Approaches to embryonic neurodevelopment: from neural cell to neural tube formation through mathematical models.

The development of the human central nervous system initiates in the early embryonic period until long after delivery. It has been shown that several neurological and neuropsychiatric diseases originate from prenatal incidents. Mathematical models offer a direct way to understand neurodevelopmental processes better. Mathematical modelling of neurodevelopment during the embryonic period is challenging in terms of how to 'Approach', how to initiate modelling and how to propose the appropriate equations that fit the underlying dynamics of neurodevelopment during the embryonic period while including the variety of elements that are built-in naturally during the process of neurodevelopment. It is imperative to answer where and how to start modelling; in other words, what is the appropriate 'Approach'? Therefore, one objective of this study was to tackle the mathematical issue broadly from different aspects and approaches. The approaches were divided into three embryonic categories: cell division, neural tube growth and neural plate growth. We concluded that the neural plate growth approach provides a suitable platform for simulation of brain formation/neurodevelopment compared to cell division and neural tube growth. We devised a novel equation and designed algorithms that include geometrical and topological algorithms that could fit most of the necessary elements of the neurodevelopmental process during the embryonic period. Hence, the proposed equations and defined mathematical structure would be a platform to generate an artificial neural network that autonomously grows and develops.

Geometrical modelling of neuronal clustering and development.

The dynamic geometry of neuronal development is an essential concept in theoretical neuroscience. We aimed to design a mathematical model which outlines stepwise in an innovative form and designed to model neuronal development geometrically and modelling spatially the neuronal-electrical field interaction. We demonstrated flexibility in forming the cell and its nucleus to show neuronal growth from inside to outside that uses a fractal cylinder to generate neurons (pyramidal/sphere) in form of mathematically called 'surface of revolution'. Furthermore, we verified the effect of the adjacent neurons on a free branch from one-side, by modelling a 'normal vector surface' that represented a group of neurons. Our model also indicated how the geometrical shapes and clustering of the neurons can be transformed mathematically in the form of vector field that is equivalent to the neuronal electromagnetic activity/electric flux. We further simulated neuronal-electrical field interaction that was implemented spatially using Van der Pol oscillator and taking Laplacian vector field as it reflects biophysical mechanism of neuronal activity and geometrical change. In brief, our study would be considered a proper platform and inspiring modelling for next more complicated geometrical and electrical constructions.

Rapid effects of S-ketamine on the morphology of hippocampal astrocytes and BDNF serum levels in a sex-dependent manner.

The prevalence of major depressive disorder (MDD) is higher in women than men. Importantly, a differential behavioral response by sex to the antidepressant response to ketamine in rodents has been reported. Mechanistically, male depressed-like animals showed an increased spine density after ketamine treatment via restoration of synaptic protein levels while those proteins were not altered in female rats. In addition, preclinical studies indicate that the impairment of astrocytic plasticity is one of the contributing mechanisms in the pathophysiology of MDD. Accordingly, in this study, we determined the effect of sex on the rapid morphological alteration of hippocampal astrocytes and the serum level of BDNF one hour after S-ketamine injection. A single intraperitoneal dose of S-ketamine (15 mg/kg) or saline was injected to the male and female Flinders Sensitive Line (FSL) rats, a genetic animal model of depression and their brains were perfused one hour after treatment. The size of the GFAP positive astrocytes in the hippocampal subregions was measured. The volume of different hippocampal subregions was assessed using the Cavalieri estimator. Moreover, serum levels of BDNF were measured with enzyme-linked immunosorbent assay (ELISA) kits. The volume of hippocampal subregions significantly increased one hour after S-ketamine in both male and female FSL animals. However, a substantial alteration in the morphology of the hippocampal astrocytes was observed only in the female rats. Additionally, significantly increased serum BDNF levels in the female depressed rats were observed one hour after S-ketamine treatment. Our results indicate that the rapid effects of S-ketamine on the morphology of the hippocampal astrocytes and the serum level of BDNF are sex-dependent.

Hippocampal Atrophy Following Subarachnoid Hemorrhage Correlates with Disruption of Astrocyte Morphology and Capillary Coverage by AQP4.

Despite successful management of ruptured intracranial aneurysm following subarachnoid hemorrhage (SAH), delayed cerebral ischemia (DCI) remains the main cause of high mortality and morbidity in patients who survive the initial bleeding. Astrocytes play a key role in neurovascular coupling. Therefore, changes in the neurovascular unit including astrocytes following SAH may contribute to the development of DCI and long-term complications. In this study, we characterized morphological changes in hippocampal astrocytes following experimental SAH, with special emphasis on glia-vascular cross-talk and hippocampal volume changes. Four days after induction of SAH or sham-operation in mice, their hippocampal volumes were determined by magnetic resonance imaging (MRI) and histological/stereological methods. Glial fibrillary acid protein (GFAP) immunostained hippocampal sections were examined by stereological techniques to detect differences in astrocyte morphology, and global spatial sampling method was used to quantify the length density of Aquaporin-4 (AQP4) positive capillaries. Our results indicated that hippocampal volume, as measured both by MRI and by histological approaches, was significantly lower in SAH animals than in the sham-operated group. Accordingly, in this animal model of SAH, hippocampal atrophy existed already at the time of DCI onset in humans. SAH induced retraction of GFAP positive astrocyte processes, accompanied by a significant reduction in the length density of AQP4 positive capillaries as well as narrowing of hippocampal capillaries. Meanwhile, astrocyte volume was higher in SAH mice compared with the sham-operated group. Morphological changes in hippocampal astrocytes seemingly disrupt glia-vascular interactions early after SAH and may contribute to hippocampal atrophy. We speculate that astrocytes and astrocyte-capillary interactions may provide targets for the development of therapies to improve the prognosis of SAH.

Rapid antidepressant effect of ketamine correlates with astroglial plasticity in the hippocampus.

BACKGROUND AND PURPOSE: Astroglia contribute to the pathophysiology of major depression and antidepressant drugs act by modulating synaptic plasticity; therefore, the present study investigated whether the fast antidepressant action of ketamine is reflected in a rapid alteration of the astrocytes' morphology in a genetic animal model of depression. EXPERIMENTAL APPROACH: S-Ketamine (15 mg·kg-1 ) or saline was administered as a single injection to Flinders Line (FSL/ FRL) rats. Twenty-four hours after the treatment, perfusion fixation was carried out and the morphology of glial fibrillary acid protein (GFAP)-positive astrocytes in the CA1 stratum radiatum (CA1.SR) and the molecular layer of the dentate gyrus (GCL) of the hippocampus was investigated by applying stereological techniques and analysis with Imaris software. The depressive-like behaviour of animals was also evaluated using forced swim test. KEY RESULTS: FSL rats treated with ketamine exhibited a significant reduction in immobility time in comparison with the FSL-vehicle group. The volumes of the hippocampal CA1.SR and GCL regions were significantly increased 1 day after ketamine treatment in the FSL rats. The size of astrocytes in the ketamine-treated FSL rats was larger than those in the FSL-vehicle group. Additionally, the number and length of the astrocytic processes in the CA1.SR region were significantly increased 1 day following ketamine treatment. CONCLUSIONS AND IMPLICATIONS: Our results support the hypothesis that astroglial atrophy contributes to the pathophysiology of depression and a morphological modification of astrocytes could be one mechanism by which ketamine rapidly improves depressive behaviour.

S-Ketamine Rapidly Reverses Synaptic and Vascular Deficits of Hippocampus in Genetic Animal Model of Depression.

Background: The neurovascular plasticity of hippocampus is an important theory underlying major depression. Ketamine as a novel glutamatergic antidepressant drug can induce a rapid antidepressant effect within hours. In a mechanistic proof of this concept, we examined whether ketamine leads to an increase in synaptogenesis and vascularization within 24 hours after a single injection in a genetic rat model of depression. Methods: Flinders Sensitive Line and Flinders Resistant Line rats were given a single intraperitoneal injection of ketamine (15 mg/kg) or saline. One day later, their behavior was evaluated by a modified forced swim test. Microvessel length was evaluated with global spatial sampling and optical microscopy, whereas the number of asymmetric synapses was quantified through serial section electron microscopy by using physical disector method in the CA1.stratum radiatum area of hippocampus. Results: The immobility time in the forced swim test among Flinders Sensitive Line rats with ketamine treatment was significantly lower compared with Flinders Sensitive Line rats without treatment. The number of nonperforated and perforated synapses was significantly higher in the Flinders Sensitive Line-ketamine vs the Flinders Sensitive Line-vehicle group; however, ketamine did not induce a significant increase in the number of shaft synapses. Additionally, total length of microvessels was significantly increased 1 day after ketamine treatment in Flinders Sensitive Line rats in the hippocampal subregions, including the CA1.stratum radiatum. Conclusion: Our findings indicate that hippocampal vascularization and synaptogenesis is co-regulated rapidly after ketamine, and microvascular elongation may be a supportive factor for synaptic plasticity and neuronal activity. These findings go hand-in-hand with the behavioral observations, where ketamine acts as a potent antidepressant.

Tissue necrosis after chemotherapy in osteosarcoma as the important prognostic factor.

OBJECTIVE: To determine the histological response to preoperative chemotherapy of the percentage of tumor necrosis, and to assess the relationship between the histological response and the oncological result. METHODS: Eighty patients with osteosarcoma were managed with preoperative and postoperative chemotherapy and operative resection at Shafa Yahyaeeyan Hospital, Tehran, Iran between 2003-2005. Sections of each operative specimen were examined, and the histological response to chemotherapy was graded. Grade 1 indicated necrosis of 50% of the tumor or less; grade 2, necrosis of more than 50% yet less than 90 percent; grade 3, necrosis of more than 90 percent. RESULTS: The mean duration of the follow-up of the surviving patients, who were continuously free from disease was 1044 days. The histological response to preoperative chemotherapy (p=0.016) was the most important predictor of event-free survival. The rate of event-free short-term survival for the 80 patients entering this study was 86 percent (69 patients) at 12 months, 50% 24 patients at 24 months, and 21% (5 patients) at 40 months, with 5 patients surviving for a median of 1096 days. CONCLUSION: The histological response to preoperative chemotherapy is an important clinical predictor of the result of operative treatment of osteosarcoma. This indicator should be used to identify patients who are at high risk for metastasis, as such patients may be candidates for more intensive or novel therapy.