Fractal Resonance: Can Fractal Geometry Be Used to Optimize the Connectivity of Neurons to Artificial Implants?

In parallel to medical applications, exploring how neurons interact with the artificial interface of implants in the human body can be used to learn about their fundamental behavior. For both fundamental and applied research, it is important to determine the conditions that encourage neurons to maintain their natural behavior during these interactions. Whereas previous biocompatibility studies have focused on the material properties of the neuron-implant interface, here we discuss the concept of fractal resonance - the possibility that favorable connectivity properties might emerge by matching the fractal geometry of the implant surface to that of the neurons.To investigate fractal resonance, we first determine the degree to which neurons are fractal and the impact of this fractality on their functionality. By analyzing three-dimensional images of rat hippocampal neurons, we find that the way their dendrites fork and weave through space is important for generating their fractal-like behavior. By modeling variations in neuron connectivity along with the associated energetic and material costs, we highlight how the neurons' fractal dimension optimizes these constraints. To simulate neuron interactions with implant interfaces, we distort the neuron models away from their natural form by modifying the dendrites' fork and weaving patterns. We find that small deviations can induce large changes in fractal dimension, causing the balance between connectivity and cost to deteriorate rapidly. We propose that implant surfaces should be patterned to match the fractal dimension of the neurons, allowing them to maintain their natural functionality as they interact with the implant.

How neurons exploit fractal geometry to optimize their network connectivity.

We investigate the degree to which neurons are fractal, the origin of this fractality, and its impact on functionality. By analyzing three-dimensional images of rat neurons, we show the way their dendrites fork and weave through space is unexpectedly important for generating fractal-like behavior well-described by an 'effective' fractal dimension D. This discovery motivated us to create distorted neuron models by modifying the dendritic patterns, so generating neurons across wide ranges of D extending beyond their natural values. By charting the D-dependent variations in inter-neuron connectivity along with the associated costs, we propose that their D values reflect a network cooperation that optimizes these constraints. We discuss the implications for healthy and pathological neurons, and for connecting neurons to medical implants. Our automated approach also facilitates insights relating form and function, applicable to individual neurons and their networks, providing a crucial tool for addressing massive data collection projects (e.g. connectomes).

Pathway specific activation of ventral hippocampal cells projecting to the prelimbic cortex diminishes fear renewal.

The ability to learn that a stimulus no longer signals danger is known as extinction. A major characteristic of extinction is that it is context-dependent, which means that fear reduction only occurs in the same context as extinction training. In other contexts, there is re-emergence of fear, known as contextual renewal. The ability to properly extinguish fear memories and generalize safety associations to multiple contexts provides therapeutic potential, but little is known about the specific neural pathways that mediate fear renewal and extinction generalization. The ventral hippocampus (VH) is thought to provide a contextual gating mechanism that determines whether fear or safety is expressed in particular contexts through its projections to areas of the fear circuit, including the infralimbic (IL) and prelimbic (PL) cortices. Moreover, VH principal cells fire in large, overlapping regions of the environment, a characteristic that is ideal to support generalization; yet it is unclear how different projection cells mediate this process. Using a pathway-specific (intersectional) chemogenetic approach, we demonstrate that selective activation of VH cells projecting to PL attenuates fear renewal without affecting fear expression. These results have implications for anxiety disorders since they uncover a neural pathway associated with extinction generalization.

The distribution of mercury and other trace metals in the sediments of the Mersey Estuary over 25 years 1974-1998.

Mercury and other heavy metals have been monitored in the surface sediments of the Mersey Estuary in NW England for a period of 25 years, using a consistent methodology and sampling grid. This has produced one of the most comprehensive data sets available in the literature and demonstrated some of the difficulties associated with undertaking long-term environmental monitoring. The data indicate that the concentration of mercury and other metals in the sediments of this estuary are strongly correlated to the organic matter and particle size content. This has resulted in the metal distribution patterns reflecting the sediment characteristics and dynamics, irrespective of the position of the input sources. The trend data has indicated a continual, although somewhat uneven, decline in the concentration of most of the metals studied. Remobilisation of previously consolidated saltmarsh sediments can cause significant perturbations in contaminant reduction trends, and needs to be considered in the design of long term monitoring programmes.

The effect of caffeine on pregnancy outcome variables.

The American public consumes a wide array of caffeinated products as coffee, tea, chocolate, cola beverages, and caffeine-containing medication. Therefore, it seems of value to inform both the scientific community and the consumer about the potential effects of excessive caffeine consumption, particularly by pregnant women. The results of this literature review suggest that heavy caffeine use (> or = 300 mg per day) during pregnancy is associated with small reductions in infant birth weight that may be especially detrimental to premature or low-birth-weight infants. Some researchers also document an increased risk of spontaneous abortion associated with caffeine consumption prior to and during pregnancy. However, overwhelming evidence indicates that caffeine is not a human teratogen, and that caffeine appears to have no effect on preterm labor and delivery. More research is needed before unambiguous statements about the effects of caffeine on pregnancy outcome variables can be made.

Field test of volatilization models.

Four volatilization models were tested against field data from the Manchester Ship Canal and the River Main. The equations byMACKAY andYEUN, using Schmidt number and wind speed for the calculation of volatilization rate, were found to give the best results for the slowly flowing Ship Canal. Models using flow velocity grossly underestimated the real values for this waterway but were found to be superior for the faster flowing River Main. The results of this work indicate that volatilization models should be carefully chosen for a particular environmental situation. Additionally, the importance of the validation of such models against field data is emphasised.

Is vanadium of human nutritional importance yet?

The trace element vanadium has been studied by the nutrition community for four decades, yet has not achieved essential status for human beings. It is found in compounds at valences of 2, 3, 4, or 5, with the tetravalent and pentavalent forms being the most common. In human beings, pharmacologic amounts of vanadium (ie, 10 to 100 times normal intake) affect cholesterol and triglyceride metabolism, influence the shape of erythrocytes, and stimulate glucose oxidation and glycogen synthesis in the liver. Vanadium's primary mode of action is as a cofactor that enhances or inhibits enzymes. Recent evidence suggests that vanadium may be essential for higher animals. After their mothers had been fed carefully formulated vanadium-deficient diets, second-generation goat kids suffered skeletal damage and died within 3 days of parturition. Although ubiquitous in air, soil, water, and the food supply, vanadium is generally found in nanogram or microgram quantities, which makes it difficult to measure. Estimates for the American intake of vanadium (based on a food intake of 500 g dry weight) are 10 to 60 micrograms/day. Vanadium levels in diets from five regions of the United States range from 30.9 +/- 1.5 in the Southeast to 50.5 +/- 1.5 micrograms/kg dry weight in the West. Although vanadium is thought to be essential for goats, new data may soon support its essentiality in human beings.

Effects of dietary aluminum and niacin on chick tibiae.

Effects of dietary aluminum chloride and niacin on bone mineral content and bone structural measurements were studied using young male Leghorn chicks. Standard chick rations containing .8% Ca and .4 or .5% available P were fed as control diets in three experiments. Experimental diets contained .05, .1, or .3% Al, or 1.0 or 1.5% niacin, or both and were fed for 2 wk. Tibia weights were decreased by 1.5% niacin, .3% Al, and by .1% Al plus 1.5% niacin (P less than .05). Breaking strength of tibiae was decreased (P less than .05) by 1.5% niacin, .1% Al, and .1% Al plus 1.5% niacin. Ultimate stress, which is force per unit area, was decreased by .3% Al and .05% Al plus 1.5% niacin (P less than .05). Niacin had no significant effect on bone mineral content. In Experiment 3, .3% Al decreased P, Ca, Mg, and Zn content of the tibiae (P less than .05). These findings indicate that feeding high levels of supplemental niacin results in decreased bone strength in chicks with no change in mineral content of the tibiae. Aluminum fed at levels of .3% of the diet causes a decrease in bone strength with concomitant changes in bone mineral content.

Nutritional status and phytate:zinc and phytate x calcium:zinc dietary molar ratios of lacto-ovo vegetarian Trappist monks: 10 years later.

A nutrition assessment of 16 members of a community of lacto-ovo vegetarian Trappist monks was conducted in 1977. Plasma zinc was found to be low-normal, which was attributed primarily to high intakes of phytate-containing foods. Individual and group counseling were instituted over a 10-year period in an attempt to emphasize the importance of wise food selection within the constraints of lacto-ovo vegetarianism. In 1987, a more comprehensive nutrition assessment of 21 members of the same community was performed. Food composites were analyzed, and 3-day instead of 24-hour dietary records were kept. Intakes of phytate-containing foods had decreased from 4,569 to 972 mg/day; intake of dietary zinc had increased from 7.4 to 9.7 mg/day; and the phytate:zinc molar ratio had decreased from 67 to 14 for the years 1977 and 1987, respectively. An analyzed phytate:zinc molar ratio of 9.8 and an analyzed phytate x calcium:zinc molar ratio of 0.3 were representative of the 1987 community. Both were within normal ranges. Plasma zinc had risen to upper-normal levels. The 1987 nutrition assessment showed that it is possible to be adequately nourished with a lacto-ovo vegetarian diet provided one has proper knowledge of the phytate-containing foods and the methods for compensating with foods of greater mineral density (primarily zinc).

Dietary model for production of experimental zinc deficiency in man.

A semipurified diet based on soy protein was developed to induce mild zinc deficiency in five male volunteers. Each of seven daily menus provided (mean +/- SD) 2248 +/- 128 kcal, 56.6 +/- 5.7 protein, 261 +/- 30 g carbohydrate, 110 +/- 21 g fat, 8.5 +/- 1.4 g fiber, and 4.8 +/- 1.3 mg zinc. The analytical value for phytate:zinc molar ratio was 21 +/- 9. One subject, who received five of the menus for 28 wk, lost approximately 200 mg body zinc and 7% weight; zinc concentration declined 25% in plasma, 30% in lymphocytes, and 55% in neutrophils. This dietary model allowed simple formulation of new menus for subjects in diverse states of health. It caused no ill effects after prolonged consumption, and all deficiency symptoms were reversed by zinc supplementation of 30 mg/d for 20 wk. With simple manipulation, this dietary model may be used safely for gradual induction of zinc and/or other micronutrient deficiencies in humans.

Anion-exchange method for determination of phytate in foods: collaborative study.

Phytate, a naturally occurring organic compound found in plant seeds, roots, and tubers, was determined in a collaborative study using a modified anion-exchange method. Seven samples (peanut flour, oats, rice, isolated soybean protein, a vegetarian diet composite, wheat bran, and whole wheat bread), supplied as blind duplicate samples, were analyzed in triplicate by 7 collaborators. Phytate concentrations in the samples ranged from 2.38 to 46.70 mg/g. Relative standard deviations (RSD = CV) for repeatability ranged from 2.5 to 10.1%, and for reproducibility, from 4.5 to 11.0%. The method has been adopted official first action.

Dietary fluoride intake of 15-19-year-old male adults residing in the United States.

The average daily dietary fluoride intakes of 15-to-19-year-old males were estimated from the analysis of 24 FDA "market basket" food collections made from 1975 to 1982. The data indicate that 15-to-19-year-old males residing in fluoridated (greater than 0.7 ppm) cities had an average daily dietary fluoride intake of 1.85 mg/day when the diet provided an estimated caloric intake of 11.72 megajoules (2800 calories). In non-fluoridated cities, with less than 0.3 ppm in the drinking water, the average dietary fluoride intake was 0.86 mg/day. The beverages and drinking water contributed an average of 75 +/- 2% of the daily dietary fluoride intake.

Dietary fluoride intake of 6-month and 2-year-old children in four dietary regions of the United States.

Based upon the analysis of 44 market basket food collections, the average daily dietary fluoride intakes of 6-mo-old and 2-yr-old children residing in cities with water fluoride levels of 0.05 to 1.04 ppm were determined. In cities with greater than 0.7 ppm fluoride in the drinking water, a 6-mo-old child (infant) and a 2-yr-old child (toddler) had mean dietary fluoride intakes of 0.418 mg/day (0.052 mg/kg body weight) and 0.621 mg/day (0.050 mg/kg body weight) respectively. The data indicate that the average dietary fluoride intake of infants and toddlers did not exceed 0.08 mg/kg, and in all but three cases was within or below the optimum range of 0.05-0.07 mg/kg. The ingestion of fluoride-containing dentifrice or milk formula diluted with fluoridated water may result in intake levels exceeding that associated with the development of dental fluorosis (0.1 mg F/kg body wt).

Determination of total dietary fiber in foods and food products: collaborative study.

A collaborative study was conducted to determine the total dietary fiber (TDF) content of food and food products, using a combination of enzymatic and gravimetric procedures. The method was basically the same as published earlier (J. Assoc. Off. Anal. Chem. (1984) 67, 1044-1052), with changes in the concentration of alcohol and buffers, time of incubation, sample preparation, and some explanatory notes, all with the intent of decreasing the coefficient of variation (CV) of the method. Duplicate blind samples of soy isolate, white wheat flour, rye bread, potatoes, rice, wheat bran, oats, corn bran, and whole wheat flour were analyzed by 9 collaborators. TDF was calculated as the weight of the residue minus the weight of protein and ash. CV values of the data from all laboratories for 7 of the samples ranged from 1.56 to 9.80%. The rice and soy isolate samples had CV values of 53.71% and 66.25%, respectively; however, each sample contained only about 1% TDF. The enzymatic-gravimetric method for determining TDF has been adopted official first action.

Selected minerals in foods surveys, 1974 to 1981/82.

The levels of 11 essential minerals in food commodity groups and total diets of adult males, infants, and toddlers were summarized from the Selected Minerals in Foods Survey, Fiscal Years (FY) 1974 through mid-1982, of the Food and Drug Administration (FDA) to evaluate the sources and adequacy of those minerals in the diets. The three diets were adequate in calcium, phosphorus, magnesium, potassium, manganese, and selenium; low in copper; and elevated in sodium and iodine. Iron was adequate in adult male but not in infant or toddler diets, and zinc was adequate in infant but somewhat low in adult male and toddler diets. Dairy products; meat, fish, and poultry; grain and cereal products; and fruits and vegetables were the major sources of the 11 minerals. Some statistically significant differences in mineral levels were found among years for total diets and food commodity groups. Regression analysis indicated several linear trends in the mineral content of food commodity groups but no linear trends in the mineral levels of total diets. FDA continues to monitor the levels of minerals in food and diets through the revised Total Diet Study program, which began in mid-FY82.