Here, in order to research the systemic processes involved in the regulation of the catalytic activities, the emerging biochemical data have been analysed using statistical mechanics tools; in concrete, by employing the use of a Boltzmann machine we have built a Hopfield network representing the dynamical properties of the DMN.The results show that the multienzymatic activities of the network are governed by systemic attractors in which the stored catalytic information patterns can be correctly recovered from specific input stimuli.The systemic attractors regulate all catalytic network patterns, modify the efficiency in the connection between the multyenzymatic complexes, and stably retain these modifications.The dissipative metabolic network can behave as an attractor metabolic network which exhibits associative memory properties.Dissipative metabolic networks (DMNs) are dynamical systems basically formed by a given number of interconnected metabolic subsystems (MSbs) which represent self-organized multienzymatic complexes The metabolic subsystems are interconnected by biochemical substrate fluxes and three classes of regulatory signals: activatory , inhibitory  and all-or-nothing type , for more details see Each subsystem transforms the input substrate fluxes and regulatory signals into the output catalytic activity. The input-output conversion is performed in two stages. In the first one, the input fluxes are transformed in an internal enzymatic activity of the subsystem by means of flux integration functions. In the second stage, the received regulatory signals modify the internal enzymatic activity converting it into output catalytic activity.The flux integration functions are based in the quantitative catalytic studies of the amplitude and frequency of the glycolytic patterns obtained by Goldbetter and Lefever in Each allosteric signal has a If the signal is of all-or nothing type, then it will use a parameter δ which is called the threshold value . When a given threshold value is reached, it fully inhibits the activity of the MSb.In agreement with experimental observations, the output activity of all the enzymatic subsystems may be oscillatory or steady state and comprise a very large number of distinct activity regimes All the explicit details on how DMNs are constructed can be found in Formally, we assume that the activity of the i-th enzymatic subsystem is defined byIn this way, the activity of each subsystem A subsystem is inactive when N the total number of subsystems.We fix Let us suppose that the i-th subsystem receives a flux from the j-th. Its internal activity represented by In this second stage, the internal activity values are modified using the signal integration functions, which depend on the combination of the received regulatory signals and their corresponding parameters (regulatory coefficients). In the metabolic subsystems, the existence of some regulatory enzymes  increases the interconnection among them. The allosteric enzymes present different sensitivities to the effectors, which can generate diverse changes on the kinetic parameters and in their molecular structure; likewise, the enzymatic activity of covalent modulation also presents different levels of regulation. These effects on the catalytic activities are represented in the dynamical system by the regulatory coefficients and consequently each signal has an associated coefficient which defines the intensity of its influence.There exist three kinds of signal integration functions:Activation function AC.Inhibition function IN.Total inhibition function TI.In this way, to compute If the allosteric signal is inhibitoryFirst, we have fixed the following elements as control parameters: (1) 18 subsystems in the DMN, (2) up to three substrate input fluxes for each subsystem (each MSb can receive a maximum of three substrate fluxes and it is not restricted the number of flows leaving of them), (3) three input regulatory signals for each metabolic subsystem and (4) the same number of signals per class . Certain metabolic subsystems may receive a substrate flux from the exterior and we have arbitrarily fixed the MSb3 and the MSb10 for this function.Having fixed these elements, the structure of the network has been randomly configured, including: (1) the topology of flux interconnections and regulatory signals, (2) the Table in .The values of We have taken the constants T and M we calculate the activity matrices m = 1,…, M using the flux integration functions and regulatory signals.Finally, given After numerical integration of the selected network, we generate a discrete time-series for the 3-tuples N of transitions. At the k-th iteration-step we suppose that the oscillation is harmonic, Eqs. (1–4). The duration of the harmonic oscillation is a given parameter k-th stage to the (k+1)-th stage then, during the k-th stage, and (k+1)-th stage. The numbers We consider a number The transition regimes are combinations of two harmonic oscillations with nonconstant coefficients the micro-states) to come out with the time-evolution of a few global measures, the ones which can properly characterize the system as a whole (ie. the macro-states).We have shown that the enzymatic activity for each MSb in the DMN can be very complex and highly non-linear; however, to understand the global-emerging properties within the DMN is not necessary to incorporate all the details in each MSb. This general flavor, it is well-known in Physics, and in particular the Statistical Mechanics is the discipline for pooling the dynamics of all the (many) system constituents  the neuronal activity was represented by binary variables, 2) the synaptic connections (or weights) were considered to be symmetric, 3) the input-output relation in the activity of each neuron was described by a sigmoid function, 4) the updating for the neural activity was sequential, the well-known During Glauber dynamics one neuron is selected at random at each time-instant and after it is updated with a probability which depends on its current state, its neural threshold, the total input arriving to that neuron and the temperature parameter, which is simply a parameter accounting for random (“not-coming from the input”) fluctuations in the neural activity.Under these four considerations, the stationary probability distribution resulting from the detailed-balance condition is the Boltzmann-Gibbs distribution. If A simple comparison between Eq. (16) and Eq. (17) gives thatThe aim of the Boltzmann Machine is to learn from the metabolic data the training the learning algorithm. At each iteration, weights and thresholds are updated with a value which is proportional to the difference between the statistics computed directly from the data (the one used for training) and the statistics performed by the Boltzmann-Gibbs distribution with the new updated parameters learned Boltzmann-Gibbs distribution  coincide with the one directly computed from the data .It is important to remark that the purpose of this paper is not to give a detailed derivation of the algorithm for the Boltzmann Machine; in contrast, we only present it in its simpler formulation, but further details can be found in We provide here a mathematical formulation for the previous explanation. After random initialization of weights and thresholds the specific iterative algorithm is given by:In each iteration, the probability Note that the sums appearing in the expectations given by Eqs. (23) and (24) are involving Although the learning algorithm given by Eqs. (19) and (20) together with the use of Monte Carlo methods to compute the expectations in Eqs. (23) and (24) is exact fp) solution which is given by:In particular, we will assume here that all neurons are susceptible for learning  Eq. (27) satisfies that Notice that to obtain Eqs. (25) and (26) one has to assume that the neuronal dynamics is stochastic and represented by the probability for a neuron to fire, i.e.Notice that Eqs. (25) and (26) have the term Known the Boltzmann-Gibbs distribution given by Eqs. (16) and (18) is possible to compute different macroscopic variables representing some of the global net properties. Thus, for instance, one can compute the net Shannon Entropy, which defined asAnother important connection between Shannon entropy is its relation with the Mutual Information, a measure for the amount of uncertainty reduction in one variable by knowing another. It can be easily proven that the Mutual information of one variable with itself is the Shannon Entropy. Thus, this self-information has been interpreted as a measure of stored information in the time-series.Another net observable one can measure having the Boltzmann-Gibbs distribution is the mean Energy, which defined amf) approximation, which is a particular situation in which the probability given by Eq. (17) has the following factorial formFor the calculation of both Entropy and Energy given by Eqs. (28) and (29), one needs to evaluate the total number of possible microstates, equal to Thus, using Eqs. (30–32), Eqs. (28) and (29) becomelearned weights given by Eq. (25).Eqs. (25) and (26) are the result of the learning algorithm given by Eqs. (19) and (20) in absence of hidden units, under the mean field approximation in addition with some corrections based on the linear response theory, details in More concrete, we have assumed that the learned weights given by Eq. (25) are the result of a Hebbian rule similar to the one considered in Hopfield nets see  as well.In the following lines, we detail this method. Firstly, we consider the most general (and simple) Hebbian rule, i.e.pure attractors, is the most simple situation but it is also possible to have mixed states, in which the attractors correspond to a combination of some of the different encoded memories.Networks of binary neurons connected by weights given by Eq. (35) have been widely popular, the so-called Hopfield nets best memories which minimize the cost given byNext, we assume that weights given by Eq. (35) can be represented by the ones learned from the data, Eq. (25). In concrete, our criteria to search the different stored memories unknown variables (the best memories) and observations : 1) there are The solution to Eq. (36) constitutes the essential of our method that can be summarized as the following: from time-series data of enzymatic activity, the matrix To test the validity of the solutions obtained after minimization of the cost given by Eq. (36), we have simulated the dynamics of a Hopfield network with weights given by Eq. (25), thresholds given by Eq. (26), encoding rule given by Eq. (35), and metabolic memories corresponding to the ones minimizing the cost given by Eq. (36). Hereon, we will refer to this as the Hopfield net which is equivalent to the DMN.If the network manifests associative memory, the activity patterns given by the metabolic memories must correspond with local minima of the dynamics. This can be easily addressed by studying how far the net activity goes after perturbing it when initially was fixed to the activity of one of the metabolic memories. The time evolution of the net activity is computed in Monte Carlo Steps (MCS), one MCS corresponding to N different movements per site in the net activity The distance from the initial activity configuration to the evolving net activity has been defined as In the Hopfield net simulations, fluctuations are coming from the temperature parameter, In the search of the population”) of candidate solutions  for the specific problem in question. The cost associated to each solution is ranked between the worst and the best solution, in a cost-function basis. Next, in an iterative fashion some of the good solutions (the parents) are probabilistically selected according to their cost, then mixed (using a crossover operator) and changed (via a mutation operator) to generate new solutions (the childs) that will replace the high-cost ones from the previous iteration; thus, imitating the evolutionary principle of survival of the fittest (i.e. the one with least cost).Initially, a genetic algorithm defines a set . After chosen the integer vector-position i at random, the new crossed individual is built taken the dad positions from the 1st to the ith and the mum positions from the (i+1)th to the Nth. Technically speaking it is said that there is a tournament selection with a tournament size equal to 2. Notice that this crossover is performed in the two Crossover operation works as follows: first, two pairs of individuals are randomly selected, and the best two of the four are considered to be crossed  and one integer vector position and flips its value. The mutation operator is applied several times.Finally, the new individuals are in-cost-evaluated and the procedure is repeated for a given number of iterations.Notice that the main purpose of the use of the genetic algorithm was not to perform a fine optimization of the fitness function given by Eq. (36). For that reason, we have not explicitly studied.To research the systemic biomolecular mechanisms involved in the regulation of the enzymatic activity when several enzymatic sets interact with each other we have built a Dissipative Metabolic Network (DMN) with 18 metabolic subsystems, each one representing a self-organized multienzymatic complex; hereon, we will name indifferently catalytic subsystem, multienzymatic subsystem or MSb.The DMN has been built according to the following concerns:The number of catalytic subsystems in the DMN is fixed to 18.The maximum number of substrate input fluxes for each subsystem is fixed to 3.The number of input regulatory signals for each metabolic subsystem is fixed to 3.There are three classes of regulatory signals in the network: activatory , inhibitory  and all-or-nothing type . The regulatory signals are affecting all the catalytic subsystems and it is not required any flux relationship.Every metabolic subsystem receives both fluxes and regulatory signals.It exists a balanced number between allosteric activation, allosteric inhibition and regulatory signals of covalent modulation.The network architecture was built by choosing a random topology of substrate flux interconnections and regulatory signals. Moreover, we have randomly defined the parameters describing the flux-integration functions, the regulatory coefficients of the allostetic activities and the values of the initial conditions for all metabolic subsystems .Under this external condition, a systemic metabolic structure emerges spontaneously in the network: the MSb12 is always in an active state (i.e. metabolic core), whereas the rest of multi-enzymatic subsystems exhibit intermittently activity transitions between on and off states.All metabolic subsystems present complex output patterns with large transitions between different oscillatory behaviors (350 transitions per period). In another condition, the biochemical network was receiving two external and simultaneous stimuli S1 and S2 (hereon Condition II).Under this new external perturbation the same network undergoes a drastic reorganization of its catalytic dynamics showing flux plasticity which involve persistent changes in the enzymatic activities of all subsystems .In condition II all subsystems change their catalytic patterns presenting complex activity with 105 transitions (per period) between oscillatory and steady state behaviors  and (26). The Boltzmann machine was applied to the two stimulation conditions (explained before). Results for condition I are given in 5 and  can either be positively correlated (when one is up the other is up) and anti-correlated (when one is up the other is down). This is illustrated in The results for the thresholds are given in After convergence in the learning, the Boltzmann machine allows to obtain a weights matrix and a vector of thresholds such as the stationary probability of the dynamics of the DMN coincides with the Botlzmann-Gibbs distribution with an Energy function given by Eq.(18). This is very important as it allows describing global (stationary) properties of the DMN from the dynamics of the catalytic subsystems. The Shannon Entropy given by Eq. (28) can be interpreted as the information in bits that can be read-out from the time series describing the dynamics of the DMN. To do this, we have considered Eqs. (30) and (31), the so-called “mean field approximation”. Under these conditions, the Shannon Entropy is given by Eq. (33).We have computed the Shannon Entropy for the two stimulation conditions I and II. It had a value of 10.45 for condition I and 10.56 for condition II. Thus, the Shannon Entropy did change very little  in the two stimulation conditions. Notice that, in contrast with the Energy in Eq. (34), the Entropy given by Eq. (33) does not depend on weights and thresholds; thus, the Entropy is a measure which has not a direct dependence on the temperature, as all the temperature dependencies come from the weights and the thresholds cf. Eqs. (25) and (26).It is important to remark that we have computed the Entropy for all enzymatic subsystems except the number 15. The reason was that for condition II, the MSb 15 was in the off state, so giving a not-a-number (NAN) contribution to the Shannon Entropy, c.f. The fact that the Shannon Entropy kept almost unchanged and independently on the stimulation condition, it can give cues about a possible invariant in the information stored in the dynamics of the DMN.The use of the Botlzmann machine allows for describing different stationary properties at the network level for the DMN by exploiting the statistics of the Boltzmann-Gibbs distribution. The net energy (see methods) is a convenient measure for global stability of the dissipative metabolic network. Similar to the calculation of the Shannon Entropy (corresponding to the metabolic network information), we have assumed also for the energy calculation the mean field approximation. The energy in this case is given by Eq. (14).We have computed the net energy for the two conditions I and II. Network energy had a value of −158.34 for condition I versus −27.83 for condition II, thus when only the stimulus S1 is stimulating the biochemical system, the DMN is 5.69 times more stable than when the two stimuli S1 and S2 are activating the network. This occurred for a temperature value of T = 0.5. The effect of the temperature was not very relevant though; thus for T = 0.1 we obtained −158.79 (condition I) and −28.13 and for T = 1.0, −157.78 (I) and −27.47 (II). Thus, increasing the temperature, the Energy function also increased, making the network to be less stable. However, despite of this (well-known) tendency, the DMN is about 6 times more stable in condition I in comparison with condition II, and this fact was independent on the value of the temperature.Interpreting in terms of the energy the transition of the MSb15 from an on-off state in condition I to an off state in condition II, it says that the dynamical condition in which all subsystems except the metabolic core are in on-off states is about 6 times more stable in comparison with the situation in which the MSb 15 was in the off-state. In other words, the situation in which all non-core subsystems are oscillating is energetically 6 times cheaper than the one to force the MSb15 to be in the off-state.We have tested the attractors stability by looking into the dynamics of the Hopfield net which is equivalent to the DMN (see methods). By fixing the initial net activity to the activity of one metabolic memory, one can study how much stable is that memory by looking the time evolution of the net activity. This is represented in For One of the most important goals of contemporary biology is to understand the elemental principles and quantitative laws governing the enzymatic processes in cellular conditions.Here, in order to research the systemic regulatory mechanisms involved in the control of the cellular enzymatic activity we have quantified macroscopic properties and essential dynamic aspects of a dissipative metabolic network formed by 18 metabolic subsystems each one representing a set of enzymes functionally associated and dissipatively structured.The enzymes, proteins and RNAs characterized by exhibiting catalytic activity, are the main functional molecules of cell, and they do not function in isolation of one another In the multienzymatic network that we have analyzed, the metabolic subsystems are interconnected through a complex topological structure of biochemical signals formed by substrate fluxes and three classes of molecular regulatory processes: activatory , inhibitory  and an all-or-nothing type . These kinds of biochemical signals constitute the main mechanisms of the enzymatic interconnection in living cells The preliminary analysis of the network catalytic activities shows that the enzymatic patterns spontaneously self-organize themselves, leading to the emergence of a Systemic Metabolic Structure characterized by a set of different enzymatic reactions which are always locked into active states (metabolic core) while the rest of the catalytic processes are only intermittently active. This global dynamic structure is in agreement with experimental results Moreover, our study shows how complex catalytic patterns emerge in the subsystems, which exhibit hundreds of different transitions between oscillatory behaviors, and some steady states, as it is expected on the cellular conditions on-off changing state or an inactive state: all these catalytic states are also due to the metabolic synaptic changes). The global self-regulations of the enzymatic processes by means of metabolic flux plasticity and structural plasticity have been experimentally observed in several unicellular organisms as the main systemic metabolic mechanisms for the adaptation to external perturbations It is interesting to remark that the dissipative metabolic network that we have studied self-adjusts the internal enzymatic activities to the external environmental changes by means of metabolic flux plasticity  and metabolic structural plasticity  the enzymes functionally associated forming self-organized multienzymatic complexes, (2) the main biochemical mechanisms for the metabolic synapses , (3) the emergence of dissipative catalytic patterns, (oscillatory and stationary enzymatic activities in far from equilibrium conditions), (4) the global enzymatic self-organization , and (5) the systemic enzymatic self-regulation .The main conclusions of the use of the Boltzmann machine are the following:The catalytic dynamics of the dissipative metabolic network are dependent on the Lyapunov function i.e, the energy function of the biochemical system, which is a fundamental element in the regulation of all the enzymatic activities.Started in any initial system state after an external stimulus, and due to the global multienzymatic dynamics, the metabolic network evolves trying to reduce the energy function, which in absence of noise will decrease in a monotone way until achieving a final system state that is a local minimum of the Lyapunov function.When the biochemical system state reaches a local minimum, it becomes a  stable state for the enzymatic network.The dissipative metabolic network has multiple stable states and each one of them corresponds to a specific global enzymatic pattern of the biochemical system.The enzymatic activities of the dissipative metabolic network are governed by systemic attractors which are locally stable states, where all the enzymatic dynamics are stabilized.The minimums of the Lyapunov function correspond to these systemic attractors which regulate the metabolic patterns of the subsystems and determine that the enzymatic network operates as an individual and completely integrated system.The energy function on which the dynamics of the metabolic network depend has a complex landscape with multiple attractors .The emerging systemic attractors analyzed here are corresponding with Hopfield-like attractors The biochemical information contained in the attractors behave as metabolic memories i.e., enzymatic activity patterns stored as stable states, which regulate both the permanent changes in the internal catalytic medium as well as the metabolic responses to properly integrate the perturbations coming from the external environment.When a stimulus pattern is presented to the system, the network states are driven by the intrinsic enzymatic dynamics towards a determinate systemic attractor which corresponds to a memorized biochemical pattern.The formation of the attractor landscape is achieved by metabolic synaptic modifications in which each biochemical synapse is involved in the storage of the metabolic memories.Metabolic synaptic plasticity seems to be the basis of the stored memories in the metabolic network.A key attribute of the analyzed systemic attractors is that when the dissipative metabolic network (DMN) is stimulated with a pattern input, the enzymatic activities converge to the stored pattern which most closely resembles the input, i. e. the attractors have “associative memory”.The metabolic network attractors seem to store functional enzymatic patterns which can be correctly recovered from specific input patterns.Our results explicitly show that indeed, there exists memory attractors and capacity to retrieve binary information patterns (from the weights) which are local minima of the catalytic activity in the DMN.Thus, if the initial condition of the network dynamics starts within the basin of attraction of such a pattern, the dynamics will converge to the originally stored pattern. As it is well known, this class of “pattern-completion” dynamics has been addressed in Hopfield nets studies for years, and it is generally named “associative memory” We have computed the mean field energy of the equivalent-Hopfield network which is built from the dynamics of the DMN, and we have found some explicit information patterns which are local minima of this energy. Notice that the original dissipative metabolic network can have much more complicated energy landscape than the one approached by the mean field solution. However, even if the calculation of a more exact energy function is beyond the scope of the present work, these results give clues that the local minima of the metabolic net energy can first store information to eventually be retrieved. And this is what researchers in neural networks studies named to have associative memory.In our case, the synaptic connectivity matrix in the Hopfield network is the result of an adaptation of a Hebbian learning rule  for which “simultaneous activation of two metabolic subsystems leads to pronounced increases in biochemical synaptic strength between both metabolic subsystems”.The stimuli sequences of vectors which are encoded into the learning rule correspond to an information pattern. In the simplest case, after learning the synaptic weights do not change their strength any more. When connecting metabolic subsystems with the weights matrix, the stable states of the entire network dynamics coincide with one of the stimulus which was stored in the learning rule. Thus, the name of information pattern comes from the fact that the information existing in the weights-encoded vector can be retrieved after learning by simply stimulating the network with a stimulus which is close to the one used for patterns encoding. Therefore, pattern information, encoding and retrieval in the dissipative metabolic network exist in the dissipative metabolic network.The metabolic network analysed here converts the biomolecular information flows into new activity patterns, modifies the efficiency in the connection between the multyenzymatic complexes, and stably retains these modifications. These enzymatic dynamic behaviors are governed by Hopfield-type attractors, and therefore, the dissipative metabolic network behaves as an attractor metabolic network which has associative memory properties.Neural networks with associative memory, addressing storage and recollection of encoded patters in the learning rule, have been studied in theoretical neurobiology since longer than 50 years ago. Starting at the preliminary work done by Willshaw et al In these pioneer theoretical studies it was suggested that such associative memory could explain the operational mechanisms for memory in neural systems; recently the theoretical predictions formulated several decades ago have been experimentally validated Here for the first time, we are suggesting that associative memory could be also present in metabolic networks, thus defining the general concept of attractor metabolic network, in which this dynamic behavior, emerging as collective phenomena, might be also observed.On the other hand, we have measured the systemic Shannon entropy (under the mean field approximation) of the enzymatic activity in the metabolic network. The Shannon entropy (the average uncertainty in the dynamics of enzymatic activity) is directly related to the concept of information. More precisely, the Shannon entropy coincides with the amount of information which on-average is required to describe the DMN system dynamics We have computed the Shannon Entropy for the two stimulation conditions: one in which only the stimulus S1 is applied to the metabolic network (condition I), and the other in which both stimuli S1 and S2 are applied (condition II). The Shannon Entropy changed very little in the two stimulation conditions and was about 10.5 bits for 17 multienzymatic subsystems in total, which gives around 0.61 bits per metabolic subsystem.Both the Energy function and the Shannon Entropy have been computed under the mean field assumption; but other more sophisticated non-equilibrium methods can be approached starting at the Boltzmann-Gibbs distribution, i.e. in Ising-like systems. For a pedagogical book on these methods see Another important feature of an associative Hopfield network is the maximum number of patterns that the network can be stored to after be retrieved, i.e. the storage capacity. Studies on the storage capacity in Hopfield networks are very abundant as this problem has been widely studied and discussed Much less studies exist on the storage capacity of Hopfield network regarding familiarity memory In light of these data, one might wonder how many metabolic information patterns a living cell could possibly store.At present, the number of metabolic subsystems present in unicellular organisms is unknown, but it is possible to get a rough estimation of its magnitude order.The genome of E. coli K12, one of the most studied cellular micro-organisms, only contains 4452 open reading frames, of which 2403 (54.1%) have an experimentally determined function, 1425 (32%) were predicted by computational analysis, and the remaining 663 (14.9%) are of unknown function However, despite this small number of genes, the amount of all synthesized proteins per cell including the enzymes is very high around 3,600,000 Like the rest of cellular organisms, the enzymes and the non-catalytic proteins of the E. coli K12 present a multiplicity of copies which can shape numerous metabolic subsystems, e.g., the number of ribosomes/cell in E. coli range from 6800–72000 units ∧2), whereas the genetic structural information for this bacteria is around 4,500 genes.E.coli very possibly exceed 100,000 self-organized multienzymatic subsystems and taking into account this minimal estimation of its magnitude order, the number of functional metabolic memories stored (recollection memory) will be well above 100,000  will be well above 13,000,000 in the hepatocyte, and familiarity scaling with NDifferent experimental works have shown that several unicellular organisms possess complex behaviors that are only possible if biomolecular information is stored and processed.Physarum polycephalum. This unicellular species belongs to the amoebozoa, an important branch of eukaryote evolution, is characterized by a large cytoplasm with many nuclei which remain suspended in a single contiguous protoplasmic volume called plasmodium. The body of the plasmodium contains a network of tubular structures by means of which nutrients and biomolecular elements circulate through the organism in an effective manner One of the most studied examples of information processing in a single cell is the The movement of plasmodium is termed shuttle streaming which is characterized by the rhythmic back-and-forth flow of the biomolecular substances. The dynamically reconfiguring network of tubular structures can redirect the flow of protoplasm towards the plasmatic membrane causing the movement of a mass of flowing pseudopods, and as a result, the organism can crawl over ground at a speed of approximately 1–5 cm/h The complex protoplasm exhibits a rich spatiotemporal oscillatory behavior, and streams rhythmically synchronised with intracellular oscillatory patterns such as the oscillations in ATP concentration, the plasmagel/plasmasol exchange rhythm and the oscillations in the cytoplasmic free calcium level Physarum polycephalum have shown that this cell is able to store information, learn and recall past events.In the last several years, a notable number of studies in For instance: this unicellular organism had the ability to find the minimum-length solution between two points in a maze, which has been considered cellular information processing All these experimental results hint at the emergence of an intrinsic memory storage device Many other experimental examples show that other different unicellular organisms have sophisticated behaviors including information storage.Dictyostelium and Polysphondylium amoebae seem to have a rudimentary memory and they can show long directional persistence (∼10 min), being able to remember the last direction that they had just turned A pioneer in revealing such behaviour was H. S. Jennings, who showed many years ago that a single cell such as Paramecium could have a primitive kind of learning and memory We have quantified essential dynamic aspects of a dissipative metabolic network among which we have found that the systemic enzymatic activities are governed by attractors with the capacity to store metabolic information patterns which can be correctly recovered from specific input stimuli (associative memory). As a consequence, the multienzymatic network has the capacity to learn, self-regulate and self-adapt to new external conditions.In a quantitative manner, our numerical analysis show indications that the systemic catalytic processes of living cells may behave as a functional attractor network and therefore it is endowed of its capacity for storing metabolic patterns.In light of our results, and, in addition to the relatively small amount of genetic information that characterizes most cells, the metabolic networks of living cells may have far more biomolecular information in the form of functional metabolic memories stored in the connectivity patterns of the self-organized multienzymatic subsystems.It has not escaped our notice that the possible duality in the storage system of molecular information in cells  are of considerable biological interest.We are now working on some elementary properties of this dynamic system capable of storing functional metabolic information. Details on the molecular mechanisms that link both storage systems (metabolic memory and genetic memory) will be published later.Understanding how the enzymes are functionally organized under the complex conditions prevailing inside the cell and which systemic mechanisms are involved in the regulation of the cellular enzymatic activity, are crucial for the unraveling of the fundamental biomolecular dynamics of cellular life.Figure S1Sketch of regulatory signals in the DMN. Each subsystem represents a set of functionally associated enzymes which are dissipatively structured. Three classes of regulatory signals are considered: allosteric activation (blue), allosteric inhibition (red) and covalent modulation (green). Non-directed edges in black represent a superposition of more-than-one classes of signals. For instance, from MSb4 to MSb5 it exist a superposition of the three classes signals.(TIF)Click here for additional data file.Supporting Information S1Metabolic Subsystems.(DOC)Click here for additional data file.Supporting Information S2Parameters of the dissipative metabolic network.(DOC)Click here for additional data file.Supporting Information S3Initial conditions of the 18 metabolic subsystems.(DOC)Click here for additional data file.


In human-robot cooperative control systems, force feedback is often necessary in order to achieve high precision and high stability. Usually, traditional robot assistant systems implement force feedback using force/torque sensors. However, it is difficult to directly mount a mechanical force sensor on some working terminals, such as in applications of minimally invasive robotic surgery, micromanipulation, or in working environments exposed to radiation or high temperature. We propose a novel force sensing mechanism for implementing force feedback in a master-slave robot system with no mechanical sensors. The system consists of two identical electro-motors with the master motor powering the slave motor to interact with the environment. A bimanual coordinated training platform using the new force sensing mechanism was developed and the system was verified in experiments. Results confirm that the proposed mechanism is capable of achieving bilateral force sensing and mirror-image movements of two terminals in two reverse control directions. For instance, rehabilitation robots –6 can deThe driver SEAT system  is a selHowever, the assistant robots described above realize force feedback/sensing by using force sensors or complex impedance controllers. As a result, system cost, hardware mounting difficulty, and spatial requirements are increased somewhat. Our previous work has introduced a master-slave robotic prototype to implement force sensing without using any force sensor or impedance/force controller ,24. The 2.M1) and powers the other (slave motor: 2M), which works in an electro-motive state and supports an end-effecter to accomplish various operations. Hence, a kind of energy recycling is achieved. The two motors have identical electromagnetic torques (MT) because of the shared closed-loop current and the same motor torque constant. Therefore, their mechanical torques are connected with each other by the current. That is, the torque variation in one motor shaft can be reflected to the contra-lateral side. Then, the operator adjusts the control force accordingly based on the sensed force to achieve a balanced torque state. Thereby, the system realizes force sensing without using a force sensor. In addition, the force sensing mechanism (closed-loop current) make the system have bidirectional controllability.As shown within the dashed wire frame in Considering the analysis in , the rel0T) and inertial torques (1T and 2T). In some applications, a high driving torque/force is required to deal with the larger reaction force. In this case, gear boxes can be applied to increase the output torque of the system  of the H-bridge driver, and further to adjust the amount of compensated energy [In the system, the rotational velocity of the master should be very high to actuate the slave. Otherwise, even though the slave can be rotated with the generated energy of the master, its rotational velocity will be much slower than that of the master due to the energy losses in the resistances and inductances of the two motors d energy . The comThe force sensing mechanism and master-slave closed-loop structure ensure the system has no directional limitations in the configuration of two motors. During operation, the motor attached with a larger torque behaves as the master and the other motor behaves as the slave. Therefore, the system has bidirectional controllability. This is favorable for hemiplegic patients performing bimanual cooperative rehabilitation training, in which the control direction depends on which side is the impaired limb and on the training modes. If the impaired limb is moved passively by the healthy one (passive mode), or it actuates a movement actively but accomplishes movements with a larger assisting force from the healthy one (active-assisted mode), the control direction is from the healthy limb towards the impaired one; if the impaired limb activates the movement and accomplishes the movement with a smaller assisting force (active-assisted mode) or with a relatively small resistant force from the healthy limb (active-resisted mode), the control direction is from the impaired limb towards the healthy one.In addition, the wired connection between the master and slave motors makes it possible to adjust the relative position of the master and slave according to application requirements. This is an advantage over conventional systems which realize force sensing by connecting the master and slave mechanically .3.3.1.A preliminary test platform supporting bimanual coordinated upper-limb training was built to verify the effectiveness of the proposed force sensing mechanism . It consThe terminal shafts of the two torque transducers were attached with two isometric handles, which were manipulated by a subject. The device supports passive-active, active-assisted, and active-resisted training modes. The first and second patterns before and after the “-” denote the working states of the weak and strong limbs, respectively. The strong limb will provide a corresponding force for the weak limb in different training modes through this master-slave device. The control direction is defined as the direction from the limb exerting a larger force to the limb imposing a smaller force. It depends on the health conditions of the two limbs and the training modes.3.2.In this experiment, the regulation of the input torque during a variation in resistance in the slave terminal was used to verify the force sensing characteristic. A DC driving motor was used to drive the master unit instead of a human operator  analysis was carried out with the velocity information collected from the two terminals during the period that the master and slave made mirror symmetric movements. The same FFT results were obtained for the data detected on the master and slave terminals. When the control force was attached to the left unit, the corresponding frequency response is shown in 3.4.The experiment was aimed at verifying that both a resistant force and an assistant force can be sensed by an operator with the system and confirming that the system is feasible to support bimanual training. An operator controlled the force acting on both terminals with two hands and drove the handles to accomplish a predefined dynamic movement (upward and downward: elbow flexion and extension) with a velocity of 8 degrees per second. The test was carried out in two steps: firstly, the left limb provided an active force while the right limb exerted a resistant force (active-resisted mode); secondly, the left hand provided a small force and the right hand exerted an assistant force (active-assisted mode). For the both cases, the same motion tracking trajectory was performed. A representative motion tracking trajectory and the corresponding velocity curve are shown in L and R denote the corresponding parameters in the left and right hand sides, respectively. The master and slave terminals realized symmetric movement accurately with the position and velocity errors between the two terminals of 0.0559 degree and 0.5681 degree per second for the resistant force test, and of 0.0613 degree and 0.5926 degree per second for the assistant force test. In this test, the velocity of 8 degrees per second was low, it is demonstrated that the system is capable of force sensing and movement reproducing for both high (experiment 1) and low velocities. Besides, it can be concluded that the slave can reproduce the master’s movements accurately. Comparing the The torque curves in the two terminals are given in 4.This paper presented a bimanual training device to confirm the feasibility of the force sensing mechanism thoroughly. Compared to the previous work , this woHowever, the required input torque was still larger than the reaction torque in the slave terminal. This was mainly caused by the gear box efficiency and the amplified unloaded and inertial torques of the motors. Thus, gear boxes and motors with high working efficiency are preferred. As for the relationship between the two terminal forces, it can be modulated by matching the lengths of the two terminal force arms. If a significantly large torque is required for the actuator on the slave side, a longer force arm in the master terminal can be considered in order to reduce the burden on the operator. With regards to the reverse case, a shorter force arm on the master terminal or a longer force arm in the slave terminal can be designed to amplify a small reaction force and make it suitable for a human operator. On the other hand, if it is difficult to change the lengths of the force arms due to restrictions on working space, the relationship between the two terminal forces can be adjusted by using different motors or matching the gear ratios of the gear boxes. That is, the magnitudes of the two terminal torques in the balanced state are matched directly in view of the expected force relation.In this paper, two terminals were controlled to implement mirror-image movements. Depending on different applications, different movement relationship of the two terminals can be achieved by attaching a scale coefficient for the velocities/positions between the two terminals, then making the movement of the slave terminal within the controllable movement range of the human operator. However, the PID parameters of the motion tracking controller should be regulated accordingly. More experiments should be performed to verify this capability.5.The proposed sensing mechanism has several characteristics that make it suitable for application to a robot development. First, the system realizes bilateral force sensing without a mechanical force sensor. Second, the system achieves master-slave motion tracking for the both control directions. Third, the relative position between the master and slave units can be adjusted thanks to the wired connection between the two motors. These advantages give this new sensing mechanism great potential in applications to the fields of rehabilitation, minimally invasive surgery, manipulation, and so on. In particularly, the features of force sensing and bidirectional controllability are very desirable in bimanual cooperative rehabilitation training systems. However, system configuration should be improved for different application studies in our future work.


Firearm injuries account for 13% to 17% of all spinal cord injuries, and are generally caused during warfare or assault with intent to kill. Spinal cord injuries caused by firearms are usually observed in patients aged 15 to 34 years old, and are especially common among men.We report the case of a 28-year-old Iraqi man who was referred to our radiology department with lower limb paraplegia secondary to a gunshot wound. We performed 64-slice computerized tomography with two-dimensional and three-dimensional reconstruction of the thoracolumbar spine. On the two-dimensional and three-dimensional reconstructed axial images of the thoracolumbar spine, an intra-canalicular bullet nucleus was found at the mid-spinal cord at the T8 level, with no evidence of vertebral bone destruction.To the best of our knowledge, there is only one previous report in the literature describing a case of a bullet nucleus lodged into the inferior epidural spinal canal without destruction of the vertebral bone. With the rise of violence worldwide the incidence of gunshot injuries continues to increase, and, thus, it is essential for radiologists to have a clear understanding of gunshot injuries and the findings on radiographic images. Gunshot wounds to the spine are potentially devastating injuries that account for approximately 13% to 17% of all spinal cord injuries every year . Spinal To the best of our knowledge, there is only one previous report in the literature  describiA 28-year-old Iraqi man was referred to our radiology department with lower limb paraplegia due to a gunshot wound. The wound occurred in the chest two days before his presentation, and was inflicted by a small-caliber handgun from a distance of approximately 6 m. Our patient was hospitalized by the emergency services after he was injured. The entrance wound caused by the traversing projectile was located at the level of the seventh rib at the left posterior axillary line. An exit wound was not observed. Neurological examination identified lower limb paraplegia. He was referred to our radiology department after initial management of the wound and after his condition became stable. We performed 64-slice computerized tomography (CT) with two-dimensional and three-dimensional reconstruction of the thoracolumbar spine. On the two-dimensional and three-dimensional reconstruction of the axial CT images of thoracolumbar spine, an intra-canalicular bullet nucleus was found at the mid-spinal cord at the T8 level, without any evidence of vertebral bone destruction Figure .The thoracic vertebrae have a stable biomechanical structure maintained by means of costovertebral joints and the thoracic cage. Thus, greater force is needed to cause injuries to the thoracic spine than to other regions. Because the canal of the thoracic vertebra is narrower than those of the cervical and lumbar zones, injuries to the thoracic spine may damage the spinal cord .Ballistics is defined as the scientific study of projectile motion ,8 and is2). Gunshot energy is further classified into low and high energy, depending on muzzle velocity. Muzzle velocities of less than 1000 to 2000 feet/second (304.8 to 609.6 m/second) are defined as low energy, whereas speeds higher than 2000 to 3000 feet/second (609.6 to 914.4 m/second) are defined as high energy [Energy from a gunshot projectile is directly related to both the mass and the square of the velocity of the bullet KE = 1/2 mv mv2. GunIt is crucial to determine the type of a weapon was used and the distance between the weapon and the victim, because treatment options will depend on these criteria. In addition to the amount of energy released from the weapon, the path of the bullet can result in severe injury because the zone of destruction may be larger than expected. Yaw refers to the tumbling of a bullet along its longitudinal axis. Therefore, long bullets produce increased yaw and can result in a large zone of destruction . Our patAfter a gunshot injury, spinal cord defect occurs as a result of direct damage by the bullet nucleus or metallic particles, or as a result of compression by the broken bone particles. Although less commonly observed, disc material can cause neural defects by compressing the canal when the bullet nucleus damages the annulus. This results in an increase in pressure on the nucleus pulposus after the bullet nucleus settles at an inter-vertebral locus . In the To the best of our knowledge, there is only one previous report in the literature  describiWith the rise of armed violence worldwide, the incidence of gunshot injuries continues to increase and, thus, it is essential for radiologists to have a clear understanding of gunshot injuries and their radiographic imaging, especially gunshot wounds to the spine that are the most problematic of all these injuries. Because of the theoretical risks associated with use of MRI and the metallic projectile, routine use of MRI for the assessment of gunshot wounds has not been advocated.Written informed consent was obtained from the patient for publication of this case report and any accompanying images. A copy of the written consent is available for review by the Editor-in-Chief of this journal.The authors declare that they have no competing interests.JH interpreted our patient's MRI results and supervised the writing of the manuscript. MJ was a major contributor to writing the manuscript. MP contributed to figure formatting. All authors read and approved the final manuscript.


This paper proposes an artificial bee colony (ABC) algorithm for solving optimal power flow (OPF) problem. The objective of the OPF problem is to minimize total cost of thermal units while satisfying the unit and system constraints such as generator capacity limits, power balance, line flow limits, bus voltages limits, and transformer tap settings limits. The ABC algorithm is an optimization method inspired from the foraging behavior of honey bees. The proposed algorithm has been tested on the IEEE 30-bus, 57-bus, and 118-bus systems. The numerical results have indicated that the proposed algorithm can find high quality solution for the problem in a fast manner via the result comparisons with other methods in the literature. Therefore, the proposed ABC algorithm can be a favorable method for solving the OPF problem. Optimal power flow (OPF) problems are the important fundamental issues in power system operation. In essence, they are the optimization problems and their main objective is to reduce the total generation cost of units while satisfying various constraints in the system. The OPF problem has been widely used in power system operation and planning . Many teThe LP methods are fast and reliable for solving optimization problems but the main disadvantage of the LP methods is that both objective and constraints of the problem need to be piecewise linear functions. The NLP methods suffer another problem of convergence and algorithmic complexity. Newton-based algorithm  suffers In this paper, the ABC algorithm is proposed for solving OPF problem with both continuous and discrete control variables. The continuous controllable system quantities are generator MW, controlled voltage magnitude, and switchable shunt devices while the discrete ones are transformer tap settings. The objective is to minimize the total fuel cost of thermal generators by optimizing the control variables within their limits so that they cause no violation on other quantities  occurring in either the normal or outage case of system operating conditions. The proposed algorithm has been tested on the IEEE 30-bus, 57-bus, and 118-bus systems for both normal and contingent cases. The obtained results from the proposed method are compared to those from EP , ant colF(x) is the objective function, g(x) represents the equality constraints, h(x) represents the inequality constraints, and x is the vector of the control variables varied by a control center operator .The OPF problem can be described as an optimization (minimization) process with nonlinear objective function and nonlinear constraints. In general, the general OPF problem can be expressed as follows:NG is the number of generation buses including the slack bus, PG is the generated active power at bus I, and ai, bi, and ci are the unit costs curve for ith generator.The essence of the OPF problem resides in minimizing the objective function and simultaneously satisfying the load flow equations  without violating the inequality constraints. The fuel cost function for thermal generators is given byei and fi are the fuel cost coefficients of ith unit with valve point effects.The smooth quadratic fuel cost function of the generating units is given by , where tWhile minimizing the fuel cost function, it is necessary to make sure that the generation still supplies the load demands plus losses in transmission lines. Usually, the power flow equations are used as equality constraints .i are defined in the following equation:Consider the following:The inequality constraints of the OPF problem reflect the limits on physical devices in power systems and they also ensure the system security. The usual types of inequality constraints are upper bus voltage limits at generations and load buses, lower bus voltage limits at load buses, reactive power limits at generation buses, maximum active power limits corresponding to lower limits at some generators, maximum line loading limits, and limits on tap settings. The inequality constraints of the problem include the following.Generation Constraint. Generator voltages, real power outputs, and reactive power outputs are restricted by their upper and lower bounds as follows:Shunt VAR Constraint. Shunt VAR compensations are restricted by their upper and lower bounds as follows:NC is the number of shunt compensators.Transformer Tap Constraint. Transformer tap settings are restricted by their upper and lower bounds as follows:NT is the number of transformers with tap. Security Constraint. Voltages at load bus are restricted by their upper and lower bounds as follows:NL is the number of load buses.Artificial bee colony (ABC) algorithm is introduced by Karaboga in 2005 . The ABCData flow creation around the beehive is a behavior of bees which involves the fundamentals of the swarm intelligence. The colony of artificial bees consists of three groups of bees including employed bees, onlookers, and scouts. Each type of bees has a different role in the optimization process. The employed bees wait above the nectar source and keep the neighboring sources in memory while the onlooker bees get that data from the employed bees and make a resource choice to collect the nectar and the scouts are very much accountable for calculation. The algorithm for solving an optimization problem is comprised of three steps. In the first step, the employed bees are sent to scamper for resources and the nectar amount is computed. In the second step, the onlooker bees make a resource choice appropriate to the data they took from the new identified nectar resources. Finally, in the last step, one of the employed bees is chosen at random as a scout bee and it is sent to the sources to identify new sources . A half xi  . Secondly, each employed bee identifies the new sources whose amounts are equal to the half of the total sources. Equation  for each method by multiplying floating-point operations per second (FLOPS) with their computational time. FLOPS can be calculated using the equation in  as folloFor most microprocessors, they can perform 4 FLOPs per clock cycle . TherefoThe IEEE 30-bus system consists of 6 generators, 4 transformers, 41 lines, and 2 shunt reactors. All generator active power, generator bus voltages, and transformer tap setting are considered as continuous for simplicity. The generators cost coefficients of the IEEE 30-bus test system are given in .In this case, the units cost curves are represented by quadratic function. The obtained results using ABC are given in In this case, the generator fuel cost curves of generator at buses 1 and 2 are represented by a quadratic function with rectified sine components as . The genIn this case, the IEEE 57-bus system is considered to investigate the effectiveness of the proposed algorithm. The IEEE 57-bus system consists of 7 generators, 15 transformers, and 80 transmission circuits. The single-line diagram of this system and the detailed data are given in . The totThe proposed ABC algorithm has been tested on large-scale system of 118 buses . The sysIn this paper, the ABC algorithm is successfully applied for solving the OPF problem. The ABC algorithm is based on the foraging behavior of honey bees for finding global solution for optimization problems. The advantages of the proposed algorithm are robustness, fast calculation, flexibility, and few setting parameters. However, the ABC algorithm also suffers a drawback of search space limited by initial solution. In fact, this drawback can be overcome using normal distribution sample in the initial step. The proposed ABC algorithm has been tested on different systems and the obtained result for each system is compared to other methods in the literature. The result comparisons have shown that the proposed algorithm can obtain better optimal solution than many other methods with a fast computational manner, especially for large-scale systems. Therefore, the proposed ABC algorithm can be a favorable method for solving OPF problems in power systems.


The eyebrow region is of utmost importance for facial movement, symmetry, and the overall cosmetic appearance of the face. Trauma or tumor resection often leave scars that may dislocate the eyebrow producing an alteration both in static symmetry of the face and in the dynamic expressivity. The authors present a technique for eyebrow's defects repair using the remaining eyebrow advancement by means of a “freestyle-like” V-Y flap. In the past two years a total of eight consecutive patients underwent excision of skin lesions in the superciliary region and immediate reconstruction with this technique. On histology, six patients were affected from basal cell carcinomas, one from squamous cell carcinoma, and one from congenital intradermal melanocytic nevus. The pedicle of the flap included perforators from the supratrochlear, supraorbital, or superficial temporalis artery. Advancement of the entire aesthetic subunit that includes the eyebrow using a V-Y perforator flap was performed successfully in all cases achieving full, tension-free closure of defects up to 3.0 cm. “Freestyle-like” V-Y flaps should be considered as a first-line choice for partial defects of the eyebrow. The greater mobility compared to random subcutaneous flaps allows to reconstruct large defects providing an excellent cosmetic result. Lesions of the superciliary arch are common during facial trauma, as the sharp bony prominences can easily lacerate the overlying skin. In contrast, tumoral lesions are quite rare and represent, according to our experience, about 6% of the tumors involving the periorbital region. Due to the relative rarity of such tumors in the superciliary arch, very little has been published regarding this topic, and there are no guidelines for reconstruction. The majority of the reconstructive techniques of the eyebrow are reported as case reports and not as case series. In this paper, we review the most recent literature on eyebrow reconstruction and we present the authors' technique for eyebrow repair using the remaining eyebrow advancement by means of a “freestyle-like” V-Y flap. This technique allows the repair of extensive defects (up to 50% of the entire eyebrow) with excellent cosmetic outcomes. The advantages of using V-Y flaps have been widely described for the reconstruction of small to medium defects of the face following postoncologic resection of skin tumors. The senior authors have already published in the 1980s and 1990s their first experiences on the use of flaps with a subcutaneous pedicle in the upper and lower eyelid regions .In 2009, Marchac et al. have published an article on lower eyelid reconstruction with a subcutaneous pedicled flap highlighting the important role of this technique , which w The most recent surgical applications of this technique –7 have sThese free stile V-Y flaps are safer, with a thinner pedicle and with a greater advancement potential for reconstruction of different body areas, including the superciliar region. In the last two years eight patients, six males and two females , underwent excision of skin lesions in the superciliary region. On histology, five of these patients were affected from nodular basal cell carcinomas, one from pigmented basal cell carcinomas, one from residual squamous cell carcinoma following prior excision, and one from congenital intradermal melanocytic nevus . In the The defect to be determined in the superciliary region is marked and included in a square or oval area. Excision of the tumor is obtained to establish oncologic radicality. A triangular flap including the entire hairy portion of the remaining eyebrow is then marked. The base of the flap is represented by the lateral margin of the defect, and on occasion, depending on the vertical dimension of the defect, it may also include a part of the non-hair bearing skin above  or below the eyebrow (eyelid region).The height of the triangle should be such to allow the closure of the donor site in a tension-free V-Y fashion. The flap is incised peripherally, and a careful exploration of the subcutaneous tissue begins, to identify and preserve a perforator vessel of adequate caliber for the nourishment of the cutaneous island in a freestyle fashion. The dissection begins from the inferior margin, where it is easier to find the branches of the supratrochlear and supraorbital arteries. The supraorbital artery, arising from the ophthalmic artery, passes through the supraorbital foramen. It divides then into a superficial branch and a deep branch, which supply the eyebrow and the forehead. If it is not affected during tumor excision, the supratrochlear artery, which lies more medial than the supraorbital vessels , should When vessels of adequate caliber are isolated, they are preserved without the need for complete skeletonization. The subcutaneous tissue around the vessels can be removed to obtain a thinner pedicle and greater mobility but still ensuring good vascularization. Once the pedicle has been carved, the flap can advance without any tension to repair up to 50% of the entire length of the eyebrow. The flap is then sutured in double layer paying attention to the correct positioning of the hair-bearing area which has to be anchored symmetrically to the contralateral brow. In some cases, quilting sutures to the periosteum can be useful to ensure the persistence of symmetry between the two orbital arches . Advancement of the entire aesthetic subunit that includes the eyebrow using a V-Y flap was performed successfully in a case series of 8 consecutive patients of partial eyebrow reconstruction, achieving full, tension-free closure of defects up to 3.0 cm in length Figures  and 3. ODespite the aesthetic and functional relevance that the eyebrow maintains in the eumorphism of the face, the scientific literature revision on eyebrow reconstruction has highlighted a lack of efficacious and reproducible surgical techniques. Several techniques have been reported as case reports and not as case series, many more refer to composite grafts and flaps harvested from the scalp, and others are extremely complex and are not justified for the use because they do not provide any advantage for the patient. Composite grafts for eyebrow reconstruction have been reported as strip grafts , 10, punPunch and micrografts cannot be implated immediately during the removal of a tumor and they are indicated for a scarring alopecia repair as a secondary reconstructive procedure. Strip grafts can allow a single-stage reconstruction of large defects but they need to be thin and narrow to receive adequate vascularization from the edges and the wound bed.  Flaps from the scalp that are pedicled on parietal branches of the superficial temporal vessels have been described for defects involving part of the entire eyebrow. Elevation of such flaps is tedious as dissection and tunneling of a long pedicle are required. The authors believe that strip grafts or local flaps from the scalp represent always an aesthetic compromise and should be reserved to defects involving the entire eyebrow.Kim et al. have recently published a case report on an elegant microsurgical reconstruction with a supraorbital artery perforator free flap sculpted from the contralateral eyebrow and anastomosed in an end to end fashion to the supraorbital vessels of the recipient site for the repair of a 1.7 cm long posttraumatic defect . We certAmong the most common techniques for partial eyebrow defects reconstruction, the use of a double-Z rhombic technique has been reported . This teMore recent and innovative is a case report in which the authors use a perforator-like flap based on the supratrochlear artery advanced in a medial to lateral direction for partial reconstruction of the lateral half of the eyebrow . In thisThe reconstructed eyebrow, despite being symmetric and well-oriented, will necessarily be shorter than the contralateral brow. As understandable, this is due to the fact that no additional hair-bearing areas are transferred. However, very often the reduction of 30–50% in length of the brow, especially in elderly patients, does not result in a noticeable cosmetic defect. This flap advances better in the lateral-to-medial direction, as the lack of hair in the lateral third of the brow is cosmetically less noticeable. For this reason, this technique is our elective method to repair defects of the medial third of the eyebrow. Nevertheless, this technique could be easily utilized for lateral defects reconstruction. In such cases, however, the distance between the two glabellar areas will increase.  The common thinking that is now widespread following the introduction of free-style perforator flaps has determined a new approach on the mobilization of advancement V-Y flaps allowing to take distance from the historical concept of random-vascularization flaps. In the case of V-Y flaps of the eyebrow here described, the greater mobility compared to random subcutaneous flaps allows to obtain easily the correct orientation of the hair-bearing areas. The scars resulting from a V-Y flap do not involve hair-bearing zones and are parallel to the minimum tension lines of the forehead and the eyelid, resulting in nonvisible scars with scar maturation. “Freestyle-like” V-Y flaps should be considered potentially as a first-line choice for partial defects of the eyebrow. Undoubtedly, this technique reduces the length of the eyebrow and is indicated for defects involving between 30 and 50% providing an excellent cosmetic result.Grafts and flaps harvested from the scalp, due to differences in annexa presence, hair orientation and growth length, should be reserved to total and subtotal reconstructions.


The human spine is often exposed to mechanical load in vocational activities especially in combination with lifting, carrying and positioning of heavy objects. This also applies in particular to nursing activities with manual patient handling. In the present study a detailed investigation on the load of the lumbar spine during manual patient handling was performed.For a total of 13 presumably endangering activities with transferring a patient, the body movements performed by healthcare workers were recorded and the exerted action forces were determined with regard to magnitude, direction and lateral distribution in the time course with a "measuring bed", a "measuring chair" and a "measuring floor". By the application of biomechanical model calculations the load on the lowest intervertebral disc of the lumbar spine (L5-S1) was determined considering the posture and action force data for every manual patient handling.The results of the investigations reveal the occurrence of high lumbar load during manual patient handling activities, especially in those cases, where awkward postures of the healthcare worker are combined with high action forces caused by the patient's mass. These findings were compared to suitable issues of corresponding investigations provided in the literature. Furthermore measurement-based characteristic values of lumbar load were derived for the use in statement procedures concerning the disease no. 2108 of the German list of occupational diseases.To protect healthcare workers from mechanical overload and the risk of developing a disc-related disease, prevention measures should be compiled. Such measures could include the application of "back-fairer" nursing techniques and the use of "technical" and" small aids" to reduce the lumbar load during manual patient handling. Further studies, concerning these aspects, are necessary. Diseases at the muscle and skeleton systems belong to the most frequent causes for health-related absenteeism in the workplace. Handling heavy objects increases the risk of low back pain. This is also a significant problem among nurses  because In Germany, the social protection of the inhabitants is based to a big part on a statutory insurance system, the social insurance . The statutory social insurance consists of the compulsory health insurance, the long-term care insurance, the pension insurance and, particularly regarding the problem discussed here, the statutory accident insurance. Supporting organisation of this statutory accident insurance for the enterprises of the German business companies and their employees are the Statutory Accident and Health Insurance Institutions. Their commission is to avert and, in case, to compensate for occupational accidents and diseases. Employees which have suffered from an occupational accident or suffer from an occupational disease are rehabilitated by the Statutory Accident and Health Insurances medically, occupationally and socially. In addition, the consequences of accidents and diseases are financially compensated for. Mainly diseases which are listed in the Occupational Diseases Regulation (Berufskrankheiten-Verordnung/BKV) can be admitted. The responsible statutory accident and health insurance institution accomplishes an occupational disease evaluation where criteria for the relationship between a possibly damaging effect of the occupational activity and the diagnosed disease are checked. For that purpose a retrospective determination and evaluation of the lifetime occupational exposure is necessary. If this association is found and the damage is confirmed medically, an occupational disease is admitted. In the context of degenerative diseases in the lower-back region, as for example intervertebral disc-related diseases of the lumbar spine caused by long-term lifting or carrying heavy objects or caused by long-term activities in extremely trunk-flexed postures, were enacted in the Occupational Disease Regulation relatively newly as the occupational disease OD 2108 (Berufskrankheit BK 2108) .For the retrospective load analysis the so-called Mainz-Dortmund Dose Model ("MDD") ,8 is useThe research project introduced here - the so-called Dortmund Lumbar Load Study 3 ("DOLLY 3")  - was caThe underlying methodology is described within three main parts. The first part overviews the adopted biomechanical simulation and evaluation tool used in this study, and the second part describes the experimental procedure applied to determine the load of the lumbar spine of healthcare workers during manual patient handling. The last part introduces the scope of investigated transfer actions. The examinations were not performed in a hospital but in the laboratory due to applying a complex measurement-assisted methodology for the determination of lumbar load based on posture-and-force capturing. For ethical and also technical reasons no real patients served as subjects. Instead, two professionally experienced female healthcare workers acted alternately as a patient or a nurse throughout the research project. They are both highly qualified in applying different measuring variables like fully versus partially co-operating patient, i.e. to give more or less support during co-operating with the carer. In this context the patient was, at least, partially co-operating and the task was executed by the healthcare worker as commonly performed in hospitals. That means the handling of totally non co-operating patients was not studied explicitly.Several measures of lumbar load were quantified by means of inverse dynamics on the basis of measured posture and action-force data via model calculations. To this end a previously developed simulation and evaluation tool, "The Dortmunder", was applied ,12. ThisThe muscular structure in the lower trunk region, spreading over the lumbar discs and connecting pelvis and rib cage biomechanically, is simulated by the effect of 14 muscles or muscle cords at the back and the abdominal wall. The back musculature, summarized in the Erector Spinae muscle group, is represented by its two main cords: the Longissimus muscle with its lumbar part and the Iliocostalis muscle with its medial part which are implemented each on both sides of the body; these muscle cords are modelled by four equivalent force vectors. The functional behaviour of the anatomically fan-like shaped Abdominal Oblique muscles is also considered in the model: The medial muscle cords of the internal and external parts of opposite sides are connected via a tendinous network which particularly enables twisting the trunk; in contrast, the lateral muscle cords are mainly activated during side-bending postures. Consequently, the muscles cords of the Abdominal Obliques are replicated by other four equivalent force vectors. The two cords of the Rectus Abdominal muscle are located beneath the tendinous texture mentioned above and are running parallel near the mid-sagittal plane; as a result, a single force vector only is considered in the model and acting as an antagonist of the back muscles mainly in sagittal procedures. Hence nine force vectors simulate the effect of fourteen muscle cords in the lower trunk region in total.Analaysis of a manual patient handling action assumes the information of two important variables: the knowledge on the action forces exerted and on the postures adopted by the healthcare worker. Knowledge of the posture was achieved by using a combination of videoanalysis and optoelectronic measurement . The vidFor the optoelectronic measuring, a 3-D motion and position measurement system "OPTOTRAK"  was applied, which tracks small infrared markers attached to the subject at relevant anatomical landmarks. Markers were attached to the shoulders, the hands, the hip joints and the heels of the healthcare worker. These body parts were chosen because of their importance for the lumbar-load level and, correspondingly, the biomechanical model calculations. Additionally two markers were applied to the bed posts at the long side of the bed - or the chair or the floor - as a reference.Two "position sensors", as the main components of the system consisting of three infrared cameras each which are arranged in a firm angle and distance to each other, are required to determine the 3-D position of each marker. These position sensors were mounted at opposite walls of the laboratory; their visual fields overlap and form a calibrated space in the middle of the room surrounding the measuring bed and the healthcare worker 4. Moving a patient towards the bed's head (nurse at bed's head)5. Moving a patient in the bed sidewards6. Lifting a leg of a lying patient or vice versa (nurse at bed's long side)7. Lifting a leg of a lying patient or vice versa (nurse at bed's foot)8. Lifting both legs of a lying patient or vice versa (nurse at bed's long side)9. Inclining the bed's head with the patient lying in the bed10. Shoving a bedpan or vice versa11. Placing a patient from sitting at bed's edge in a chair or vice versa12. Raising a patient from sitting to upright standing position or vice versa13. Raising a patient from lying on the floor to standing positionThe photos of Figure The exemplarily described activity, elevating a patient from lying in the bed to a sitting position at the bed's edge and vice versa, was divided into sequential segments which were denoted as basic posture, bending, grasping the upper part of the body of the patient, transposing the upper body of the patient, holding the patient, laying back the patient, straighten up and basic posture again. In this context, Figure The total procedure starts with the healthcare worker just standing at the bedside and waiting for the signal announcing the start of the measurement. Thereupon she was bending forward to the patient in the bed. In detail, caregiver's trunk was flexed forward considerably and turned a little to the left side. The left arm was strongly bent in the elbow joint, the right arm was almost straightened. This posture was also maintained while grasping the upper body of the patient by putting her left arm underneath patient's shoulder and grasping patient's legs at the knee joints with her right arm. After transposing the upper body from a horizontal to an upright position, the patient was stabilised in a constant posture while sitting at the bed's edge with hanging lower legs. After a short phase of holding the sitting patient, patient's upper body was laid back on the mattress to the left side combined with swaying the legs upwards. The healthcare worker bent her own upper body strongly forward and at the same time to the left, both arms were bent in the elbows. After finishing the transfer action, the healthcare worker re-straightened up.The forces which are transferred from the healthcare worker to the patient during an activity's execution represent the "action forces" at the hands. For the exemplarily chosen activity, the temporal courses of the recorded horizontal and vertical action-force components are shown in Figure As mentioned in the subchapter "postures" the relatively complex motion sequence was divided into eight sequential phases. The first noticeable load-relevant segment is the third one, i.e. grasping the upper part of the body of the patient. The temporal courses of the hand-action forces reach a peak value of the force component in downward direction, i.e. supporting caregivers upper body, of nearly -140 N applied with her left arm to patient's shoulder (lower trace) and a component "to the right" of -60 N (middle trace). In the following phase "transposing the upper part of the body of the patient", the direction of the vertical force component was inverted (lower trace) and reached a value of nearly +150 N upwards due to elevating patient's trunk from a lying to a sitting position. Immediately after this local maximum, the action force "backward" reached its peak value with an amount of nearly -130 N (upper trace), resulting from pulling patient's leg from bed's midline to bed's edge. At the end of the transposing procedure, forces of about -100 N each, were exerted by the healthcare worker in the directions "downward" and "to the right", respectively, due to pushing the legs downward accompanied by pushing patient's trunk sideward into an upright position. The clearly highest action-force values, however, were determined for the segment "laying back the patient". In this period four successive peaks in the different traces of the hand-action force components can be identified: The first and second local maximum appear in the vertical component with nearly +140 N and +200 N, respectively ; the first load maximum is traced back to swaying patient's hanging legs upwards ("lifting"), and the second one is caused by both the aforementioned leg-lifting action and the holding of patient's trunk against gravity during the laying-back action. These actions are followed by two pushing-the-legs actions directed horizontally, first of all pointing leftward to the bed's head and then forward to the bed's middle axis. Seen from the carer's point of view, the third action-force peak of this transposing section resulted in "leftward" direction , and the fourth local maximum of +140 N is shown in the course for forward pushing .In analogy to the courses of the hand-action forces in Figure The lumbosacral sagittal shear force reaches its extreme value of about -0.9 kN at laying back the patient  whereas the highest compressive forces were reached for moving a patient towards the bed's head (no. 3). In most cases, higher values were found for positioning a more passive patient than moving a more active patient (compare closed vs. open symbols). Furthermore the diagram shows that there is no explicit evidence whether the way there or the way back leads to higher lumbar load. For instance, for "Inclining a bed's head with the patient" (no. 9) higher values were found with the way there than with the way back (rhombi vs. triangles), while for "Elevating a patient from lying to sitting at the bed's edge" (no. 2) the back way lead to higher values.An essential purpose of the study introduced here was to examine the load of the lumbar spine occurring with manual patient handlings to enable a scientifically supported derivation of characteristic values for lumbar load to be applied in occupational-disease statement procedures concerning the association between biomechanical load of the lower back through manual patient handling and the risk for developing degenerative diseases like disc narrowing and herniation . The respective list of activities with the corresponding characteristic lumbar-load values are presented in table The values provided in table This paper presents characteristic values of the lumbar load of healthcare workers for typical activities with manual patient handling. The collection of data made a very complex procedure necessary. For this purpose measuring systems were implemented to determine the main influencing factors on lumbar load, in particular the posture of the healthcare worker and the forces brought forward to the patient. This information regarding posture and action force was therefore also necessary to carry out the biomechanical simulation calculations with the help of the three-dimensional dynamic simulation tool The Dortmunder to determine characteristic values of the task-induced lumbar load. A comprehensive measuring configuration, consisting of video-system, optoelectronic system and action-force measuring systems, was applied allowing a determination of the lumbar load of the healthcare worker very close to reality . Skotte Another difference between the study described here and the investigations made by Skotte and Schibye concerns the used calculation model. While in the present case a 30-segment biomechanical model for the upper body parts (top down model) is used, both Skotte and Schibye underlayed their investigations a 7-segment model for the lower body parts (bottom up model). This "bottom up" calculation method, in combination with the derivation of the hand-action forces based on measuring the ground reaction forces, is considered less accurate for the calculation of spinal forces than the "top down" method, as comparative calculations with both approaches have shown .Last but not least the activities investigated by Skotte et al.  related Possible disadvantages of the whole measuring configuration used here originate from the limited spatial flexibility which restricts an application to the lab and makes an application to the clinical surroundings nearly impossible. On the other hand it is of positive relevance that with the lab measurements variables like postures, movements and forces of the healthcare worker, but also behaviour patterns of the patient which influence the lumbar load substantially can be controlled sufficiently.Furthermore it could be marked critically that the sample is rather small. This was due to the complex measuring methods, which needed among other things, a huge amount of time for evaluation. To compensate for this constraint two professionally experienced healthcare workers acted as subjects, alternatively as patient or caregiver. They were both highly qualified in performing the tasks and in replicating different levels of patient's co-operatingness. The selected approach of the analysis of typical executions seems to be approved since exemplary evaluations of repeated measurements have shown a good correspondence of the results: 18 measurements for lifting a leg of a lying patient were accomplished and resulted in a mean value of 2.8 kN of compressive force with a range of 1.9 to 4.0 kN.The inclusion of two experienced and trained physiotherapists acting as carer or patient could have led eventually to the fact that the activities were carried out in a too good manner in contrast to reality and it could therefore lead to an underestimation of the lumbar load in real environments . As a rule the investigations were arranged with partially co-operating patients. As mentioned before, in certain cases, however, handling was performed with a fully co-operating patient in order to protect the caregiver, hazarding again the consequence to underestimate the lumbar load in real environments.A systematic overview especially to investigations with the main focus "patient transfer" is found with Hignett , HignettFor the same reason this study does not even deal with the option of the use of lifters for patient transfers like Marras et al.  did. TheAnother interesting approach represents the investigation of Freitag et al. . They stOther studies  do not fThe results of the study have shown that manual handling of patients - as it is routinely practised in hospitals or nursing homes - is associated with high lumbar load for healthcare workers and a considerable risk of developing intervertebral disc-related diseases must be taken into account. Prevention measures to avoid the appearance of lumbar overload are strongly needed. Future investigations should take various measures of the behavioural prevention by the application of "back-fairer" nursing techniques into consideration and also include the effect of applying technical aids (e.g. lifters) and small aids (e.g. sliding sheets) to reduce the lumbar load during manual patient handling. Quantitative measurements such as determined in this study, can help to evaluate the effectiveness of such preventive measures and to investigate dose-response relationships between the load on the lumbar spine and resulting diseases, to identify overload and - in the long run - to contribute to the reduction of low-back pain and musculoskeletal diseases.The authors declare that they have no competing interests.All authors designed and conducted the study. NW and STK initiated the study and configured the essentials for OD application. AL, MJ, NW and STK supervised the measurements. MJ and AL guided the evaluations and descriptions. CJ and AT developed the measuring devices and carried out data analysis. CJ prepared the manuscript. All authors have read and approved the manuscript.