Phycomyces blakesleeanus have been used as a model system to study sensory transduction, helical growth, and to establish global biophysical equations for expansive growth of walled cells. More recently, local statistical biophysical models of the cell wall are being constructed to better understand the molecular underpinnings of helical growth and its behavior during the many growth responses of the sporangiophores to sensory stimuli. Previous experimental and theoretical findings guide the development of these local models. Future development requires an investigation of explicit and implicit assumptions made in the prior research. Here, experiments are conducted to test three assumptions made in prior research, that (a) elongation rate, (b) rotation rate, and (c) helical growth steepness, R, of the sporangiophore remain constant during the phototropic response  and the avoidance response (bending away from solid barriers). The experimental results reveal that all three assumptions are incorrect for the phototropic response and probably incorrect for the avoidance response but the results are less conclusive. Generally, the experimental results indicate that the elongation and rotation rates increase during these responses, as does R, indicating that the helical growth steepness become flatter. The implications of these findings on prior research, the “fibril reorientation and slippage” hypothesis, global biophysical equations, and local statistical biophysical models are discussed.The sporangiophores of  Phycomyces blakesleeanus are large cylindrical single-celled hyphae that grow vertically from a mycelium. They undergo five stages of development , and stage IV is further divided into three sub-stages 3, see Fig. Wild type sporangiophores of 4 (~ 35 μm min−1) and rotation growth rates (~ 12 degrees min−1) for many hours. A ratio R (R = rotation rate ÷ elongation rate) can be used to measure of the steepness of the helix traced out in time and space by a particle on the surface of the growth zone or on the sporangium. When R is large the helix is relatively flat and when R is small the helix is steeper. It was implicitly presumed that R is approximately constant for stage IVb sporangiophores.Stage IVb sporangiophores are often used for experiments because they exhibit nearly constant growth zone lengths (~ 2.5 mm), elongation growth ratesP. blakesleeanus have been used as a model system for studies in sensory transduction because of their growth responses to many sensory stimuli7. The sporangiophore can detect gravitational acceleration, ethylene, mechanical stretch, gases, temperature, wind, light intensity, spatially asymmetric distribution of light, the presence of solid objects and changes in turgor pressure. Stage IVb sporangiophores respond to these stimuli with symmetric and asymmetric changes in elongation growth rate, and are termed “growth responses” and “tropic responses”, respectively. For example, the light growth response is an increase in elongation rate that begins approximately four minutes after an increase in light intensity8. Experimental evidence demonstrates that the increase in elongation rate is transient, i.e. it returns to its original elongation rate within ten to fifteen minutes. It is shown that this occurs because the cell’s photoreceptors “adapt” to the higher light intensity9. Another growth response is the pressure response10, a transient decrease in elongation rate that occurs immediately after an increase in turgor pressure exceeding 0.02 MPa. This response appears to be related to the “stretch” response reported by Dennison and Roth11.The large single-celled sporangiophores of 13. It was postulated that the cross-section of the transparent cylindrical stalk of the sporangiophore acts like a lens, focusing the light on the distal side of the stalk and increasing the light intensity on the distal side. Interestingly, the phototropic response is not transient, i.e. it will continue indefinitely providing the unilateral light stimulus remains. In other words, the cell does not adapt to the unilateral light stimulus. The bending that occurs during the phototropic response was quantitatively explained by differential growth that occurs on the proximal and distal sides of the cylindrical stalk of the sporangiophores. Castle14 calculated the differential growth that is required to bend the sporangiophore stalk during the phototropic response by assuming that the proximal wall decreases in elongation rate and the distal wall increases in elongation rate, so that the cell’s overall elongation rate was constant. That the phototropic response does not adapt, and can continue indefinitely, was explained by the rotation of the cell wall in the growth zone during bending. Dennison and Foster15 postulate that the rotation of the cell wall during helical growth continuously introduces photoreceptors  into the higher intensity of the focused light on the distal side of the stalk. In this way it is postulated that the rotation converts a spatial stimulus into a temporal stimulus that prevents adaptation to the unilateral light stimulus. Experimental results support this hypothesis15. It was implicitly assumed that the rotation rate was constant but different along the length of the growth zone.Stage IVb sporangiophores’ responses to asymmetric distribution of light (phototropic response) and to the presence of a solid barrier (avoidance response) are two examples of tropic responses. The phototropic response can be described as follows. When a stage IVb sporangiophore is subjected to two identical light sources on opposite sides and equal distance away, the sporangiophore will grow vertically between the two. If one of the light sources is turned off, producing a unilateral light stimulus, the sporangiophore will grow (bend) toward the remaining light source after a latency period of approximately four minutes. This is the phototropic response6. Similar to the phototropic response, the avoidance response does not adapt, i.e. the sporangiophore will continue to bend away from the barrier as long as the barrier remains within one millimeter of the growth zone. Gamow and Bottger16 reported experimental evidence demonstrating that rotation of the stalk during helical growth is responsible for the lack of adaptation. It is not known how the sporangiophore detects the presence of the barrier and many studies have been conducted in an attempt to elucidate the intermediate stimulus17. A significant amount of research has been conducted to study the phototropic and avoidance responses3, so it is surprising that the behavior of the elongation rate, rotation rate, and R has not been studied during these two tropic responses. It was generally assumed that elongation rate, rotation rate, and R remain constant during tropic responses15. More recently, two mutants (C149 and C216) have been obtained whose sporangiophores exhibit very diminished phototropic and avoidance responses20. These mutants have been termed “stiff” mutants. A recent study has shown that the elasticity of these mutant sporangiophores is essentially the same as that of wild type sporangiophores21. Thus the term “stiff” is not an accurate characterization of these mutants and should probably be termed “viscous” mutants. However to retain continuity of terminology we will continue to call them stiff mutants.When a stage IVb sporangiophore that is growing between two identical light sources on opposite sides and equal distance away is subjected to a barrier stimulus, the sporangiophore will detect its presence and grow away after a latency period of one to three minutes. This is the avoidance response22 and algae23 exhibit helical growth. Early attempts to describe and explain helical growth have inspired many experimental investigations and hypotheses27. Generally these studies and hypotheses have focused on the relationship between the architecture and anisotropic mechanical properties of the primary wall. It is noteworthy that most of these early experimental studies were conducted with the sporangiophores of P. blakesleeanus27. Subsequent experimental research produced new results concerning the distribution of rotation and elongation rates along the length of the growth zone31. This experimental research inspired the proposal of a “fibril reorientation” hypothesis  sporangiophores  and predicts exactly when the reversal in rotation occurs33. In prior research it was implicitly presumed that R was constant and independent of the magnitude of steady elongation rate31. However, subsequent research conducted to verify this assumption demonstrated that R changes with the magnitude of the steady elongation growth rate34. It was found that R is largest for slow growing sporangiophores and decreases almost exponentially to a smaller value (but not zero) for faster growing sporangiophores. Furthermore, it was found that R increases during the pressure response. These findings were used to modify the fibril reorientation hypothesis to produce the “fibril reorientation-slippage” hypothesis34. The fibril reorientation-slippage hypothesis can explain the decrease in R for stage IVb sporangiophores undergoing faster steady elongation growth rates and the increase in R during the pressure response. Also it can explain older findings that were previously unexplained35. During steady growth it was found that in the lower region of the growth zone (that farthest from the sporangium), rotation rate was measured without measurable elongation rate35. But during the light growth response, it was observed that elongation rate was measured in the same lower region that previously showed no elongation rate and in regions below it, i.e. the growth zone was extended and became longer. Furthermore, there was no measureable rotation rate in the extend growth zone region35. This interesting behavior can be explained by the fibril reorientation-slippage hypothesis.Importantly, the fibril reorientation hypothesis was able to explain the reversal in rotation that occurs during bulging of piloboloid mutant  regulate their volumetric growth, cell shape, and sensory responses by controlling the magnitude and direction of the plastic deformation of their cell walls. Volumetric (expansive) growth rates of these walled cells are mediated by wall stress relaxation rates that couple water uptake rate and wall deformation rate37. Three coupled global biophysical equations for the (i) rate of water uptake, (ii) rate of plastic and elastic wall deformation, and (iii) rate of change of turgor pressure have been derived, validated, and established for algal, fungal, and plant cells40. These global biophysical equations have been extended to plant cells in tissue41. Many experiments conducted with the sporangiophores of P. blakesleeanus have been used to validate these biophysical equations43. Relevant to this study is the finding that the turgor pressure did not increase during the light and avoidance growth responses44. Furthermore, dimensional analysis has been conducted on these established biophysical equations and dimensionless numbers have been identified that reveal the relative magnitudes of the relevant biophysical processes that occur during expansive growth45. These dimensionless numbers can be used to compare the magnitude of biophysical processes in a specific walled cell or compare the magnitude of corresponding processes in different species of walled cells47. An important dimensionless number, Πpe, was identified48 that describes the inverse of the dimensionless time constant for stress relaxation of growing cell walls and establishes a quantitative relationship between the steady relative volumetric growth rate, vs, wall extensibility, ϕ, and volumetric elastic modulus, ε.The sporangiophores of 14. Thus, modeling the tropic responses requires the development of a local biophysical model of the wall that can describe the growth rates in relevant locations of the wall.Even though these global biophysical equations have revealed and continue to reveal new insights into expansive growth, they cannot be used to study tropic (bending) responses because they describe the behavior of the whole cell. Bending in a single cylindrical cell requires differential growth rates at opposite sides of the cylindrical cell wall49. This model takes a mechanistic view of the “slippage” zone (~ 1000–2500 µm below the base of the sporangium), where two sets of long microfibrils are oriented longitudinally and slip past one another during wall extension. The model describes the elastic and plastic relative displacements between fibrils during elongation growth, stress relaxation, and steps-up in turgor pressure. As the cell wall is viewed as a network of fibrils connected by polymeric tethers, the shearing motions of the fibrils induce tensile stress in the tethers. However, this stress varies among the population of tethers as they are subject to stochastic attachment and detachment events due to biochemical and thermodynamic forces. The molecular mechanisms behind the plastic extension of the wall under stress can be understood as follows. The connecting tethers (a) initially undergo an elastic stretch , (b) dissociate from a connecting fibril (resulting in sporadic events of stress relaxation), and (c) re-associate to a different location of the microfibril in a minimum energy configuration. This endows the wall with viscoelastic properties, where viscous flow and elastic deformation are dictated by deformation rate50. The model uses a statistical framework to mathematically extrapolate these individual events to a large population of tethers53. After statistical averaging operations, the model recovers the global biophysical equations for (i) rate of plastic and elastic wall deformation and (ii) rate of change of turgor pressure. The key finding of the statistical model is that global biophysical variables like wall extensibility, ϕ, and volumetric elastic modulus, ε, could be expressed in terms of molecular properties like tether stiffness K, tethers dissociation rate kd and re-association rate ka. Consequently, the stress relaxation rate of the wall is found to be kd, and the dimensionless number, Πpe, can be re-interpreted asThe fibril reorientation-slippage hypothesis was used as a conceptual guide for the development of a local statistical mathematical model of the cell wall extension during expansive growth54. Continued development of this local statistical mathematical model requires knowledge of helical growth behavior during bending, i.e. during the phototropic and avoidance responses. Knowledge of how helical growth behaves during these tropic responses will allow a determination of whether the fibril reorientation-slippage hypothesis can explain the helical growth behavior, or if it must be modified in order to provide a conceptual template for the further development of a local statistical mathematical 3-D biophysical model of expansive growth of the cell wall.While still a first order approximation that focuses only on fibril-slippage, this model captures the essential molecular features of the cell wall mechanics that can be extended to include fibril-reorientation and helical deformationR of stage IVb sporangiophores remain constant during the phototropic response and avoidance response. It is found that the elongation and rotation rates increase during the phototropic response, and to a lesser extent during the avoidance response. Similarly, R increases during the phototropic response, and to a lesser extent during the avoidance response. Thus the assumption that elongation rates, rotation rates, and R are constant during the phototropic response and avoidance response is not supported by these experimental results. The second objective is to determine how the ratio R changes with steady elongation rates for stage IVb sporangiophores of the stiff mutants C149 and C216 to learn if they are smaller than R of wild type and can offer insight into their diminished phototropic and avoidance responses. The results demonstrate that the “R vs. elongation rate” curves for C149 and C216 stiff mutants are similar to that obtained for wild type sporangiophores and not smaller. The ramifications of these results on previous and future research are discussed.The first objective of this investigation is to determine whether the elongation rate, rotation rate, and Figure Figure p values presented on the time scale indicate 95% confidence that the values are different when p = 0.05, and smaller values indicate higher confidence that the values are different (blue type). The red p values indicate less than 95% confidence. It can be seen that the rotation rate and elongation rate increase during the phototropic response.Figure R (R = rotation growth rate ÷ elongation growth rate). The R value was determined for each 10 min interval during the experiments to determine whether the steepness of the helical growth changed during the phototropic response. Figure R values for each 10 min interval for all ten experiments conducted. The “ratio of averages” method was used to calculate R. R is calculated from their corresponding mean values and standard errors (SE) using the following formulae.R, 〈RR, and 〈ER are the mean values for R, rotation rate, and elongation rate, respectively.The steepness of the helical growth can be determined by the ratio R value increases during the phototropic response. Statistics are conducted to determine whether the R values during the phototropic response are larger than the R value during the first ten-minute interval i.e. steady growth. To determine the statistical significance of the change in R, consider the following ratio, Z.R in the reference time interval (0–10 min) before the stimulus is applied and R in a time interval t after the stimulus. A mean value of R after the application of the stimulus. The standard error in Z may be used to calculate confidence intervals for this ratio to determine its statistical significance. Using the same formula for the mean and standard error of a ratio previously defined, the 80% and 95% confidence intervals are calculated for Z as Figure mentclass2pt{minimZ is greater than unity (Z > 1) for the time intervals greater than 20 min for both 80% and 95% confidence intervals. Thus the results indicate 95% confidence that R has increased during the time interval of 20–60 min of the phototropic response.It is noted that Figure Figure p values presented on the time scale indicate 95% confidence that the values are different when p = 0.05, and smaller values indicate higher confidence that the values are different. The blue p values indicate 95% confidence or higher, and the red p values indicate less that 95% confidence. It is seen that the rotation rate significantly increases during the avoidance response, but the elongation rate does not.Figure R values for each 10 min interval for all ten experiments conducted. As before, the “ratio of averages” method was used to calculate R from their corresponding mean values and standard errors (SE) using Eqs.  for the all time intervals in the 95% confidence interval. Z is greater than unity in the 80% confidence interval for time intervals 10–20 min and 30–40 min. This result indicates only 80% confidence that R has increased during the time intervals of 10–20 and 30–40 min of the avoidance response.It is noted that Rave was determined for stiff mutant stage IVb sporangiophores (C149 and C216) during steady elongation growth using the same method and analyses that were previously used for wild type sporangiophores34. The elongation and rotation rates were measured concurrently for mutant stage IVb sporangiophores during steady growth. The natural variation of steady elongation growth rate ranged between approximately 5 μm/min and 76 μm/min. The ratio, R, was calculated for each sporangiophore and averaged with values of R obtained from other sporangiophores growing within a specified range of elongation rates. These averaged values, Rave, are plotted together with those obtained from wild type stage IVb sporangiophores as a function of elongation rate in Fig. R values) than that for the wild type sporangiophores56.Figure The average bend rate, rotation rate, and elongation rate of all ten experiments conducted are presented in Fig. R values for each ten-minute interval for all ten experiments conducted. Table R values are significantly larger for the second, third, and fourth ten-minute intervals. It is concluded that the average R value increases during the phototropic response. The results indicate that the steepness of the helical growth rate becomes flatter during the phototropic response.Figure 14 assumed constant elongation rates during the phototropic response. It was postulated that bending was produced by differential growth between the proximal and distal sides of the sporangiophore stalk. It was assumed that the proximal wall decreases in elongation rate and the distal wall increases in elongation rate, so that the cell’s overall elongation rate was constant. This assumption is not supported by the results presented in Fig. 14 remain the same. Similarly, the finding that both elongation and rotation rates increase during the phototropic response do not appear to alter the main conclusions of Dennison and Foster15, that the rotation converts a spatial stimulus into a temporal stimulus that prevents adaptation to the unilateral light stimulus.CastleFigure The average bend rate, rotation rate, and elongation rate of all ten experiments conducted are presented in Fig. R values for each ten-minute interval for all ten experiments conducted. Table R values may be larger for the first and third ten-minute intervals . It is concluded that the R value may slightly increases during the avoidance response.Figure R value during the avoidance response. A stronger response can be obtained by putting the barrier closer to the sporangiophore17, but this was not possible in these experiments because it would constrain the rotation of the fiber on the sporangium. The observation that the sporangiophores exhibit sharp curvature in the lower region of the growth zone during the phototropic response, but not during the avoidance response, may indicate that there may be underlining differences between these tropic responses.A comparison of the curves in Figs. 15. This wall rotation argument is extended to the avoidance response16 and may be extended to the gravitropic response that can also continue indefinitely. A question that arises is whether the diminished tropic responses of the stiff mutants are the result of a diminished rotation rate of the wall in the growth zone. Little is known about the helical growth of these stiff mutants.A distinguishing feature between “growth” responses and “tropic” responses is that growth responses are transient but tropic responses can continue indefinitely, as long as an effective stimulus can be maintained. In the phototropic response, it has been hypothesized that the photoreceptors rotate with the cell wall, and this rotation prevents the photoreceptors from adapting to the light stimulus56. However, the length of the growth zones for the C216 and C149 sporangiophores are shorter than wild type sporangiophores. So it is speculated that the shorter growth zones of the stiff mutant sporangiophores may reduce the overall rotation rate that could contribute to the diminished tropic responses. Therefore, R was measured as a function of steady elongation rate for both C216 and C149 stage IVb sporangiophores.The average elongation growth rates of C216 and C149 stage IVb sporangiophores are similar to those of wild typeR as a function of elongation rate for C149, C216, and wild type (WT) stage IVb sporangiophores are presented Fig. R decreases as the elongation rate increases, similar to wild type sporangiophores. But the results clearly demonstrate that the R values for C149 and C216 stiff mutant stage IVb sporangiophores not smaller than those of wild type55. Therefore, it is concluded that the mutation that produces the diminished phototropic and avoidance responses are not mutations in the helical growth of their sporangiophores. It is still possible that the shorter growth zones of these stiff mutant sporangiophores may contribute to the diminished tropic responses56.The curves of 35. It is proposed that microfibrils are deposited somewhat transverse to the longitudinal axis on the inner wall surface of the growth zone with a concentration in the upper region of the growth zone, that nearest the sporangium. The upper region of the growth zone is shown to be the most extensible and exhibits the largest amount of plastic deformation57. It is thought that the transverse orientation of microfibrils allows for more resistance to wall deformation in the radial direction compared to the longitudinal direction. It is postulated that because of longitudinal plastic wall deformation and deposition of new materials to the inner wall during elongation growth, the microfibrils reorient towards the longitudinal direction and concurrently migrate to lower regions of the growth zone. Now if the fibril reorientation occurs in a preferred direction because of some asymmetry in the molecular bonding or because of its initial orientation, then the displacement vector of the reorienting microfibrils will produce transverse displacement on the elongating (stretching) wall  per longitudinal displacement produced by fibril reorientation changes along the length of the growth zone. The amount of rotation per longitudinal displacement increases as the microfibrils become more longitudinally oriented. Importantly, the fibril reorientation hypothesis predicts that the ratio of the rotation rate and elongation rate, R, increases in the lower region of the growth zone. This prediction is consistent with experimental results indicating that there is measurable rotation without measurable elongation in lower region of the growth zone during steady elongation growth35.The fibril reorientation hypothesis was proposed to explain the origin of helical growth in the elongating cell wall in the growth zoneall Fig. a. In a cPil-mutant stage IVb sporangiophores exhibit increased radial expansion during elongation growth and form a bulge in the growth zone of the stage IVb sporangiophore33. Interestingly, the direction of rotation of the wall switches from clockwise to counter-clockwise during the increase in radial expansion. It is postulated that the mutation is that the microfibrils are deposited somewhat longitudinally, instead of the transverse direction, on the inner wall surface of the growth zone. The longitudinally oriented microfibrils will permit more wall deformation and strain in circumference, thus initiating radial expansion. It is thought that the microfibrils will begin to reorient toward the transverse direction because of the increased wall deformation in the circumferential direction. If the direction of fibril reorientation is the same as before (during elongation growth) but simply reversed, then the transverse wall displacement caused by the reorienting microfibrils will be in the opposite direction and the wall rotation will be counterclockwise. The fibril reorientation hypothesis predicts that the reversal from clockwise to counterclockwise will occur when the rate of wall deformation in the circumferential direction and longitudinal direction are equal. Analyses of the experimental results confirm this prediction33.R is a function of elongation rate34 . It is postulated that there exists a fibril reorientation subzone and fibril slippage subzone in longer, faster elongating growth zones and the fibril slippage zone does not produce transverse wall displacement or rotation. The fibril reorientation-slippage hypothesis predicts that during fast steady growth, longer growth zones will have a fibril slippage subzone. Furthermore, longer growth zone with both fibril reorientation and fibril slippage subzones will produces less average rotation compared to a shorter growth zone with only a fibril reorientation subzone. In other word, it predicts that the ratio of rotation rate and elongation rate, R, will be smaller for faster growing sporangiophores34  and why “measureable elongation rate without measureable rotation rate” is observed during the light growth response (transient increase in elongation growth) in the lowest region of a longer growth zone35.The findings that s34 Fig. . PreviouR are measured during two tropic responses, the phototropic and avoidance responses. It is found that the rotation rate increases during both tropic responses. The elongation rate increases during the phototropic response and appears to increase slightly during the avoidance response. Similarly R increases during the phototropic response and appears to increase slightly during the weaker avoidance response. Here we ask whether the fibril reorientation-slippage hypothesis can explain the behavior of the rotation rate, elongation rate, and R that is observed during the phototropic and avoidance responses. It is thought that the increase in elongation growth rate during the phototropic response is produced by an increase in wall loosening  that increases the plastic wall deformation. If it were assumed that the microfibrils are added to the inner wall at the same rate and location as in steady growth, then the fibril reorientation-slippage hypothesis would predict a decrease in the magnitude of rotation rate and R during the phototropic response. This is expected because the increase in elongation rate will be accompanied by an increase in growth zone length and most of the added length will be fibril-slippage subzone that does not produce rotation. On the other hand, if it is assumed that microfibrils are added to the inner wall at a higher rate and to larger (lower) areas of the growth zone during the phototropic response, then the fibril reorientation-slippage model will predict an increase in rotation rate and R, as shown in Fig. 61. This would increase the population of reorienting microfibrils in the lower region of the longer growth zone, thus converting the “fibril slippage” subzone to a “fibril reorientation” subzone. The reorienting fibrils will continue to produce rotation in the lower region and increase the overall rotation rate and R during the phototropic response.In this study, the rotation rate, elongation rate, and lower regions of a slightly longer growth zone (the larger elongation rates are accompanied by a longer growth zones60). It is envisioned that the increase in population of reorienting microfibrils in lower regions of the growth zone will effectively convert some of the fibril-slippage subzone into a fibril-reorientation zone that produces rotation. Recent evidence indicates that the addition of polysaccharide chains to synthesized microfibrils may occur below the growth zone62. The introduction of a population of reorienting microfibrils in the lower regions of the growth zone will increase the rotation rate and the magnitude of R as shown in Fig. The fibril reorientation-slippage model can explain the experimental results obtained in this study if it is postulated that the phototropic response is initiated by producing additional wall loosening on the distal side of the cylindrical wall of the sporangiophore. Then the distal wall would experience more loosening than the proximal wall, producing bending toward the unilateral light and increasing the overall elongation rate. When the sporangiophore approaches a barrier, the proximal wall will experience additional wall loosening, producing bending away from the barrier and increasing the overall elongation rate. In both cases, it is postulated that the production rate of microfibrils in a transverse direction is increased and extended to Figure local model of the cell wall that is being developed54 to explore how fibril reorientation, fibril slippage, and the addition of wall material produce helical growth, and the changes in helical growth that occurs during sensory responses.In the near future, we plan to test these predictions using a 41 implicitly assume that mass is added to the cell wall during expansive growth to prevent thinning and eventual rupture of the wall. In order to maintain a constant wall thickness during steady growth rate, the rate at which mass is added to the wall is considered to be constant, i.e. (dmw/dt)ss = constant. It is not known how the wall mass changes during sensory responses or which species of biomolecules and polymers are added. Here we present evidence that there is an increase in the rate of production of chitin microfibrils during the phototropic and avoidance responses. So in general, Eq.  we can write a more explicit equation, Eq. , when thj-species of biomolecules and polymers added to the wall.Similarly for the avoidance response (AR) we can write Eq. , when thi) and during the avoidance response (n = j) are unknown at this time. However, as they become known they can be added to Eqs. The number of species of biomolecules and polymers added to the cell wall during the phototropic response , Living, Tube Culture, from which a small amount was cultivated on a petri dish of prepared 4% potato dextrose agar. Spores were obtained from the sporangiophores and stored in distilled water and saved. The growth medium was prepared from potato dextrose agar manufactured by Alpha Biosciences. Vegetative spores were inoculated in the culture medium and grown in small glass vials (capacity: 1 g) in a box at a temperature of 23 °C and high humidity. After the appearance of sporangiophores, they were plucked  every evening so that a fresh crop of sporangiophores would be available the next day. Stage IVb sporangiophores, 2–5 cm in length, from the third to fifth crop was used for experimentation.Hypha were purchased from Carolina Biological supply in the form of 3) to house two light bulbs on opposite sides and camera along with the sporangiophore in its glass vial. Light bulb specifications are: Fiet electric BPEFC40/850/LED/2 DAYLIGHT 220–16-44 E330072, 4.5 W/5000 K/300 lm 120VAC/60 Hz/33 mA. A Sony DSLR-A200 with a Tamron P 90 mm f/2.8 Di Macro Lens camera was used to capture front view images of the sporangiophore to determine change in length (elongation rate) and bending towards the light source (bend angle), while a Celestron 5MP handheld digital microscope captured top view images of the sporangium which has a 1–2 mm long fiber (hair) attached to it. This fiber is used to determine the rotation rate. The duration of each experiment was sixty minutes and the cameras capture an image at every minute. The test sporangiophore  was transferred to the prescribed location inside the red box in order to adapt to the experimental conditions and lights. Each experiment begins with both light bulbs turned on for the first ten minutes. The bend angle, rotation angle, and length were measured every minute for the rest of the experiment. This ten-minute interval was used to determine the elongation rate, rotation rate, and bend rate before the phototropic stimulus. At the end of ten-minute interval, one light is turned off. The sporangiophore begins to bend and grow towards the remaining light source. The digital microscope used to capture top view images has a flexible neck and can also be bent along with the sporangiophore to track the rotation rate. At the end of the experiment the images are saved for analysis using MATLAB.To conduct the phototropic response experiments a box was constructed of red plexi-glass sheet (8 × 10 × 8 in3) with two light bulbs on opposite sides and camera used for the phototropic response experiments were reused. The right side of the box was fitted with a threaded bolt and a cover slip (barrier) was attached to its end. This bolt can be screwed in and out , to change the distance between the barrier (cover slip) and growth zone of the sporangiophore. This arrangement orients the surface of the barrier so that it is parallel to the sporangiophore stalk and the light from the light sources on either side, and does not to interfere with the light impinging on the sporangiophore from the side. A Sony DSLR-A200 with a Tamron P 90 mm f/2.8 Di Macro Lens camera was used to capture front view images of the sporangiophore to determine a change in length (elongation) and bending towards the light source (bend angle), while a Celestron 5MP handheld digital microscope is used to capture top view images of the sporangium which has a 1–2 mm long fiber (hair) attached to it. The duration of each experiment was sixty minutes and the cameras capture an image at every minute. The experimental protocol was as follows. Initially, a stage IVb sporangiophore in its vial was placed inside the red box in order to adapt it to the experimental conditions and lights. Each experiment begins with the barrier being at a long distance from the sporangiophore with both lights illuminated. The bend angle, rotation angle and length were measured every minute for the rest of the experiment. A ten-minute interval was used to determine the elongation rate, rotation rate and bend rate before the barrier stimulus was given. At the end of the ten-minute interval, the barrier was moved closer to the sporangiophore using the threaded bolt until a distance of less than a millimeter between the two was reached. Soon after, the sporangiophore begins to bend away from the barrier. The digital microscope used to capture the top view images has a flexible neck and can also be bent along with the sporangiophore to track the rotation rate. At the end of the experiment the images are saved for analysis using MATLAB.To conduct the avoidance response experiments the red plexi-glass sheet box (8 × 10 × 8 ingeo -(-) were originally obtained from Ishinomaki Senshu University, Miyagi, Japan. The C149 madD120(-) strain was obtained from ATCC: The Global Research Center, Virginia, USA. Sporangiophores were inoculated on sterile growth medium consisting of 4% (w/v) YM agar. After inoculating, the sporangiophores were incubated under diffuse incandescent light and constant temperature (22 ± 2 °C). Stage IVb sporangiophores, 1.5–2.5 cm in length, were selected for experiments from the second to the seventh crop55.Vegetative spores of the stiff mutant gene strain C216 63. Prior to initiating photographic measurements, the diameter of the sporangium was measured and later used as a scale reference in ImageJ55.The elongation rate of the sporangiophore was determined by measuring the change in length, ∆L, of the bottom edge of the sporangium at 1-min intervals. The length of the sporangium was measured by taking images with a customized camera-microscope set-up made of a web camera  attached to a long focal length horizontal microscope  mounted to a 3-D micromanipulator . The images were acquired using open source software Vividia Ablescope and were analyzed using open source software ImageJ63. Figure A short piece of hair (7–10 mm long) was attached to the top of the sporangium of the stage IVb sporangiophore to track the sporangium’s rotation. The hair was placed perpendicular to the longitudinal axis of the cell and secured using a small amount of petroleum jelly. A USB microscope was used to take photographic images of the hair attached to the sporangium and to help determine the rotation rate. The images were acquired using open source software Vividia Ablescope and were analyzed using open source software ImageJ


The uncertainties originate from the assumption of a constant VER at every given altitude, resulting in errors where the assumption is not valid when limb sounders, such as MIGHTI, observe regions with significant VER gradients. In this work, we introduce a new wind retrieval algorithm (Wu20) with the ability to account for VER that is asymmetric along the line of sight with respect to the tangent point. Using the predicted ICON orbit and simulated global VER variation, the greatest impact of the symmetric airglow assumption to the ICON vector wind product is found within 30° from the terminator when the spacecraft is in the dayside, causing an error of at least 10 m/s. The new algorithm developed in this study reduces the error near the terminator by a factor of 10. Although Wu20 improves the accuracy of the retrievals, it loses precision by 75% compared to Harding17.The Michelson Interferometer for Global High‐resolution Thermospheric Imaging (MIGHTI) on NASA's Ionospheric Connection Explorer (ICON) mission is designed to measure the neutral wind and temperature between 90 and  An algorithm is introduced that improves the accuracy of limb‐sounding wind retrievals, accounting for the asymmetric volume emission rateThe algorithm is tested with simulated measurements of the ICON/MIGHTI instrument and shown to significantly improve retrieval's accuracyThe algorithm improves accuracy but at the expense of precision in regions of large asymmetry The highest pointing LOS and the corresponding top altitude layer are represented by nth layer for the mth LOS and nth layer in the mth LOS.As discussed in Harding17, we use Bmobs(k) in Equation mth LOS, Replacing k, with the so called uniform wind assumption: Harding17 assumes the Doppler shift of the wind is the same throughout each altitude layer, so that the wave number‐related term, k, can be replaced by M is the total number of observation angles. Additionally, Bn(k)ejΔϕncosαmn, where nth layer and mth LOS and the tangential direction of the nth layer at their intersection. At the end, we combine the spectrum nth layer Equation The angle between the zeroth LOS and tangent of the zeroth layer The major steps in the onion peeling method are summarized below: (1) using the observed intensity of the tangent layer of the top LOS to estimate the averaged brightness of the same spherical layer; (2) estimating the pathlength of each layer on the same LOS under the spherical Earth assumption; and (3) with 1 and 2, once we know the brightness of the top layer, the brightness of the layer below can be obtained by removing (“peeling”) the brightness of the top layer from the intensity of that LOS.nth layer in the mth LOS is given as mth LOS and nth layer that needs to be removed.In order to perform the onion peeling method on the lower layers, Equation mth LOS through the nth layer: nth and  is Since 99% of the data in the region of 200–300 km from the simulation using Harding17 have an error less than 10% of the mission uncertainty requirement of 8.7 m/s (Immel et al., Similar to Figure The middle panels in the example demonstrated in Figure Compared with the mission requirement of 8.7 m/s, the impact of the symmetric assumption on the green line product is minor. However, the error can be propagated and enhanced when more noise is introduced in the real data. Additionally, unlike random errors, the error in the onion peeling retrievals is not expected to reduce upon averaging.4In section We performed a Monte Carlo simulation to show the trade‐off between accuracy and precision at 70° latitude where Harding17 has the largest error for the MIGHTI‐A red line. We added noise to each row of a synthetic ICON interferogram to simulate measurement noise sources such as shot, dark, and read noise and then obtained the LOS wind errors from the retrieval of the simulations using Harding17 and Wu20. In total, 500 profiles with random noise are included in the analysis.In Figure Although the trade‐off between accuracy and precision might limit the degree to which Wu20 can improve over Harding17, if the transition of the wind vector at the terminators is the target, Wu20 can still make significant correction for the lower altitudes and for the regions and periods with significant spatial airglow changes.5In this study, we described an algorithm to improve the accuracy of the wind vector retrieved from a spaceborne Doppler interfermetry instrument by considering the asymmetric VER before and after the tangent point of the FOV. The key step in the proposed algorithm is allowing the VERs to be different before and after the tangent point in the onion peeling procedure. A model run showed that if the VER variation along the LOS is well known, the input wind profile can be reconstructed to a higher accuracy using the asymmetric airglow procedure in Wu20 compared to Harding17.An instrument that measures the Dopper shift in an interferogram to remotely retrieve the wind phase receives the integrated VER over the LOS; therefore, the VER variation along the LOS is generally unknown. One can reconstruct the VER variation by imaging tomography from different LOSs, but that requires viewing the same airglow from multiple directions, which is usually hard to implement by a single spacecraft. A simplified method with the assumption that the VER variation as a function of longitude is the same for all altitudes is demonstrated in this paper for a spaceborne measurement in a low‐inclination angle orbit like that of the ICON spacecraft. In this way, the continuous VER observation by MIGHTI itself provides the reference VER variation that can be applied in Wu20 and the actual MIGHTI wind retrievals.We compared the accuracy of the LOS wind retrieval for a completed ICON orbit between Harding17 and Wu20. For the altitudes at which the signal‐to‐noise ratio of the emission is sufficient for retrieving LOS wind, the greatest impact of the symmetric airglow assumption of Harding17 to the ICON vector wind product is where the angle between the FOV and the terminator boundary is the greatest within a 30° longitude range from the terminators, which causes an error of at least 10 m/s. Our results showed that Wu20 can effectively reduce this error by a factor of 10 in general. Although Wu20 improves the accuracy, it loses precision by 75% compared to Harding17. Note that these results only apply to the simulations conducted in this study and could vary depending on circumstances such as different shape of VER variation in longitude and VER changes with season and solar flux.A few caveats are worth noting when applying Wu20 to the other Abel transform‐related retrieval algorithms. The algorithm in Wu20 assumes that VER can change along LOS the in addition to changing in altitude, while the wind only changes in altitude. This limitation in uniform wind assumption has not been relaxed in Wu20. In the demonstration of the application on ICON/MIGHTI, we assumed that the VER ratio (


To document with spectral-domain optical coherence tomography the structural stabilization of the fovea and the sealing of outer macular defects by Müller cells.A retrospective case series of 45 eyes of 34 patients is described.In cases of a cystic disruption of the foveola as in macular telangiectasia type 2 and vitreomacular traction, the Müller cell cone provides the structural stability of the fovea. In cases of a detachment or disruption of the Müller cell cone, e.g., in foveal pseudocysts, outer lamellar holes, and degenerative and tractional lamellar holes, Müller cells of the foveal walls may provide the structural stability of the fovea by the formation of a hyperreflective external limiting membrane (ELM) which bridges the holes in the central outer nuclear layer (ONL). Müller cells of the foveal walls and parafovea mediate the regeneration of the foveal architecture in cases of outer lamellar and full-thickness macular holes. The regeneration proceeds by a centripetal displacement of photoreceptor cell somata which closes the holes in the central ONL. The closure may be supported by the formation of a glial tissue band at the ELM which seals the hole.The Müller cell cone provides the foveal stability in cases of a cystic disruption of the foveola. The structural stability of the outer foveal layers is mainly provided by the Müller cells of the foveal walls and parafovea; these cells also mediate the regeneration of the outer fovea in cases of a defect of the central ONL. The Ml center –12.The structural stability of the outer layers of the fovea  is suggested to be mainly provided by the outer processes of the Müller cells of the foveal walls and parafovea . These pMüller cells of the foveal walls and parafovea are also implicated in the regeneration of the outer retinal structure after surgical or spontaneous closure of FTMH –19. FollThis retrospective study followed the ethical standards of the Declaration of Helsinki for research involving human subjects. The patients were referred to the Department of Ophthalmology, University of Leipzig, Germany, between February 2008 and September 2019. Thirty one patients with different types of partial-thickness macular defects and three patients with surgical closure of a FTMH were included in the study. Cross-sectional images of the macular area were obtained with spectral-domain optical coherence tomography . Best-corrected visual acuity (BCVA) was determined with a Snellen chart and is given in decimal units.All patients were Caucasians. SD-OCT images of the macular regions of both eyes of 6 patients with macular telangiectasia type 2 were investigated  peeling, and SF6 tamponade in one eye of 3 women was also investigated  –28. FiguFigure Figure Figure Figure Outer lamellar holes are characterized by a large pseudocyst in the foveola which causes a detachment of the inner foveolar layer. The elevation of the inner layer is associated with an elevation of the inner layers of the foveal walls (NFL to OPL) which causes an oblique stretching and straightening of the Müller cells of the foveal walls that transmit the tension to the outer retina. This produces a centrifugal displacement of the central ONL and photoreceptors resulting in a disruption of the ELM and a hole in the outer retina , 11.Figure The SD-OCT scans in Fig. The SD-OCT scans in Fig. Figure Figure During the next 18 months, the foveal morphology regenerated spontaneously Fig. a. WithinThe regeneration of the foveal architecture after the closure of FTMH may involve the formation of a glial tissue which seals the hole at the outer layers. The FTMH shown in Fig. The FTMH shown in Fig. Figure In the normal fovea, the Müller cell cone provides the resistance of the foveal tissue against mechanical stress resulting from anteroposterior and tangential tractions Fig. a. It wasThe present data may suggest that the Müller cell cone provides the foveal stability in cases of a cystic disruption of the foveola. In cases of a central photoreceptor degeneration without vitreomacular traction which may detach or tear the Müller cell cone as in macular telangiectasia type 2, the foveal contour remains normal Fig. a–f. In cMacular telangiectasia type 2 was suggested to be caused by a dysfunction and/or degeneration of Müller cells; Müller cell dysfunction may produce the vascular symptoms and the degeneration of photoreceptors , 31. TheIn various types of foveal defects, which are characterized by a detachment and/or a disruption of the Müller cell cone, Müller cells of the foveal walls may support the structural stability of the foveal center Fig. b, d–m. TA tractional disruption of the Müller cell cone is often associated with a dehiscence of the central ONL; the foveal center is only stabilized by the ELM Fig. c–f. The Shortly after the closure of a FTMH, the central ONL displayed a gap and an absence of photorecpetors while the gap in the ELM was closed Fig. a–c. The The cellular origin of the hyperreflective tissue bands at the ELM is unclear. The central fovea only contains Müller and photoreceptor cells , 4, 13. In most cases described in this study, the formation of glial tissue bands which seal outer retinal holes at the ELM was associated with a narrowing of the hole by the Müller cell-mediated centripetal displacement of the ONL. It was shown that small FTMH with a diameter of less than 400 µm may close spontaneously , 39. TheFigure In summary, the present data suggest that the Müller cell cone maintains the structure of the central fovea in cases of a cystic disruption of the foveola when no tractions are present which detach or disrupt the cone. Müller cells of the foveal walls may provide the stability and may mediate the regeneration of the outer fovea in cases of defects of the central ONL by two mechanisms: a centripetal displacement of the photoreceptor cell somata and the formation of a glial tissue band at the ELM and the outer part of the ONL which bridges the hole in the central ONL.


Background: Sensing the grasping force and displaying the force for the operator are important for safe operation in robot‐assisted surgery. Although robotic forceps that senses the force by force sensors or driving torque of electric motors is proposed, the force sensors and the motors have some problems such as increase in weight and difficulty of the sterilization.Method: We developed a pneumatically driven robotic forceps that estimates the grasping torque and display the magnified torque for the operator. The robotic forceps has a master device and a slave robot, and they are integrated. In the slave side, the grasping torque is estimated by the pressure change in the pneumatic cylinder. A pneumatic bellows display the torque through a linkage.Results: We confirmed that the slave robot follows the motion of the master, and the grasping torque is estimated in the accuracy of 7 mNm and is magnified and displayed for the operator.Conclusions: The pneumatically driven robotic forceps has the capability in the estimation of the grasping torque and display of the torque. Regarding future work, the usability and fatigues of the surgeons must be evaluated. This surgical method hastens patient recovery and reduces the size of the surgical incision. Although laparoscopic surgery has been adopted for various procedures, it requires increased surgical skill because surgeons have to operate a forceps inserted into a narrow cavity. To clear the space around the organ of interest, a surgeon frequently grasps and pulls up other organs with a grasping forceps. The forceps used in this surgery is long, so insufficient grasping torque is transmitted to the handle and felt by the surgeon.Control of grasping force has depended on the skill of the surgeon. Surgeons may damage delicate organs such as a liver by excessive forceThe design of force‐sensing systems for robotic forceps has been studied by many researchers.Therefore, several methods have been proposed to estimate the grasping force or torque without installing force sensors. Li et al developed a robotic forceps driven by electric motors that estimates the grasping force at the tip by modeling the forceps dynamics.To avoid the problems of these sensing systems, we used pneumatic cylinders to enable direct drive of the robotic forceps.The system also has a function of displaying the estimated force to the operator. Display of the grasping torque to the surgeon is important for patient safety,This paper presents a handheld type robotic forceps that is driven by the pneumatic actuator. The robotic forceps has the master device and the slave robot, and these devices are integrated into a handheld robotic forceps. It is lightweight, compact, and low cost compared with the robot for the telesurgery. This robotic forceps makes the risk of the electric accident smaller than the electrically driven robots. In this paper, we propose the position control system for the grasping task that can generate the large grasping torque with the small deviation between the master and the slave. The control system can also estimate the grasping torque at the tip without the force sensors, and the master device displays the magnified grasping torque for the operator. The range of the magnification ratio is confirmed by a stability analysis of the pneumatic bilateral control system. The proposed control system and the estimation performance were confirmed by several experiments.This paper is organized as follows: The developed robotic forceps is introduced in Section 2Figure The system is based on the ready‐made laparoscopic grasping forceps tip and shaft shown in Figure 3Kb=2.5 N/mm. The bellows works with expanding and contracting, and it does not have sliding parts. As the friction in the bellows is negligibly small, the pressure control can realize a precise torque haptic display.The master device displays the torque haptically with a pneumatically driven bellows actuator . The bellows used in the device can withstand 0.1 MPa of pressure, and the bellows spring constant is Figure ϕm is derived from the bellows displacement xm.The PI control gains were determined by trial and error, and the adopted values are shown in Table τm and the bellows driving force Fb is calculated using the principle of virtual work. The relation between the handle torque τm=0.7 Nm at xm=0 mm. The bellows cross‐sectional area Ab is obtained by dividing the driving force by the pressure. Therefore, we selected the initial length and inner diameter of the bellows as 12 and 15 mm, respectively. The handle range of motion was set to 8°, which is similar to that of a conventional forceps. The bellows displacement is 5.2 mm when the handle is fully closed.A driving force of 17 N is needed to generate the torque 4Figure ϕs is derived from the cylinder piston displacement xs.ϕmax is the maximum opening angle (50°). The gripping torque τs and the cylinder driving force f are obtained using the principle of virtual work, as follows:Js is the Jacobian of the gripping mechanism. According to the other researches, the required force for the grasping organ is about 3 N.f=51.9N is needed to generate a gripping torque of 80 mNm with r=2.4 mm and xs=1.84 mm. This made it clear that a large force is required to actuate the gripper and that the backdrivable actuator is suitable for estimating the gripping torque. Therefore, we used a low‐friction pneumatic cylinder with an inner diameter of 16 mm, rod diameter of 5 mm, and stroke of 10 mm . The cylinder can directly generate 100 N of force at a pressure of 0.5 MPa without using a reduction mechanism. The pressure of both chambers in the cylinder, P1 and P2, is measured by pressure sensors . The cylinder is controlled by a five‐port spool‐type servo valve . The piston range of travel is 1.84 mm, and its displacement is measured by a magnetic encoder  attached to the cylinder rod. The encoder has minimal noise reduction such as a differential driver.The gripper opening angle m is the mass of the slave mechanism, xs is the piston position, c is the viscosity coefficient of the slave mechanism, and A1 and A2 are the cross‐sectional areas of the cylinder chambers.The pneumatic servo system is nonlinear. However, at the equilibrium point, a linear model is effective for the control design.R is the ideal gas constant, θ is the temperature of air in the cylinder, P10 and P20 are the chamber pressures at equilibrium, V10 and V20 are the chamber volumes at equilibrium, and G1 and G2 are the mass flow rates for each chamber. The mass flow rate is calculated as follows:Ps is the supply pressure, Se is the effective area of the servo valve, κ is the specific heat ratio, b is a ratio between P20 and Ps, Ksv is a proportional constant between the opening of the valve and the input voltage, and u is the control signal to the servo valve.The state change of the pressurized chambers is treated as isothermal since the movement is rather slow. Total differentiation of the ideal gas state equation is given as follows:xm.xsr is the reference of the slave and α is a constant value set to α=1.845.2 so that the gripper and handle both close completely at the same time. The position is controlled by a proportional‐derivative controller, whereas the minor loops use PI control, as shown in Figure Figure τext applied to the gripper on the position deviation. The position deviation ep=xsr−xs is calculated as follows for step inputs of xsr and τext. GP is the PD controller, GV and GF are the PI controller, and KA and KB are given asThe operability deteriorates when the position deviation between the master and the slave is large, so we evaluated the influence of the external torque ep is given from the final‐value theorem.Since the grasping forceps are mainly used to grasp tissue for periods of time, the system can be regarded as a steady state. Therefore, It is clear from 5F to the pneumatic cylinder is derived from the block diagram in Figure The input force F at a steady state is given as The force τext can be estimated from the piston position and the generated force of the pneumatic cylinder. The force f is obtained from the measured pressures as shown in xs is measured by the encoder.It is clear from The driving force is increased by the viscosity of the slave mechanism during the motion. Therefore, the viscosity is compensated by the following equation.c=8.0 Ns/mm, was determined experimentally. To display the estimated gripping torque to the operator, the target value of handle torque is given by the following equation:β is a scaling ratio to magnify the haptic display force. The operator can more easily feel a small force when β is increased.The viscous friction, Fb is calculated from τm. This force is given as the reference input to the master device.The force 6τo and the bellows contracts. The bellows deformation xm is given as a reference input to the slave side of the controller. The xm is filtered by a low‐pass‐filter to cancel the noise. Here, the scaling factor α can be multiplied by xm to change the scaling ratio. When the forceps grasps tissue, the grasping torque τext is estimated from the driving force of the pneumatic cylinder, F. Then, the estimated torque is amplified by β, transmitted to the master force controller, and displayed to the operator as torque in the handle, as shown in Figure A force‐reflecting bilateral control was implemented in the developed robotic forceps. Figure α and β affect the stability of the bilateral control system. The control system is analyzed by using MATLAB to see the effect of the scaling factors. In typical laparoscopic surgery, the motion scaling from the master to the slave is set under 1.0.α is 1.84/5.2 considering the motion range of the master and the slave grippers. Since the motion range of grippers is small compared with translational motions, changing the scaling by software is unpractical, and we fixed the α in this analysis. Therefore, we deal with the β the feedback gain of the bilateral control system. The bellows is assumed as a mass‐spring‐damper system. The impedance parameters are determined such that the damping ratio is 0.7. The dynamics of the operator is regarded as a mass‐spring‐damper system, and the parameters are set to a literature value.τo, and the output is xm. Figure β is less than 34.5.The 7The performance of the developed robotic forceps was evaluated experimentally.First, the performance of the position control system was confirmed. Then, the torque estimation ability of the forceps was confirmed from static and bilateral experiments.7.1First, the experiment of the position control was conducted to confirm that the slave follows the reference angle and that the viscosity compensation is effective. A sinusoidal reference position with an amplitude of 20°, an offset of 25°, and a frequency of 0.5 Hz was input into the slave. The gripper grasps no obstacles during the position control. Figure 7.2In the following experiments, a six‐axis force sensor was grasped by the forceps, and the measured and estimated torques were compared. As shown in the right side of Figure Figure Figure Next, the angle of the gripper was varied from 10° to 50° increments to see whether the estimation accuracy depends on the gripper angle. The reference of the grasping torque is set to a constant value of 56 mNm. Figure Figure 7.3β is set to 12 that is determined by surgeon's opinions. Figure xm and Fb.Bilateral control experiments were conducted to confirm the effectiveness of the developed forceps. A reference position was input by the operator's gripping motion. The gripper grasps the force sensor at the angle of 25°. The resulting torque was measured, and then the positions of the master handle and slave gripper were compared. The Figure 8In this paper, we described the development of a master‐slave robotic forceps with pneumatic actuators. The developed robotic forceps can prevent the surgeons from grasping the organ with large grasping torque. The weight of the proposed forceps is heavy compared with the conventional grasping forceps. However, the weight of 280 g is similar to commercial needle driver; thus, the weight is acceptable in practice. Also, in the pneumatically driven system, the risk of the electric accident is greatly smaller than the electrically driven forceps. The pneumatic actuator provides an estimation of the grasping torque. The robotic forceps estimates the grasping torque and displays it in the handle at any magnification ratio selected by the operator. The magnification ratio can be set up to 34.5, and the grasping task was carried out at the ratio of 12. Experimental results indicate that the robotic forceps can estimate the grasping torque with an error of 7 mNm and haptically display a magnified torque precisely to the operator.Regarding future work, evaluating in detail the effect of the displaying the magnified grasping torque, the usability, fatigues of the surgeons must be conducted.


This paper addresses the question of the contribution of azimuthally localized flow channels and magnetic field dipolarizations embedded in them in the global dipolarization of the inner magnetosphere during substorms. We employ the high‐resolution Lyon‐Fedder‐Mobarry global magnetosphere magnetohydrodynamic model and simulate an isolated substorm event, which was observed by the geostationary satellites and by the Magnetospheric Multiscale spacecraft. The results of our simulations reveal that plasma sheet flow channels  and elementary dipolarizations  occur in the growth phase of the substorm but are rare and do not penetrate to the geosynchronous orbit. The substorm onset is characterized by an abrupt increase in the occurrence and intensity of BBFs/DFs, which penetrate well earthward of the geosynchronous orbit during the expansion phase. These azimuthally localized structures are solely responsible for the global  dipolarization of the inner magnetosphere toward the end of the substorm expansion. Comparison with the geostationary satellites and Magnetospheric Multiscale data shows that the properties of the BBFs/DFs in the simulation are similar to those observed, which gives credence to the above results. Additionally, the simulation reveals many previously observed signatures of BBFs and DFs, including overshoots and oscillations around their equilibrium position, strong rebounds and vortical tailward flows, and the corresponding plasma sheet expansion and thinning. During substorm expansion all magnetic flux transport into the inner magnetosphere occurs via azimuthally localized earthward flowsSubstorm onset is characterized by an abrupt increase in the number of such flows penetrating to the geosynchronous orbitProperties of simulated bursty bulk flows/dipolarization fronts are similar to those observed including flux tube oscillations and rebounds However, the idea of SCW composition by wedgelets was first suggested to explain observations of multiple onsets of magnetic perturbations on the ground in the course of the same substorm  is a result of an accumulation of many localized dipolarizations.Regional magnetotail simulations  along with the storm time Sym‐H index. To place the simulation discussed below in the overall context of geomagnetic activity on that day, the figure covers a multihour interval that is substantially longer than the period covered by the simulation. Before the expansion phase of the substorm (starting after 09:00 UT), the AL/AU indices were insignificant for more than 3 hr. The expansion phase ended at about 09:57 UT, when the AL index magnitude started to decrease. According to the AL index, the recovery phase was interrupted by further auroral activity starting after ∼11:00 and lasting until ∼18:00 UT, after which the geomagnetic activity subsided. The Sym‐H index magnitude remained below ∼20 nT throughout the simulated period affirming that the ring current was inconsequential to magnetospheric dynamics. Accordingly, we use a standalone global MHD model of the magnetosphere without including a coupled ring current component  on 9 August 2016, studied recently observationally by Panov et al. . Figure Bx component, which was set to 0. Prior to the substorm onset around 09:20 UT  exhibiting fluctuations and occasional sign flips. After about 08:30 UT, the IMF Bz turned southward and intensified before returning to almost 0 nT around 09:00 UT and then turning southward again. It is these dynamics that presumably resulted in the observed substorm after 09:20 UT.Figure The results presented below concentrate on the 09:00–10:00 UT 1‐hr period including partly the growth, the entire expansion phase, and the first few minutes of the recovery phase of the substorm. It should be noted that there was a gap in the OMNI data after about 09:40 UT, during which time the simulation was driven with constant SW/IMF values as shown in Figure 3z≈0.1 RE in the inner plasma sheet  model , the auroral Pedersen and Hall conductances at midnight were 6°S and 16°S, respectively.The ionospheric boundary is treated as a thin spherical shell where the field‐aligned currents generated in the magnetosphere close via Ohm's law. The full details of this approach are given by Merkin and Lyon . An ionoThe MHD simulation was started at 05:00 UT and thus preconditioned for 4 h with the observed upstream SW/IMF parameters Figure  prior to4https://www.ngdc.noaa.gov/stp/satellite/goes; see also GOES N SERIES DATA BOOK, Revision D, February 2010) and from the fluxgate magnetometers of the FIELDS instrument suite  Space Environment Monitor Magnetometers , but its exact location is unclear from the figure  because it may be located away from the SM equator due to significant IMF By and non‐Vx SW velocity components (note that the Bz=0 contour in the Vx panel is shown to guide the eye but does not necessarily coincide with the X‐line since the simulation lacks north‐south symmetry.) This time instance is interesting because it indicates a significant BBF penetrating close to the geosynchronous orbit near midnight with its earthward edge reaching the GOES‐15 satellite. Also evident are strong rebound flows , most pronounced near the midnight and at the dusk flank. The midnight BBF penetrates to the GOES‐15 location, and it is this BBF, along with the associated DF, that starts the global substorm dipolarization (see below). The localized dipolarization associated with the midnight BBF is evident with the characteristic “mushroom” shape discernible also in the regional magnetotail simulations by Birn et al.  that generally penetrate to geosynchronous orbit and rebound as is evident from intermittent weak tailward flows between, roughly Rxy=6 RE and Rxy=15−20 RE on the nightside, where Rxy is the geocentric distance in the plane. The magnetic field has further dipolarized at the spacecraft locations and, more generally, across a broad range of MLT on the nightside. This is the result of the global substorm dipolarization discussed in detail below. The thermal pressure distribution now shows a significant enhancement relative to the preonset level  and magnetic field dipolarizations (DFs) to the overall dipolarization of the inner magnetosphere during the expansion phase of the substorm. Figure RE) in the equatorial plane and plotted the result as a function of time. The panels in the top row  show such a representation of the radial flow velocity, Vr. The arrival of multiple BBFs is evident in both panels, and it is also clear that the first three major BBFs ocurring before t=20 min do not make it to the 6 RE radial distance. The first of them is the one that we already observed in Figure t=20 min, multiple BBFs penetrate to 6 RE, the first of which is the one depicted in Figure RE each earthward moving BBF (indicated by the blue color) is accompanied by two tailward moving flows flanking it marked by the red color. These flows are part of the vortical BBF structure  the magnetic field starts accumulating already with the impact of the precursor BBFs before t=20 min but the BBF frequency increases after this time, and as a result of these multiple dipolarizations the overall magnetic field grows substantially across the nightside between t=0 min and t=60 min . Figure Figures t=12 min between 160° and 180° azimuthal angle  After the earthward flow subsides and the BBF stops (this can be confirmed in Movie S1 and its zoomed‐in Version S2 in the SI), the flow exhibits clear earthward‐tailward oscillations. The black dashed line in Figure Vr(t) traces are shown in Figure Vr oscillation with a period of 2–3 min in the black trace after the earthward (Vr<0) flow stops  and t=30 min (light‐red trace). Furthermore, while midnight and premidnight exhibit a rather complex magnetic field evolution after the onset due to the constant bombardment by the BBFs and DFs , since virtually no convective electric field exists outside of them. In the bottom panels of Figure Eϕ between 20:00 and 04:00 MLT to assess the total magnetic flux transport rate dΨ/dt=Rxy∫2004Eϕdϕ toward Earth, where Rxy=6 or 8 RE is the radial distance in the equatorial plane (negative dΨ/dt corresponds to earthward transport under this definition). A few points are evident from these plots. First, the onset is clearly discernible just after t=20 min as an abrupt increase in the flux transport rate at both radial distances. Second, the integrated magnetic flux transport is all earthward, despite the existence of tailward rebound flows. Third, not only does the earthward flux transport occur exclusively via the azimuthally localized flow channels, it is also bursty in time even after integrated over azimuth.To address specifically the question of magnetic flux transport from the tail in a more quantitative fashion, we plot in Figure RE circles and the 20:00 and 04:00 MLT radial lines. The orange trace shows the cumulative earthward (negative) magnetic flux transport through the 8‐RE arc, while the blue trace shows the same for the 6‐RE arc. Clearly, much more flux flows earthward through the 8‐RE boundary than through the 6‐RE boundary. The green trace shows the imbalance between the two. To check how much of this unbalanced flux accumulates in the wedge region versus escaping azimuthally, we also calculate the azimuthal flux transport through the side (fixed MLT) boundaries of the wedge. The result is the red trace , which demonstrates an interesting detail: Before the onset, the azimuthal outflow from the wedge region exceeds the total radial inflow leading to the overall flux depletion; on the contrary, after the onset, the total radial influx surpasses the azimuthal outflow leading to the accumulation of the magnetic flux in the wedge region. This is indicated by the black trace, which is the difference between the green and red traces. Once presented this way, the simulation data clearly delineate the substorm onset as the time where the cumulative flux (black trace) changes sign. These results are consistent with the previous regional magnetotail simulations by Hsieh and Otto . Note also that since MMS was in the southern lobe, the field stretching is less pronounced at its location than at the more equatorial GOES satellites. The stretching is also accompanied by the intensification of Bx (By at GOES‐13 due its dawnward location) consistent with magnetic flux loading into the lobes. The simulation tends to underestimate Bx (and By at GOES‐13 and GOES‐14), which we discuss below. Second, toward the end of the simulation (10:00 UT) both the data and simulation indicate a significant increase in Bz at all spacecraft locations, indicating a global dipolarization. The magnitude of the dipolarization, and the degree of agreement between the simulation and observations, varies between the spacecraft, but what is important is that the overall strength of dipolarization is consistent between the model and data, which was the primary purpose of this comparison and gives credence to the simulation results reported above.While we discuss the time around the onset in more detail below, we remark here on two primary details seen in Figure By and Bz also agree quite well with those observed but Bx is underestimated at the actual spacecraft location (dashed lines). For GOES‐14, which is more dawnward, By is also underestimated. Since in this region the dipole magnetic field is still strong but quickly changing, a small shift in the spacecraft location will make a large difference in the observed field. To take this possibility into account, we shifted the virtual GOES‐14 and GOES‐15 spacecraft by 0.4 RE in the positive SM z direction. The data from thus modified virtual spacecraft are plotted with solid lines in panels (d) and (f) and show a much better agreement with the observations. Such a displacement of the virtual spacecraft could occur if the nightside magnetic configuration was shifted slightly southward . The figure complements Figures z coordinates of the spacecraft and confirms that the coordinate shift required for better agreement with the measurements in Figure By and Bz magnetic field components in the same format.We now turn to a more detailed discussion of Figure Bz=25, 40, and 55 nT  isocontours in the equatorial plane. The figure along with Movie S2 indicates that the equatorial projection of the MMS probe  was disturbed by the tailward return flow and a concomitant magnetic field fluctuation (more on this below.) However, since the probe was located significantly southward of the magnetic equator, it actually observed a dipolarization corresponding to the increased Bz in the tailward portion of the DF seen in Figure By component , resulting in the plasma sheet expansion  carrying significant magnetic field enhancements (DFs) penetrating to these near‐Earth distances from the plasma sheet. Figures t=20 min). Following it were many more such localized flows that cumulatively were responsible for the global dipolarization of the inner magnetosphere about 40 min after the onset , while after the onset the flux was elevated.We demonstrated above with the help of a global magnetosphere MHD simulation that in the expansion phase of the isolated substorm considered, all plasma convection and, therefore, magnetic flux transport within 8 t Figure . FurtherBy and non‐Vx SW velocity components) and ionospheric conductance . The total amount of earthward flux entering the 8 RE region between 20:00 and 04:00 MLT (∼50 MWb over roughly 30 min after onset) is much more in line with expectations from observations in the plasma sheet , the agreement with the above observational estimates is not surprising. In fact, the simulated electric field and flux transport rates in Figure The amount of magnetic flux accumulated on the nightside Figure  in the sBz) than its counterpart in reality  min  and magnetic field dipolarizations (DFs) were observed in the simulation during the growth phase of the substorm but did not penetrate to the geosynchronous orbit.The substorm onset was characterized by an abrupt increase in the number and intensity of BBFs/DFs, which penetrated well within the geosynchronous orbit.The global dipolarization of the inner magnetosphere toward the end of the substorm expansion phase was due exclusively to these azimuthally localized flows and dipolarizations. Negligible plasma convection or magnetic field transport occurred outside of these structures.Over the course of the expansion phase the penetration of BBFs within the geosynchronous orbit lead to a gradual accumulation of thermal plasma pressure there. Comparison with MMS plasma moments  showed a very good agreement between the model and observations both in terms of the magnitude and temporal evolution.RE and 20:00 and 04:00 MLT in our analysis), the expansion phase was characterized by magnetic flux accumulation.While the growth phase of the substorm was characterized by magnetic flux depletion in the nightside near‐Earth region (represented by a wedge‐shaped region between 6 and 8 RE radial distance. In particular, the strength of flows and dipolarizations were within a factor of 2 of those observed. Moreover, if the dipolarization was overestimated, the flow was underestimated, suggesting an even better agreement in the magnetic flux transport. Due to sporadic nature of BBFs/DFs, we do not expect the simulation to reproduce ideally even multipoint measurements. Thus, the above results serve as a strong confirmation of the validity of our results.The properties of the near‐Earth flows and dipolarizations were in general agreement with the observations by the GOES satellites at the geosynchronous orbit and MMS, located at ∼8.2 The simulations reproduced many previously reported observational signatures of BBFs and DFs in the near‐Earth region. In particular, we have demonstrated the existence of oscillating flux tubes that overshoot their equilibrium position and rebound tailward multiple times. The existence of strong vortical tailward flows on the flanks of the intruding BBF has also been demonstrated.Spacecraft located away from the intruding BBF can still observe significant disturbances due to it. In particular, if the spacecraft is located away from the equatorial plane, it can observe a complex mixture of reconnection, rebound, and dipolarization signatures, resulting in plasma sheet expansion, thinning, and expansion again. This leads, in turn, to multiple spacecraft excursions from the lobe into the plasma sheet and back. Furthermore, BBFs disturb the plasma and magnetic field ahead and on the side of them in a region significantly exceeding their azimuthal size, which can be seen by spacecraft not necessarily located directly in the path of the penetrating structure.In this paper, we carried out a high‐resolution global MHD simulation of the magnetosphere during an isolated substorm event. Through simulation analysis and cross examination with the observations by MMS and GOES spacecraft, which were fortuitously aligned in the inner magnetosphere, we have drawn the conclusions that are summarized as follows:Overall, this work demonstrates the power of high‐resolution simulations in providing deep physical insight, particularly, when used in conjunction with observations from multiple magnetospheric spacecraft. Given the high quality and sophistication of the underlying numerical algorithms running on modern computational resources, global models can now clearly capture many details of the real magnetospheric behavior, including processes occurring at mesoscale such as BBFs and DFs. It is when such model results are cross‐examined with the corresponding observational signatures that robust answers to physical questions can be gleaned.Supporting Information S1Click here for additional data file.Movie S1Click here for additional data file.Movie S2Click here for additional data file.


Social networks require active relationship maintenance if they are to be kept at a constant level of emotional closeness. For primates, including humans, failure to interact leads inexorably to a decline in relationship quality, and a consequent loss of the benefits that derive from individual relationships. As a result, many social species compensate for weakened relationships by investing more heavily in them. Here we study how humans behave in similar situations, using data from mobile call detail records from a European country. For the less frequent contacts between pairs of communicating individuals we observe a logarithmic dependence of the duration of the succeeding call on the time gap with the previous call. We find that such behaviour is likely when the individuals in these dyadic pairs have the same gender and are in the same age bracket as well as being geographically distant. Our results indicate that these pairs deliberately invest more time in communication so as to reinforce their social bonding and prevent their relationships decaying when these are threatened by lack of interaction.The online version of this article (doi:10.1140/epjds/s13688-016-0097-x) contains supplementary material. For intensely social species like primates, close friendships buffer the individual against the stresses of living in enforced proximity to others, and so make living in social groups possible , 2. In bIn this paper, we use a large dataset from a mobile phone service provider in a European country, spanning over seven consecutive months in the year 2007, to investigate whether humans adjust their investment effort to compensate for reduced contact. To do this, we first examine whether the duration of calls is related to the time since last contact, and then ask whether this is especially true of individuals who are geographically further apart (and hence cannot meet up in person so easily). For a given ego  we study the data on mobile phone communication with the alters  with whom the communication events are sufficiently spaced in time yet showing a degree of regularity. In the offline world, individuals who are contacted at least once a month fall into the category of close, as opposed to intimate, friends, and constitute the second most important group of network alters , 26. As i and its alter j, we construct the set of ordered pairs ij, we define For a given ego-alter pair we measure the inter-event time (‘gap’) between two successive calls in number of days irrespective of the directionality of the calls. Then we examine the variation in the duration of the succeeding call (in seconds) as a function of the length of the inter-event time. For analytical convenience, instead of considering individual calls we aggregate all calls in a given day and ignore the days in which the total calling time is less than 10 seconds. Thus by mentioning ‘call’ or an ‘event’ with respect to a given pair on a particular day we refer to the aggregated voice communication on that day. For a given ego We concentrate on the ego-alter pairs for which the communication is sufficiently spaced over time by considering the set of pairs, iven ego  and for mentclass2pt{minimmentclass2pt{minimFirst we show the probability distribution of the gaps and the call durations corresponding to pairs belonging to the set mentclass2pt{minimmentclass2pt{minimβ, the stronger is the dependence. The coefficient α provides a basal value for the duration of the calls. In Figure β for the different ages and genders (filled symbols). Overall, the effect is strongest in the age range of 25-40 year olds and for same-sex pairs. In Figure entclass1pt{minimaij, we construct an ensemble of artificial sets β’s resulting from the regression on the randomized data in Figure The dependence of entclass1pt{minimaTo extract the behaviour in a form that is independent of the characteristics of the ego-alter pairs, we scale the variables for a given pair with their corresponding averages. The dependence of the scaled variable To closely examine the nature of the ties we construct the distribution of alter age-ego age for the pairs in mentclass2pt{minimWe further categorized the pairs in the set ower law . Also, aower law . We choomentclass2pt{minimmentclass2pt{minimα, β and α with the increase in distance. However, variation with average gap is not significant. The fact that females are involved in longer calls than the males is also evident. For the β’s we observe a variation with distance very similar to α. However, there is a marginal dependence on the average gap. These facts suggest that the reinforcement effect is stronger when the calling frequency is low and the distance of separation is large. The values of β’s persist when the data is scaled. It also shows a strong gender homophily as the In Figure mentclass2pt{minimOur main focus in the study has been with whether individuals adjust the time investment they make in relationships that matter to them when these are at risk. Our index of being ‘at risk’ was a greater than the average gap between contacts . Friendships require constant time investment for their maintenance, and failure to match quite specific investment schedules leads inexorably to a rapid reduction in relationship quality , 22, 26.If we assume the complete or partial lack of face-to-face contact in such relationships , then the lack of opportunity for face-to-face communication would naturally make it difficult to maintain relationship quality over time. The increase in the duration of the succeeding call after a long gap  could thus serve as an act of relationship repair. The nature of the calls can also be inferred from the peaks (in multiples of 7 days) in the distribution of gaps  are known and who are active over the entire period of seven months. We use the following criteria to select ego-alter pairs for whom the communication is sufficiently spaced over time. We consider the pairs for whom the maximum number of calls in any calendar month does not exceed α, β and α. However, both β and We find that the qualitative nature of our findings is sufficiently robust and is not delicately dependent on the choice of the different thresholds to define mentclass2pt{minimmentclass2pt{minimquantity .Supplementary material. (pdf)Below is the link to the electronic supplementary material.