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In this work, we couple a lumped-parameter closed-loop model of the cardiovascular system with a physiologically-detailed mathematical description of the baroreflex afferent pathway. The model features a classical Hodgkin-Huxley current-type model for the baroreflex afferent limb (primary neuron) and for the second-order neuron in the central nervous system. The pulsatile arterial wall distension triggers a frequency-modulated sequence of action potentials at the afferent neuron. This signal is then integrated at the brainstem neuron model. The efferent limb, representing the sympathetic and parasympathetic nervous system, is described as a transfer function acting on heart and blood vessel model parameters in order to control arterial pressure. Three in silico experiments are shown here: a step increase in the aortic pressure to evaluate the functionality of the reflex arch, a hemorrhagic episode and an infusion simulation. Through this model, it is possible to study the biophysical dynamics of the ionic currents proposed for the afferent limb components of the baroreflex during the cardiac cycle, and the way in which currents dynamics affect the cardiovascular function. Moreover, this system can be further developed to study in detail each baroreflex loop component, helping to unveil the mechanisms involved in the cardiovascular afferent information processing.

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Pancreatic islets are mini-organs composed of hundreds or thousands of ɑ, ß and δ-cells, which, respectively, secrete glucagon, insulin and somatostatin, key hormones for the regulation of blood glucose. In pancreatic islets, hormone secretion is tightly regulated by both internal and external mechanisms, including electrical communication and paracrine signaling between islet cells. Given its complexity, the experimental study of pancreatic islets has been complemented with computational modeling as a tool to gain a better understanding about how all the mechanisms involved at different levels of organization interact. In this review, we describe how multicellular models of pancreatic cells have evolved from the early models of electrically coupled ß-cells to models in which experimentally derived architectures and both electrical and paracrine signals have been considered.

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Objective.The diagnosis of nerve disorders in humans has relied heavily on the measurement of electrical signals from nerves or muscles in response to electrical stimuli applied at appropriate locations on the body surface. The present study investigated the demyelinating subtype of Guillain-Barré syndrome using multiscale computational model simulations to verify how demyelination of peripheral axons may affect plantar flexion torque as well as the ongoing electromyogram (EMG) during voluntary isometric or isotonic contractions.Approach.Changes in axonal conduction velocities, mimicking those found in patients with the disease at different stages, were imposed on a multiscale computational neuromusculoskeletal model to simulate subjects performing unipodal plantar flexion force and position tasks.Main results.The simulated results indicated changes in the torque signal during the early phase of the disease while performing isotonic tasks, as well as in torque variability after partial conduction block while performing both isometric and isotonic tasks. Our results also indicated changes in the root mean square values and in the power spectrum of the soleus EMG signal as well as changes in the synchronization index computed from the firing times of the active motor units. All these quantitative changes in functional indicators suggest that the adoption of such additional measurements, such as torques and ongoing EMG, could be used with advantage in the diagnosis and be relevant in providing extra information for the neurologist about the level of the disease.Significance.Our findings enrich the knowledge of the possible ways demyelination affects force generation and position control during plantarflexion. Moreover, this work extends computational neuroscience to computational neurology and shows the potential of biologically compatible neuromuscular computational models in providing relevant quantitative signs that may be useful for diagnosis in the clinic, complementing the tools traditionally used in neurological electrodiagnosis.

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The therapeutic use of classical psychedelic substances such as d-lysergic acid diethylamide (LSD) surged in recent years. Studies in rodents suggest that these effects are produced by increased neural plasticity, including stimulation of the mTOR pathway, a key regulator of metabolism, plasticity, and aging. Could psychedelic-induced neural plasticity be harnessed to enhance cognition? Here we show that LSD treatment enhanced performance in a novel object recognition task in rats, and in a visuo-spatial memory task in humans. A proteomic analysis of human brain organoids showed that LSD affected metabolic pathways associated with neural plasticity, including mTOR. To gain insight into the relation of neural plasticity, aging and LSD-induced cognitive gains, we emulated the experiments in rats and humans with a neural network model of a cortico-hippocampal circuit. Using the baseline strength of plasticity as a proxy for age and assuming an increase in plasticity strength related to LSD dose, the simulations provided a good fit for the experimental data. Altogether, the results suggest that LSD has nootropic effects.

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Successful partnerships between researchers, experts, and public health authorities have been critical to navigate the challenges of the Covid-19 pandemic worldwide. In this collaboration, mathematical models have played a decisive role in informing public policy, with findings effectively translated into public health measures that have shaped the pandemic in Costa Rica. As a result of interdisciplinary and cross-institutional collaboration, we constructed a multilayer network model that incorporates a diverse contact structure for each individual. In July 2020, we used this model to test the effect of lifting restrictions on population mobility after a so-called "epidemiological fence" imposed to contain the country's first big wave of cases. Later, in August 2020, we used it to predict the effects of an open and close strategy (the Hammer and Dance). Scenarios constructed in July 2020 showed that lifting restrictions on population mobility after less than three weeks of epidemiological fence would produce a sharp increase in cases. Results from scenarios in August 2020 indicated that the Hammer and Dance strategy would only work with 50% of the population adhering to mobility restrictions. The development, evolution, and applications of a multilayer network model of Covid-19 in Costa Rica has guided decision-makers to anticipate implementing sanitary measures and contributed to gain valuable time to increase hospital capacity.

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A number of H-reflex studies used a moderate steady voluntary contraction in an attempt to keep the motoneuron pool excitability relatively constant. However, it is not clear whether the voluntary muscle activation itself represents a confounding factor for the elderly, as a few ongoing mechanisms of reflex modulation might be compromised. Further, it is well-known that the amount of either inhibition or facilitation from a given conditioning depends on the size of the test H-reflex. The present study aimed at evaluating the effects of voluntary contraction over a wide range of reflex amplitudes. A significant reflex facilitation during an isometric voluntary contraction of the soleus muscle (15% of the maximal voluntary isometric contraction-MVC) was found for both young adults and the elderly (p < 0.05), regardless of their test reflex amplitudes (considering the ascending limb of the H-reflex recruitment curve-RC). No significant difference was detected in the level of reflex facilitation between groups for all the amplitude parameters extracted from the RC. Simulations with a computational model of the motoneuron pool driven by stationary descending commands yielded qualitatively similar amount of reflex facilitation, as compared to human experiments. Both the experimental and modeling results suggest that possible age-related differences in spinal cord mechanisms do not significantly influence the reflex modulation during a moderate voluntary muscle activation. Therefore, a background voluntary contraction of the ankle extensors (e.g., similar to the one necessary to maintain upright stance) can be used in experiments designed to compare the RCs of both populations. Finally, in an attempt to elucidate the controversy around changes in the direct motor response (M-wave) during contraction, the maximum M-wave (Mmax) was compared between groups and conditions. It was found that the Mmax significantly increases (p < 0.05) during contraction and decreases (p < 0.05) with age arguably due to muscle fiber shortening and motoneuron loss, respectively.

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Introduction: Staphylococcus aureus is one of the most prevalent and relevant pathogens responsible for a wide spectrum of hospital-associated or community-acquired infections. In addition, methicillin-resistant Staphylococcus aureus may display multidrug resistance profiles that complicate treatment and increase the mortality rate. The ability to produce biofilm, particularly in device-associated infections, promotes chronic and potentially more severe infections originating from the primary site. Understanding the complex mechanisms involved in planktonic and biofilm growth is critical to identifying regulatory connections and ways to overcome the global health problem of multidrug-resistant bacteria. Methods: In this work, we apply literature-based and comparative genomics approaches to reconstruct the gene regulatory network of the high biofilm-producing strain Bmb9393, belonging to one of the highly disseminating successful clones, the Brazilian epidemic clone. To the best of our knowledge, we describe for the first time the topological properties and network motifs for the Staphylococcus aureus pathogen. We performed this analysis using the ST239-SCCmecIII Bmb9393 strain. In addition, we analyzed transcriptomes available in the literature to construct a set of genes differentially expressed in the biofilm, covering different stages of the biofilms and genetic backgrounds of the strains. Results and discussion: The Bmb9393 gene regulatory network comprises 1,803 regulatory interactions between 64 transcription factors and the non-redundant set of 1,151 target genes with the inclusion of 19 new regulons compared to the N315 transcriptional regulatory network published in 2011. In the Bmb9393 network, we found 54 feed-forward loop motifs, where the most prevalent were coherent type 2 and incoherent type 2. The non-redundant set of differentially expressed genes in the biofilm consisted of 1,794 genes with functional categories relevant for adaptation to the variable microenvironments established throughout the biofilm formation process. Finally, we mapped the set of genes with altered expression in the biofilm in the Bmb9393 gene regulatory network to depict how different growth modes can alter the regulatory systems. The data revealed 45 transcription factors and 876 shared target genes. Thus, the gene regulatory network model provided represents the most up-to-date model for Staphylococcus aureus, and the set of genes altered in the biofilm provides a global view of their influence on biofilm formation from distinct experimental perspectives and different strain backgrounds.

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The COVID-19 disease has forced countries to make a considerable collaborative effort between scientists and governments to provide indicators to suitable follow-up the pandemic's consequences. Mathematical modeling plays a crucial role in quantifying indicators describing diverse aspects of the pandemic. Consequently, this work aims to develop a clear, efficient, and reproducible methodology for parameter optimization, whose implementation is illustrated using data from three representative regions from Chile and a suitable generalized SIR model together with a fitted positivity rate. Our results reproduce the general trend of the infected's curve, distinguishing the reported and real cases. Finally, our methodology is robust, and it allows us to forecast a second outbreak of COVID-19 and the infection fatality rate of COVID-19 qualitatively according to the reported dead cases.

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Axolotls are uniquely able to resolve spinal cord injuries, but little is known about the mechanisms underlying spinal cord regeneration. We previously found that tail amputation leads to reactivation of a developmental-like program in spinal cord ependymal cells (Rodrigo Albors et al., 2015), characterized by a high-proliferation zone emerging 4 days post-amputation (Rost et al., 2016). What underlies this spatiotemporal pattern of cell proliferation, however, remained unknown. Here, we use modeling, tightly linked to experimental data, to demonstrate that this regenerative response is consistent with a signal that recruits ependymal cells during ~85 hours after amputation within ~830 µm of the injury. We adapted Fluorescent Ubiquitination-based Cell Cycle Indicator (FUCCI) technology to axolotls (AxFUCCI) to visualize cell cycles in vivo. AxFUCCI axolotls confirmed the predicted appearance time and size of the injury-induced recruitment zone and revealed cell cycle synchrony between ependymal cells. Our modeling and imaging move us closer to understanding bona fide spinal cord regeneration.

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In pancreatic α-cells, intracellular Ca2+ ([Ca2+]i) acts as a trigger for secretion of glucagon, a hormone that plays a key role in blood glucose homeostasis. Intracellular Ca2+ dynamics in these cells are governed by the electrical activity of voltage-gated ion channels, among which ATP-sensitive K+ (KATP) channels play a crucial role. In the majority of α-cells, the global Ca2+ response to lowering external glucose occurs in the form of oscillations that are much slower than electrical activity. These Ca2+ oscillations are highly variable as far as inter-spike intervals, shapes and amplitudes are concerned. Such observations suggest that Ca2+ dynamics in α-cells are much influenced by noise. Actually, each Ca2+ increase corresponds to multiple cycles of opening/closing of voltage gated Ca2+ channels that abruptly become silent, before the occurrence of another burst of activity a few tens of seconds later. The mechanism responsible for this intermittent activity is currently unknown. In this work, we used computational modeling to investigate the mechanism of cytosolic Ca2+ oscillations in α-cells. Given the limited population of KATP channels in this cell type, we hypothesized that the stochastic activity of these channels could play a key role in the sporadic character of the action potentials. To test this assumption, we extended a previously proposed model of the α-cells electrical activity (Diderichsen and Göpel, 2006) to take Ca2+ dynamics into account. Including molecular noise on the basis of a Langevin type description as well as realistic dynamics of opening and closing of KATP channels, we found that stochasticity at the level of the activity of this channel is on its own not able to produce Ca2+ oscillations with a time scale of a few tens of seconds. However, when taking into account the intimate relation between Ca2+ and ATP changes together with the intrinsic noise at the level of the KATP channels, simulations displayed Ca2+ oscillations that are compatible with experimental observations. We analyzed the detailed mechanism and used computational simulations to identify the factors that can affect Ca2+ oscillations in α-cells.

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Although inductive effects in organic compounds are known to influence chemical properties such as ionization constants, their specific contribution to the properties/behavior of amino acids and functional groups in peptides remains largely unexplored. In this study we developed a computationally economical algorithm for ab initio calculation of the magnitude of inductive effects for non-aromatic molecules. The value obtained by the algorithm is called the Inductive Index and we observed a high correlation (R2 = 0.9427) between our calculations and the pKa values of the alpha-amino groups of amino acids with non-aromatic side-chains. Using a series of modified amino acids, we also found similarly high correlations (R2 > 0.9600) between Inductive Indexes and two wholly independent chemical properties: i) the pKa values of ionizable side-chains and, ii) the fluorescence response of the indole group of tryptophan. After assessing the applicability of the method of calculation at the amino acid level, we extended our study to tryptophan-containing peptides and established that inductive contributions of neighboring side-chains are transmitted through peptide bonds. We discuss possible contributions to the study of proteins.

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The growing importance of astrocytes in the field of neuroscience has led to a greater number of computational models devoted to the study of astrocytic functions and their metabolic interactions with neurons. The modeling of these interactions demands a combined understanding of brain physiology and the development of computational frameworks based on genomic-scale reconstructions, system biology, and dynamic models. These computational approaches have helped to highlight the neuroprotective mechanisms triggered by astrocytes and other glial cells, both under normal conditions and during neurodegenerative processes. In the present review, we evaluate some of the most relevant models of astrocyte metabolism, including genome-scale reconstructions and astrocyte-neuron interactions developed in the last few years. Additionally, we discuss novel strategies from the multi-omics perspective and computational models of other glial cell types that will increase our knowledge in brain metabolism and its association with neurodegenerative diseases.

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BACKGROUND: Mucopolysaccharidoses (MPS) are a group of inherited metabolic diseases caused by impaired function or absence of lysosomal enzymes involved in degradation of glycosaminoglycans. Clinically, MPS are skeletal dysplasias, characterized by cartilage abnormalities and disturbances in the process of endochondral ossification. Histologic abnormalities of growth cartilage have been reported at advanced stages of the disease, but information regarding growth plate pathology progression either in humans or in animal models, as well as its pathophysiology, is limited. METHODS: Histological analyses of distal femur growth plates of wild type (WT) and mucopolysaccharidosis type VI (MPS VI) rats at different stages of development were performed, including quantitative data. Experimental findings were then analyzed in a theoretical scenario. RESULTS: Histological evaluation showed a progressive loss of histological architecture within the growth plate. Furthermore, in silico simulation suggest the abnormal cell distribution in the tissue may lead to alterations in biochemical gradients, which may be one of the factors contributing to the growth plate abnormalities observed, highlighting aspects that must be the focus of future experimental works. CONCLUSION: The results presented shed some light on the progression of growth plate alterations observed in MPS VI and evidence the potentiality of combined theoretical and experimental approaches to better understand pathological scenarios, which is a necessary step to improve the search for novel therapeutic approaches.

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Atrazine is an herbicide that is applied in corn around the world and in sugarcane in Brazil. It is known to be hazardous for animals' health, mobile in the soil, and its analysis is considered expensive and onerous. Solute movement studies are essential to provide information about dangerous molecules movement, which can avoid contamination. While field investigations demand time and financial resources, numerical models are an alternative to describe water and solute distribution in the soil profile. Thus, the objective of this work was to use HYDRUS 2-D model for simulations of atrazine movement in containers packed with tropical soil cultivated with corn and to compare simulated and observed data through statistical parameters. The research was carried out in a greenhouse during 116 days after planting. Atrazine was analyzed in the soil solution at three different depths to validate HYDRUS-2D. Simulations were carried out using hydraulic properties fitted directly to measured retention data and parameters for corn growing and atmospheric characteristics. The mixed procedure analysis indicated that there are differences in atrazine concentration among depths and along time. In general, atrazine concentration is higher at shallow depths and right after application. However, it is possible to find atrazine in deeper soil layers, which might be a concern regarding contamination. RMSE, Willmott and Pearson coefficients indicated a favorable capacity of the model to simulate atrazine concentration on corn cultivation. HYDRUS-2D is a reliable tool to obtain trends in atrazine movement under these experiment's conditions. The uptake parameters, the crop root growth and distribution parameters depend on further specific studies to better describe the relationship between the plant and atrazine and meteorological parameters need to be updated.

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O Brasil é o maior produtor mundial de cana-de-açúcar destinada às usinas e tem produtividade média, superior aos demais países produtores dessa matéria-prima. A aplicação de defensivos agrícolas em canaviais das agroindústrias é realizada em extensas áreas de cultivo, com pulverizadoreshidráulicos autopropelidos, tratorizados e aéreo. Para tanto é necessário sistematizar as áreas de cultivo, tornando os talhões com longo comprimento de fileiras de cultivo, a fim de diminuir as manobras de cabeceira das máquinas. O objetivo do trabalho é avaliar o impacto causado pelo comprimento das fileiras de cultivo no custo operacional de pulverizadores hidráulicos para os tratos culturais de cana-de-açúcar. Pela dificuldade que existe em realizar o trabalho e atender o objetivo nas condições de campo, optou-se em desenvolver um modelo computacional denominado TratoCana, em planilha eletrônica e em linguagem de programação. O modelo foi verificado quanto a possíveis erros de rotina, validado, utilizado na análise dos fatores e na geração de cenários. Os resultados evidenciaram que o comprimento das fileiras de cultivo, impacta positivamente no desempenho operacional e econômico dos equipamentos.

Brazil is the world's largest producer of sugarcane destined for mills and has average productivity, higher than the other countries producing this raw material. The application of pesticides in sugar cane fields in agribusinesses is carried out in extensive cultivation areas, with self-propelled, sprayed and aerial hydraulic sprayers. Therefore, it is necessary to systematize the cultivation areas, making the plots with a long length of cultivation rows, in order to reduce the machines' headboard maneuvers. The objective of the work is to evaluate the impact caused by the length of the cultivation rows on the operational cost of hydraulic sprayers for the sugarcane crop treatments. Due to the difficulty in carrying out the work and meeting the objective in the field conditions, it was decided to develop a computational model called TratoCana, using an electronic spreadsheet and programming language. The model was checked for possible routine errors, validated, used in the analysis of factors and in the generation of scenarios. The results showed that the length of the cultivation rows has a positive impact on the operational and economic performance of the equipment. is Veja também be

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Dengue infection is a public health problem with a complex distribution. The physical means of propagation and the dynamics of diffusion of the disease between municipalities need to be analysed to direct efficient public policies to prevent dengue infection. The present study presents correlations of occurrences of reported cases of dengue infection among municipalities, self-organized criticality (SOC), and transportation between areas, identifying the municipalities that play an important role in the diffusion of dengue across the state of Bahia, Brazil. The significant correlation found between the correlation network and the SOC demonstrates that the pattern of intramunicipal diffusion of dengue is coupled to the pattern of synchronisation between the municipalities. Transportation emerges as influential in the dynamics of diffusion of epidemics by acting on the aforementioned variables.

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ABSTRACT We proposed a 3D model to evaluate the role of platybasia and clivus length in the development of Chiari I (CI). Using a computer aided design software, two DICOM files of a normal CT scan and MR were used to simulate different clivus lengths (CL) and also different basal angles (BA). The final posterior fossa volume (PFV) was obtained for each variation and the percentage of the volumetric change was acquired with the same method. The initial normal values of CL and BA were 35.65 mm and 112.66º respectively, with a total PFV of 209 ml. Ranging the CL from 34.65 to 29.65 – 24.65 – 19.65, there was a PFV decrease of 0.47% – 1.12% – 1.69%, respectively. Ranging the BA from 122.66º to 127.66º – 142.66º, the PFV decreased 0.69% – 3.23%, respectively. Our model highlights the importance of the basal angle and clivus length to the development of CI.

RESUMO No presente estudo, propusemos a criação de um modelo computacional em 3D com elaboração de software onde dois arquivos em formato DICOM com uma TC e RNM de crânio foram usados para simular diferentes mensurações na extensão do clivus (EC) e no ângulo basal (AB). O volume final da fossa posterior (VFP) foi obtido em cada variação, bem como a percentagem de volume alterada. O tamanho inicial da EC era de 35,65 mm e o do AB era de 112.66º, com um VFP de 209 ml. Variando a EC de 34,65 para 29,65 – 24.65 e 19.65, houve uma diminuição do VFP de 0.47%, 1.12% e 1.69%, respectivamente. Variando o AB de 122,66º para 127,66º e 142,66º, o VFP diminui para 0.69% e 3.23%, respectivamente. Nosso modelo enfatiza a importância da patogênese do aumento do AB e do encurtamento do clivus no desenvolvimento do Chiari I.

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Biomechanical models are important tools in the study of human motion. This work proposes a computational model to analyse the dynamics of lower limb motion using a kinematic chain to represent the body segments and rotational joints linked by viscoelastic elements. The model uses anthropometric parameters, ground reaction forces and joint Cardan angles from subjects to analyse lower limb motion during the gait. The model allows evaluating these data in each body plane. Six healthy subjects walked on a treadmill to record the kinematic and kinetic data. In addition, anthropometric parameters were recorded to construct the model. The viscoelastic parameter values were fitted for the model joints (hip, knee and ankle). The proposed model demonstrated that manipulating the viscoelastic parameters between the body segments could fit the amplitudes and frequencies of motion. The data collected in this work have viscoelastic parameter values that follow a normal distribution, indicating that these values are directly related to the gait pattern. To validate the model, we used the values of the joint angles to perform a comparison between the model results and previously published data. The model results show a same pattern and range of values found in the literature for the human gait motion.

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Convection-enhanced delivery as a means to deliver therapeutic drugs directly to the brain has shown limited clinical efficacy, primarily attributed to the phenomena of backflow, in which the infused fluid flows preferentially along the shaft catheter rather than forward into the tissue. We have previously developed a finite element model of backflow that includes both material and geometric nonlinearities and the free boundary conditions associated with the displacement of the tissue away from the external surface of the catheter. However, that study was limited to predictions of the tissue deformation and resulting convective fluid velocity in the interstitial space. In this study, we use results from that model to solve for the distribution of the infused therapeutic agent. We demonstrate that a significant percentage of the infused drug is not transported into the region of tissue located forward from the catheter tip, but instead is transported into the region along the lateral sides of the catheter. For lower flow rates, this study suggests that the use of a catheter with a larger radius may be preferable since it will provide the higher amount of drug to be transported to the tissue in front of the catheter. In contrast, for higher flow rates consistent with clinical infusions, the radius of the infusion catheter had minimal effect on the distribution of the infused drug, with most being transported into the tissue around the shaft of the catheter.

Convection-enhanced delivery es una técnica que permite transportar drogas directamente en el cerebro para el tratamiento de enfermedades del sistema nervioso central. Este método ha mostrado una eficacia limitada debido principalmente al fenómeno de reflujo (backflow), según el cual, el fluido inyectado fluye preferiblemente a lo largo del catéter y no hacia el tejido delante de la punta. Previamente desarrollamos un modelo de elementos finitos para representar el reflujo, el cual incluye las no linealidades geométricas y del material y las condiciones de borde libre asociadas con el desplazamiento del tejido en la superficie externa del catéter. Sin embargo, ese modelo solo predice la deformación del tejido y el campo de velocidades en el espacio intersticial. En este estudio, hemos utilizado los resultados provenientes del mencionado modelo bifásico para resolver la ecuación de transporte de masa y predecir la distribución de droga suministrada. Se pudo demostrar que un porcentaje significativo de droga no penetra en el tejido ubicado delante de la punta del catéter, sino que es transportado hacia el tejido ubicado alrededor del catéter. Para bajo caudales, este estudio sugiere que el uso de un catéter con un radio mayor permitiría transportar una mayor cantidad de droga hacia el tejido al frente de la punta. Por otro lado, para los mayores caudales usados en la práctica clínica, el radio del catéter tiene un efecto marginal en la distribución del fármaco, y la mayor cantidad de droga se transporta hacia el tejido ubicado alrededor del catéter.

Convection-enhanced delivery é uma técnica para o transporte de drogas directamente no cérebro para tratar doenças do sistema nervoso central. Este método tem demonstrado eficácia limitada devido, principalmente, ao fenómeno de refluxo (refluxo), através do qual, de preferência, o fluido injectado flui através do cateter para o tecido e não à frente da ponta. Anteriormente desenvolvido um modelo de elementos finitos para representar a refluxo, que inclui geométricas e não-linearidades do material e as condições associadas com a extremidade livre de deslocamento da trama na superfície exterior do cateter. No entanto, este modelo apenas prevê deformação do tecido e campo de velocidades no espaço intersticial. Neste estudo, foram utilizados os resultados do modelo de duas fases acima referidas, para resolver a equação de transporte e prever a distribuição de massa de medicamentos fornecidos. Demonstrou-se que uma percentagem significativa da droga não penetra no tecido localizado em frente da ponta do cateter, que é transportado para o tecido que rodeia o cateter. Para as taxas de fluxo baixas, este estudo sugere que o uso de um cateter com um raio maior do que transportar uma maior quantidade de droga para o tecido em frente da ponta. Além disso, para taxas de fluxo mais elevadas utilizadas na prática clínica, o raio do cateter tem um efeito marginal sobre a distribuição da droga, e tanto fármaco é transportado para o tecido que rodeia o cateter.

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Motion detection is one of the most important and primitive computations performed by our visual system. Specifically in the retina, ganglion cells producing motion direction-selective responses have been addressed by different disciplines, such as mathematics, neurophysiology and computational modeling, since the beginnings of vision science. Although a number of studies have analyzed theoretical and mathematical considerations for such responses, a clear picture of the underlying cellular mechanisms is only recently emerging. In general, motion direction selectivity is based on a non-linear asymmetric computation inside a receptive field differentiating cell responses between preferred and null direction stimuli. To what extent can biological findings match these considerations? In this review, we outline theoretical and mathematical studies of motion direction selectivity, aiming to map the properties of the models onto the neural circuitry and synaptic connectivity found in the retina. Additionally, we review several compartmental models that have tried to fill this gap. Finally, we discuss the remaining challenges that computational models will have to tackle in order to fully understand the retinal motion direction-selective circuitry.

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