Thermoelectric materials are sometimes prepared using a sintering process in which the achievement of a high density is often one of the objectives. However, it has recently been shown that the introduction of a highly porous material is desirable in synthetic transverse thermoelements. Porosity may also be an advantage in conventional longitudinal thermoelectric modules in which a high thermal flux density creates problems, but heat transfer within the pores can degrade the thermoelectric figure of merit. The amount of this degradation is calculated and it is shown that it can be small enough to be acceptable in practical devices. The theory of thermoelectric energy conversion shows that the performance depends on the ratio of electrical to thermal conductance in each of the thermoelements . It is uAt first sight it might appear that porosity should not affect the performance since it should not change the ratio of electrical to thermal conductance, if there is no transport of electricity or heat within the pores. In fact, there may well be an advantage in reducing both conductances by the same proportion. The cost of material is a significant factor for the manufacturers of thermoelectric modules and there is a trend towards the use of thermoelements of reduced length and cross-section . Howeverx0 direction the Seebeck coefficient is dominated by the component with the higher thermal resistance whereas in the y0 direction it is dominated by the component with the higher electrical conductance. We shall show that the performance of synthetic transverse thermoelements can be improved if one of the components is porous.There has recently been renewed interest in the practical use of the transverse thermoelectric effects . TransveIn theory the behaviour of a thermoelement should not change if the length and cross-section area are increased or decreased by the same proportion. However, as the dimensions of the thermoelements are reduced, the performance of the module in which they are incorporated is impaired. This is because of the increasing importance of electrical contact resistance and thermal gradients at the faces of the module. It is possible to reduce the thermal flux density by increasing the spacing between the thermoelements but there is then the possibility of heat losses by radiation and conduction in the unoccupied space . An alteZ defined by the relation:α is the Seebeck coefficient, λ is the thermal conductivity, ρ is the electrical resistivity and the subscripts A and B denote the two branches.The performance of a thermoelectric energy converter  can be eThe effect of electrical contact resistance is to increase the apparent electrical resistivity. Thermal resistance between the module and the source and sink, associated with a high flux density, decreases the coefficient of performance or the efficiency. Both these effects have been discussed previously with a view to minimising the volume of thermoelectric material by using widely spaced thermoelements of small length and cross-section . Here wel separated by material of width 2w. Each cell then consists of a cubic space surrounded by a wall of thickness w. It is assumed that the electrical and thermal flow is linear, an approximation that improves as the porosity becomes greater. It is appreciated that the pores in an actual material will probably be quite different from those in our model but the effect on the transport properties is likely to be realistic. One characteristic that will probably exist in any material with a high porosity is inter-connection between the pores. This feature does not exist in our model.We make use of the model for a porous material shown in The heat losses will obviously be smallest if the pores are evacuated since then only radiative transfer will take place. The radiation loss can be reduced to any desired level by making the number of cells in a given volume as high as possible, so that the temperature difference between the opposite faces of a pore is very small. There will be applications in which evacuated pores can be realised but it has to be remembered that thermal conduction in a gas does not disappear until the mean free path of the molecules is much greater than the width of the containing vessel. This requires a very high vacuum. Inter-connection between the pores will assist in allowing the penetration of a vacuum or any filling gas throughout the material.pλ, which will generally be much less than the thermal conductivity λ of the thermoelectric material. We then find that the thermal conductance of each cell is given by:Usually the pores will be filled with a gas of thermal conductivity If the thermal conductivity in the pores were equal to zero the thermal conductance per cell would be:cK/K0 and this is equal to the ratio of the figure of merit pZ of the porous material to that Z of a fully dense specimen. We have calculated this ratio for the pores being filled with air, carbon dioxide and krypton. The thermal conductivity of air is 0.026 W/m K. The losses are reduced by using carbon dioxide (pλ = 0.013 W/m K) instead of air and become still less if the filling gas is krypton (pλ = 0.008 W/m K) [p for these three cases. We define the porosity factor p as the ratio of the electrical conductivity in fully dense material to that of the porous material. Since the electrical conductivity is zero within the pores:The ratio of the effective thermal conductivity of the porous material to that which would exist if the pores did not conduct the heat is 8 W/m K) . In Figuλ might be 1.0 W/m K. This value has been assumed in our calculations. The thermal conductivity of the fully dense thermoelectric material will, of course, depend on its composition. We shall assume that the material is a sintered bismuth telluride alloy for which a typical value of p is equal to 10 when the relative density is about 0.15.x,y and the axes x0,y0. One can then determine a transverse figure of merit φZ that has the same significance in a transverse energy converter as does the figure of merit Z for a conventional thermocouple [We now turn to the inclusion of a porous component in a synthetic transverse thermoelement. It is supposed that the specimen is cut from a layered structure as shown in mocouple .B layers is much higher than that of the A layers in the y0 direction. Then the Seebeck coefficient in that direction will lie close to its value for the B layers. We also suppose that the thermal resistance in the x0 direction is dominated by the A layers. Then the Seebeck coefficient in that direction will be nearly equal to that of component A. It is most desirable that the Seebeck coefficient should be very different and preferably of opposite sign in the two components. It is also necessary that the two materials, A and B, should have a high thermoelectric figure of merit Z when used as a conventional thermocouple [Z, because of internal thermoelectric eddy currents, but the difference may be quite small.Let us assume that the electrical conductance of the mocouple . The traB much larger than that of component A in one direction and the thermal resistance of component A much the larger in the other direction. One really requires AλBσ/BλAσ >> 1. Kyarad and Lengfellner [In the past, it has been difficult to satisfy these requirements using fully dense materials. The best conventional couples for use at ordinary temperatures make use of p-type and n-type bismuth telluride alloys . Howevergfellner  resolvedgfellner  using a AλBσ/BλAσ >> 1 can be achieved in principle when both components consist of bismuth telluride alloys if one of them is porous. However, it would be necessary to have an extremely high porosity with no significant heat transfer through the pores. A high transverse figure of merit could be reached much more easily by combining porous p-type sintered bismuth-antimony telluride with the metallic conductor, YbAl2.96Mn0.04, which has the reasonably high negative Seebeck coefficient of -90 μV/K [φTZ equal to almost 0.7 when the porosity factor p in the p-type component is about 10 and when the pores are evacuated. We have shown previously  that the-90 μV/K . We haveWe have now determined the variation of the transverse figure of merit with the porosity of the p-type component taking into account heat conduction within the pores. The results are shown in φTZ is equal to about 0.56 when the porosity factor is 6. Values of φTZ in excess of 0.6 should be achieved for a porosity factor of about 10 if the pores are filled with carbon dioxide or krypton. This means that a rectilinear thermomagnetic cooler made from porous bismuth-antimony telluride and YbAl2.96Mn0.04 operating from a heat sink at 300 K should be able to achieve a maximum temperature depression in excess of 60º. In view of the ease with which an infinite-staged cascade can be produced using a shaped transverse thermoelement, it is likely that a temperature depression of more than 100º might be achieved using a positive component with evacuated pores.It is apparent that porosity in the p-type component produces a substantial increase in the transverse figure of merit even when the pores are filled with air. In this case, the maximum value of We have shown that there may be a practical advantage of economical use of material without reduction in performance if porous thermoelectric materials are used in the fabrication of modules. However, the most important use of such materials is likely to be in synthetic transverse thermoelements. The transverse thermoelectric figure of merit reaches a substantially higher value if a fully dense bismuth-antimony telluride alloy is replaced by material with a porosity factor of about 10. The improvement is greatest if the pores are evacuated but is still large if the pores are gas-filled particularly if a gas with a low thermal conductivity, such as krypton, is employed.


The simulated contrast scans confirmed that the use of contrast‐enhanced CT scans for routine treatment planning would result in a systematic change in the dose delivered to the isocenter. The devised correction strategy had no clinically relevant effect on the dose distribution for the original CT scans. The application of the correction strategy to the simulated contrast CT scans led to a reduction of the mean difference in the overall MUs to 0.1 ± 0.2% compared to the original scan, demonstrating that the effect of contrast was eliminated with the correction strategy. This work has highlighted the problems associated with using contrast‐enhanced CT scans in heterogeneity corrected dose computation. Contrast visible in the CT scan is transient and should not be accounted for in the treatment plan. A correction strategy has been developed that minimizes the effect of intravenous contrast while having no clinical effect on noncontrast CT scans. The correction strategy allows the use of contrast without detriment to the treatment plan.The aim of this study was to investigate and, if possible, compensate for the effect of intravenous contrast‐enhanced CT scans on the treatment planning dose distributions for lung patients. The contrast and noncontrast CT scans of 3 patients were registered, and the effect of contrast on the Hounsfield units (HU) was assessed. The effect of contrast was then simulated in the CT scans of 18 patients receiving radiotherapy of the lung by modification of the CT numbers for relevant sections of noncontrast‐enhanced CT scans. All treatment planning was performed on the PinnaclePACS number: 87.53.Tf Three‐dimensional conformal radiotherapy has led to a more accurate delivery of radiotherapy and the possibility for dose escalation and lower toxicity. However, to fully gain from this, accurate delineation of the gross tumor volume (GTV) is essential. In the case of the lung, large margins are added to the GTV to compensate for breathing and cardiac motion, leading to increased toxicity as a larger volume of normal lung tissue is irradiated. The accurate definition of the GTV in this case is important in minimizing the overall treatment volume. However, studies have shown that this can be difficult, and GTV definition in the lung has been found to vary significantly among professions, centers, and levels of experience.,2Modern 3D treatment‐planning systems use the density information within the CT scan to account for the different tissue densities within the body. This is to ensure that the dose calculated will be a true representation of the dose distribution within the body. The attenuation of radiation at therapeutic energies is dominated by Compton scatter, which is dependent on electron density. The Hounsfield units (HU) from the CT scan are converted to either electron or physical densities via a CT number to density conversion table within the planning system. From this, the mass attenuation coefficient can be found using a look‐up table; the degree of attenuation can therefore be predicted. In the case of the Pinnacle treatment‐planning system, the fluence attenuation table is stored as a function of radiological depth, physical density, and off‐axis angle. The physical density allows the attenuation of the fluence to be based on the mass attenuation of the specific material within a given voxel. This correction is particularly important in lung cancer treatment planning due to the low density of lung tissue. If this is not corrected for in the dose calculation, the delivered dose can be as much as 15% greater than expected.Lung cancer is the most common cause of cancer death in the developed world. Both small cell and non‐small‐cell lung cancers tend to involve central structures within the thorax by local invasion and lymph node metastases. As part of diagnosis and staging, CT scans of the thorax are performed using intravenous contrast to differentiate the numerous vascular structures from other tissue that may be involved with the cancer. When the patient attends at a later date for treatment planning, this advantage is lost if contrast material is not used as part of the radiotherapy planning CT scan. Contrast‐enhanced CT scans can be used to aid in the definition of the GTV to distinguish the tumor from vascular structures, particularly in the mediastinum.Contrast agents are made up of elements with high attenuation coefficients peaks in the diagnostic energy range, such as iodine. These peaks result in a high HU, which is interpreted as higher‐density tissue on the CT scan. The dose distribution computed by the planning system may therefore be misleading. A previous study has shown that the use of contrast media in CT scanning does lead to a change in the dose calculated by a 3D treatment‐planning system. If the absolute volume containing contrast agent and the corresponding increase in HU are limited, the difference will be 1% to 3%.A possible method to avoid this calculation error is to register pre‐ and postcontrast scans. This has the advantage of increased visualization, and the treatment could be planned on the noncontrast scan to ensure an accurate dose calculation. This can be done with accuracy for other sites that are anatomically stable, such as brain tumors. However, the movement associated with the lungs due to respiration and cardiac motion makes this less feasible. With fast CT scanning the breathing phase of each slice is slightly different than the previous and next slices. Consecutive scans of the patient are therefore unlikely to be easily registered unless the same phase of the breathing cycle is present at the start of the acquisition for both scans and the patient breathing is consistent between them. Another possibility is to ignore heterogeneity in the dose calculation, but, as already stated, the effect on the dose distribution is unacceptable in the lungs.The aims of this study were to investigate the magnitude of the effect of an intravenously administered contrast agent on the dose distributions computed by a 3D treatment‐planning system, to develop a strategy for using intravenous contrast scans without significantly altering the dose distribution, and, finally, to quantify the residual error as a result of using this strategy.The treatment plans of 18 patients who had undergone radiotherapy for lung cancer at the Christie were collated for this investigation. The 18 patients were chosen as a representative sample of differing tumor size and location as expected from clinical experience. All had been planned on the Pinnacle120 kV/210 mA. The contrast was intravenously injected using an Envision CT™ injection system and the scan acquisition initiated after a predefined threshold CT number had been reached. This threshold was set at 50 HU above the baseline value in a region of interest within the ascending thoracic aorta. Two hundred milliliters of Omnipaque® contrast agent containing 140 mg/mL of iodine was used as standard contrast. The contrast‐enhanced diagnostic scans were exported to Pinnacle for comparison to the corresponding radiotherapy treatment‐planning (RTP) scans performed on either the GE Medical Systems Lightspeed or GE Medical Systems CTI scanner at 120 kV. The relationship between HU and physical density for the two scanners has been investigated and found to be equivalent, allowing a comparison of density to be made irrespective of the CT scanner used. An example of the difference between the two scans is shown in Fig. The initial part of the investigation evaluated the effect of using a contrast‐enhanced CT scan on the dose calculation. For three patients in the investigation, diagnostic quality contrast‐enhanced CT scans had been acquired as part of the patients' management and were available in DICOM format. These were acquired on the GE Medical Systems Lightspeed Plus CT scanner at To simulate the effect of using a contrast CT scan in the planning stage, the density of the mediastinum in the RTP scan was increased corresponding to the typical increase in HU seen on the contrast scans. The density of the GTV was also increased by the same amount. A similar degree of enhancement was assumed due to the increased vascularization of the tumor and a worst‐case scenario. The mediastinum was outlined in each of the 18 patients, and the mean HU was found from the Pinnacle software. The CT number in the mediastinum region and the GTV was then increased in turn by 50 HU, 100 HU, and 200 HU to include the range of HU increase seen in a contrast‐enhanced CT scan and an estimation of an expected upper limit for HU enhancement given the limited available data. This range is due to the variation in circulation and heart rates of the patients. This was achieved by overriding the CT number for the region of interest within Pinnacle with the new value. This is illustrated in Fig. The dose distributions within the 80% isodose were compared using a software tool developed in‐house1 g⋅cm−3 and 1.2 g·cm‐3 were set equal to a density of 1 g⋅cm−3. This range covers the increased densities resulting from simulating contrast in the CT scan. At densities above 1.2 g⋅cm−3, the CT to density table corresponded to its original clinical values (bone region). This will correct the effect of the artificially high‐density tissue regions arising due to the contrast media, but would also allow a heterogeneity correction for the effects of high‐density materials such as bone. The two CT to density tables used in the study are shown in Fig. A strategy was developed in order to minimize the effect of using a contrast‐enhanced CT scan in the radiotherapy planning stage without significantly altering the dose distribution computed by the planning system. The CT to density conversion table used clinically was altered to reduce the effect of the increased density due to the contrast agent. Tissues with a density between The final stage was to investigate the effect of using the correction strategy on the simulated contrast‐enhanced CT scans. The dose distribution for each patient (with the varying degrees of HU increase) was computed using the modified CT to density table. The MUs to prescribe the required dose were then compared to those for the original plan. Finally, the dose distribution analysis using the gamma evaluation software was repeated to ensure that any variations in the dose distribution resulting from the use of contrast‐enhanced scans were reduced by applying this correction strategy.For the three representative patients the comparison of contrast with noncontrast CT scans showed that the difference in HU for the majority of soft tissue was negligible between the two scans. However, the HU for the mediastinum increased in the contrast scan by an average of approximately 100 HU, ranging from 60 HU to 130 HU. The HU of the lungs was found to decrease by an average of 70 HU in the contrast scans.Because the soft tissue showed no significant increase in HU in the contrast‐enhanced scan, the soft tissue density of the RTP scan was not altered in the investigation. A slight decrease in HU was seen for the lung tissue, but this must be treated with caution. As already stated, the setups of the diagnostic scan and the RTP scan are very different. One of the main differences is in the breathing protocol; during the RTP scan, the patients are free to breathe, whereas the patients are asked to hold their breath at inhalation for the diagnostic scan. This results in a larger volume of air within the lungs for the diagnostic scan, hence decreasing the apparent density of the lung tissue on the scan. This is the likely reason for the apparent decrease in the lung density rather than any effect of the contrast administered. In the treatment setting the patient will be breathing freely; therefore, no alteration to the lung tissue density was made.Increasing the CT number of the mediastinum and GTV in the range 50 HU to 200 HU was sufficient to cover the range of values found in the limited datasets available with contrast media and to investigate the effect of using higher concentrations of contrast media in the scans.0.99 g⋅cm−3 and 0.94 g⋅cm−3, respectively), the effect of contrast on the GTV was still taken into account by simply increasing the density of the mediastinum in these cases.In the noncontrast scans, the densities of the mediastinum and the GTV were overridden to simulate the presence of contrast agent in the CT scan. For 3 of the 18 patients in the study, the clinician had not outlined the GTV. However, in all of these cases, the GTV was within the mediastinum. Because the densities of the mediastinum and the GTV were found to be similar , but an increase of 100 HU had a larger effect on the MUs with an average percentage difference of 0.7 ± 0.8% and a maximum difference of 3.5%. An increase of 200 HU led to an average 1.0 ± 1.0% increase in the number of MUs prescribed with a maximum increase of approximately 5%. From the range of increased HU values of 60 to 130 seen in the diagnostic scans, it would appear that the contrast‐enhanced CT scans can be used for treatment planning without significant changes to the dose distribution or the MUs prescribed.In general, the percentage difference in MUs prescribed increased as the density was increased, as expected. This is due to the increased attenuation of the beam as it passes through higher‐density tissue. More MUs are therefore required to achieve the prescribed dose to the isocenter. To summarize the results for individual beam data, little difference was seen with an increase of 50 HU , so the effect of contrast is diluted. Despite this, the average increase in MUs is still approximately 1% with a maximum increase of over 3% when a 200 HU enhancement of the mediastinum and GTV is observed.The difference in the MUs prescribed to deliver a dose to the isocenter with contrast present in the CT scans provides a measure of the potential overdose to the prescription point at treatment because the density predicted by the planning system will not be present at that time. However, the difference in the MUs does not offer an indication of the variation in the dose distribution due to the presence of contrast. In order to examine this variation, gamma evaluation was used to determine differences in the dose distributions between the original plan and the plan created when the MUs from the plan with the contrast were applied to the original noncontrast scan. The results are summarized in Fig. 1.01 g⋅cm−3 to 1.18 g⋅cm−3, usually describing tissue from fat and water (1.0 g⋅cm−3) through to muscle (1.1 g⋅cm−3). Higher‐density bone such as the spine was found to have a mean density of around 1.3 g⋅cm−3.When the mediastinum and GTV were outlined, the ranges of density for contrast and noncontrast scans were taken into account when designing a modified CT to density table. The density range was found to be −0.2±0.2% for individual beams and −0.2±0.2% for the overall patient MUs. The results are shown in Fig. −0.6%. This demonstrates that using the modified CT to density table on the noncontrast CT scans has negligible effect on the dose distribution when compared to the original plan. Therefore, the correction strategy can be further explored and tested on the simulated contrast CT scans.The mean difference between the MUs for noncontrast scans calculated using the clinical CT to density table and those calculated using the modified CT to density table devised for this project was −0.2% for both the individual beams and the overall patient with maximum values of −1.0% and −0.5%, respectively. There was no variation in the differences seen with increasing HU, demonstrating that the modified CT to density table achieves its goal in eliminating the effects of contrast.The results of applying the modified CT to density table are presented on an individual beam basis as well as an overall difference for each patient. The results shown in Figs. 2%/mm criterion. Again, the results have been produced on the same scale as in Fig. The gamma evaluation also produced excellent results as shown in Fig. Ideally, contrast‐enhanced CT scans would be used to assist in delineating the GTV in carcinoma of the lung. However, due to the heterogeneity correction applied in the calculation of dose for this site, the presence of contrast introduces an error in the dose calculation that must be considered and corrected for if significant; otherwise, a systematic error will be introduced into the treatment at the planning stage. Using simulated contrast scans of the lung, we have shown that the error resulting from using a heterogeneity correction in the presence of contrast is as high as 5% for an individual beam. This assumes an increase of 200 HU in the CT number of the mediastinum and GTV, but even with only a 100 HU rise in the CT number a maximum increase of 4.5% was seen. However, if low concentrations of contrast media are used for the visualization, then the resulting dose distribution without any correction strategy will only contain approximately 1% error on average. Given the improvement in the delineation of the GTV that may be achieved with low concentrations of contrast, the introduction of a 1% systematic error in the dose distribution is likely to be clinically acceptable.The MUs increased when the contrast CT scan was used because the CT numbers of the mediastinum and GTV were artificially high. This resulted in the dose algorithm assuming a greater attenuation of the incident radiation and calculating that more MUs would be required to deliver the prescribed dose to the isocenter.The results highlight the error that could result from using a contrast scan in the dose calculation of the planning stage. This error may in fact be worse when a true contrast‐enhanced CT scan is used. In the simulated scans, only the mediastinum and GTV were overridden with an increased CT number. Due to outlining limitations and structure delineation, the CT number enhancement of all structures within the limited contrast scans available could not be assessed. Therefore, there may be areas of contrast uptake that have not been fully taken into account in this study. The range of HUs considered does, however, seem comparable to the findings of other studies.In order to use a contrast‐enhanced CT scan in the planning stage without significantly altering the dose computation, a correction strategy was developed that involved modification of the CT to density table in the planning system to eliminate the effect of the contrast agent on the dose calculation. The results were very promising when this modified CT table was applied to a noncontrast scan with the overall patient MUs within 0.6% of the MUs for the original plan for all 18 patients. The modified CT table also had the desired effect when it was applied to the simulated contrast scans. The differences between the MUs calculated and the MUs for the original plan were all within an acceptable clinical uncertainty of 1% for each individual beam as well as for the overall patient, reducing possible systematic errors of up to 5%. This means that a contrast‐enhanced CT scan may be used in the planning stage of the radiotherapy treatment without significantly affecting the delivered dose distribution with no contrast present.; therefore, the dose computation would be less affected. Oral administration of contrast agent, for example, in enhancement of the bladder, produces a bolus distribution of enhancement with large HU increases. Often the density is similar to cortical bone, calcifications, or metal prostheses, so this cannot be ignored in the dose calculation without serious detriment to the resulting dose distribution. This is a separate problem, and a correction strategy such as described here would not be suitable in this case.This work has considered chest scans using contrast administered intravenously. A similar technique could therefore be used for intravenous contrast in other sites such as the brain. However, the presence of the blood brain barrier results in less contrast enhancement in the brain,14; This work has highlighted the problems associated with using contrast scans when a heterogeneity correction is applied in the dose calculation. A correction strategy has been developed that minimizes the effect of contrast on the dose computation. This has been shown to work well on simulated contrast scans and potentially allows the use of intravenous contrast CT scans for routine treatment planning in the thorax region. To take the investigation further, the next stage would be to assess the use of the correction strategy on true contrast scans of the lung. This will ensure that the strategy is suitable to be used clinically.


Low-intensity pulsed ultrasound (LIPUS) has presented good results in the healing of chronic wounds. The objective of this study was to compare the effect of LIPUS on the viability of transverse rectus abdominal muscle (TRAM) flap in different regions  in rats.Twenty-one Wistar male rats were homogeneously distributed into three groups as follows: group 1 (control), animals submitted to surgery only; group 2, animals submitted to surgery and application of LIPUS at the center of the flap; and group 3, animals submitted to surgery and application of LIPUS at the flap area corresponding to the right inferior epigastric artery pedicle. Stimulation was performed immediately after the surgery and within the following 2 days. The percentage of flap necrosis was evaluated by using the ImageJ® software as well as by measuring the temperature variation with infrared thermography (FLIR® T300).In the percentage calculation of the necrosis area, the application of LIPUS at the center of the flap (group 2) showed significantly smaller difference (26.2 %) compared to group 1 (54.50 %) and group 3 (44.01 %). Analysis of the temperature variation between the groups was performed by using the one-way ANOVA followed by Tukey’s test. The results showed that both forms of LIPUS application showed significant differences compared to the control group.In view of our results, one can conclude that the application of LIPUS at the center of the flap was effective for the viability of TRAM flap in reducing the necrosis area. Silicone implants, deep inferior epigastric perforator, and transverse rectus abdominis myocutaneous flaps are used for reconstruction of the breast tissue. Silicone-gel prosthesis is a popular option which is naturally associated with shorter surgery time and shorter hospital stays as the use of autologous tissues allows more natural and apoptotic breast cells to grow, with the breast tissue becoming less edematous and smoother as the patient ages , 2.The transverse rectus abdominal muscle (TRAM) flap has been widely used for breast reconstruction, but there is a high risk of failure due to necrosis , which mSeveral therapeutic resources are indicated in the literature for minimizing the necrosis of flaps, such as transcutaneous nerve electrical stimulation , electroThe low-intensity pulsed ultrasound (LIPUS) was developed for consolidation of complex bone fractures by promoting an increase in the migration of osteoblasts , 10. HowThe incidence of necrosis in TRAM flaps occurs at different levels, affecting the further areas of the epigastric artery where the highest necrosis rates are found . TherefoThis study has been approved by the Animal Research Ethics Committee of the Medical School of Ribeirão Preto, University of São Paulo, Brazil, according to protocol number 058/2014.Twenty-one Wistar male rats weighing 280–300 g were randomly distributed into three groups of seven animals each: group 1 (control), animals submitted to surgery with TRAM flap only; group 2, animals submitted to surgical procedure and application of LIPUS at the center of the flap; and group 3, animals submitted to surgical procedure and application of LIPUS at the area corresponding to the pedicle with irrigation of the right inferior epigastric artery (flap zone 1).. Prior to the surgical procedure, the animals were anesthetized with intra-peritoneal injection of ketamine (Agener União®) and xylazine (Dopaser®) at concentrations of 0.1 and 0.07 mL/100 g, respectively. Next, the animals were positioned on a surgical board and submitted to hair removal by means of manual traction followed by surgical procedure for obtaining the myocutaneous flap from the transverse rectus abdominal muscle (TRAM) unilaterally and caudally. The flaps measuring 5 cm in the lateral-lateral direction and 3 cm in the cranial-caudal direction were positioned at 1 cm  from the xiphoid process [The animals were maintained and housed in individual cages with a 12-h light-darkness cycle and fed with proper food and water ad libitum process .2, 1.5 MHz resonance frequency, pulsed mode with pulse width 200 μs and 1 kHz repetition frequency, circular transducer of 22 mm and piezoelectric element PZT [The parameters of the device were set to the following values: SATA low intensity 30 mW/cmment PZT . The ultThe transducer was coupled with sterile gel water-based and water-driven equipment through an on/off button. The application of ultrasound was performed once a day for 20 min on a stationary basis immediately after the surgery and within the following 2 days for a total of three applications. Group 2 had the ultrasound transducer positioned at the center of the flap, whereas group 3 had it positioned at the flap zone 1, as shown in Fig. The percentage of necrosis area was assessed on the fourth day following the surgery by using the ImageJ® software. In order to delimit the area of viable tissue from the necrotic one—the former characterized by a pinkish color and smooth surface and the latter being cold and darkened, a paper template schematized on vegetable paper was used. Calculation was performed by dividing the necrotic flap area by the total area and then by multiplying the result by 100.For analysis of the temperature variation of the flap, images were made on the fourth day following the surgery by using the Flir QuickReport® software. The images were recorded with an infrared camera . The flaps were analyzed by dividing them into four zones or areas, with zone 1 (Z1) corresponding to the vascular region of the right inferior epigastric artery Fig. . The fouone-way ANOVA and post hoc Tukey’s test. The SPSS version 13.0 software (SPSS Inc. USA) was used for data analysis with a significance level set at 5 %.Data normality was assessed by using Shapiro Wilk’s test for all variables, whereas analysis of the necrosis percentage and temperature variation between groups was performed by using The results found by the use of the ImageJ® software were applied to the formula to calculate the percentage area of flap necrosis. The corresponding values are shown in Fig. p < 0.05).The analysis of necrosis percentage was performed by using one-way ANOVA and post hoc Tukey’s test, demonstrating that there was a significant difference between controls and the group stimulated with ultrasound applied to the center of the flap  is a therapeutic resource whose efficacy has been demonstrated in the processes of healing , 20, thuThermography has been widely used for detection of circulatory alterations by means of temperature , 22. In In the present study, the viability of myocutaneous flaps was found to be higher in the group stimulated at the center of the flap compared to that with stimulation of the epigastric artery and controls. These findings may be related to the increase in microcirculation as a result of mechanical waves .The use of LIPUS reduces the damage to cells caused by the applied energy as both fibroblast proliferation and circulatory increment are stimulated, which contributes to cell repair . In addiIn a study using pluripotent stem cells, artificially induced in culture plates, LIPUS was applied for 7 days and improvement in cell viability was observed soon on the second day of application. The most significant results were found on the fourth day in terms of viability and proliferation of the cells, thus corroborating our study as viability was also observed on the fourth and last days after the surgery .Based on the results found in the present study, one can conclude that the viability of TRAM flap was higher with the application of low-intensity pulsed ultrasound at the center of the myocutaneous flap.


We present the idea and design of a dual polarized metasurface for electromagnetic energy harvesting. A 4 × 4 super cell with alternating vias between adjacent cells was designed to allow for capturing the energy from various incident angles at an operating frequency of 2.4 GHz. The collected energy is then channeled to a feeding network that collects the AC power and feeds it to a rectification circuitry. The simulation results yielded a radiation to AC and an AC to DC conversion efficiencies of around 90% and 80%, respectively. As a proof of concept, an array consisting of 9 super cells was fabricated and measured. The experimental results show that the proposed energy harvester is capable of capturing up to 70% of the energy from a planewave having various polarizations and converting it to usable DC power. Such applications include cloaking6, energy harvesting10, negative index of refraction11, perfect lensing12, and perfect absorption13. In metamaterial perfect absorbers, the unit cells are designed in such a way to produce a surface impedance matched to free space. This can be achieved by tuning the Metamaterials can be made by assembling electrically-small resonators which can take different shapes and composite materials. The fact that a metamaterial surface can be engineered to produce an effective medium having simultaneously negative permeability and permittivity has ignited a number of unprecedented applications in various frequency bands from acoustics7. In the paper, an array of 14 unit cells was used to fully absorb an incoming plane wave at 3 GHz. Unlike metamaterial absorbers, here the absorbed energy is mainly dissipated across resistive loads placed at the feed of each resonator. However, the work was focused on maximizing the radiation to AC conversation efficiency. The array was also sensitive to the polarization of the incoming wave, maximizing the efficiency for only one single polarization. What is important for electromagnetic microwave energy harvesting/scavenging is to maximize the captured ambient energy from all polarizations. Moreover, instead of resistive loads, a rectification circuit has to be implemented to maximize the radiation to DC efficiency forming a full rectenna (rectifying antenna) system19.In a recent article, a metamaterial surface inspired by the perfect absorption concept was introduced for electromagnetic energy harvestingIn this paper, we propose a dual polarized electromagnetic energy harvester using an array of ELC resonators to form a metamaterial medium. The radiation to AC and the AC to DC conversion efficiencies of the array are studied numerically and experimentally.μm. The side length of the super cell is P = 70 mm having a footprint area of A = 49 cm2.A unit cell of the proposed dual polarized harvester is shown in Fig. mentclass2pt{minimThe choice of the number of cells contained within the super cell is specifically important for the feeding network. One can choose a super cell that contains only two cells as showing in the inset of Fig. 20. The super cell was placed in a waveguide where the lateral walls were assigned periodic boundary conditions in order to simulate an infinite periodic surface. The waveguide was excited by a Floquet port having a power level of 1 W and two incident wave polarizations as shown in Fig. The unit cell was studied using the full wave simulator HFSSWhen each cell is terminated by a load resistance of R = 175 Figure mentclass2pt{minim16. In this method16, the number of diodes were equal to the number of cells in the system. This can be in the range of hundreds depending on the size of the harvester, thus the total cost of the system will increase. In addition, the AC to DC conversion losses increase linearly with the number of diodes. Other channeling mechanism reported recently use a feeding network to channel all the collected AC power to a single diode or rectification circuitry21. In these methods the AC losses of the feeding network, especially for large footprints, can be significant.To channel the energy to the desired load, each cell can be terminated by a diode instead of the resistor. Thus, each individual cell converts the incident electromagnetic energy directly to DC. Then the DC power contribution from each cell can be combined through DC buses to a single load as was done in a recent workIn this paper, we propose a new channelling mechanism that combines both AC and DC channeling networks as shown in Fig. The feeding network is placed on top of an RO4003 Rogers dielectric substrate having a thickness of 1.524 mm, loss tangent of The simulated scattering parameters are shown in Fig. The complete system is then analysed in the receiving mode to test the amount of energy captured from each incident polarization. The two feeds where terminated by R = 175 Ω and the super cell was excited by an incident wave having a normalized power of 1 W. The radiation to AC efficiency of both polarizations is shown in Fig. Taking into consideration the results obtained for the radiation to AC power conversion, a rectification circuitry was designed to build a full rectenna system. A rectifier circuit was simulated in ADS for each polarization. In the simulation, the Z parameters that was obtained from the full-wave numerical simulation for each polarization were extracted and imported into ADS. Then a 1-tone frequency power source was used to mimic the super cell looking from the feeding location see Fig.  for eachIn the simulation, the Harmonic Balance (HB) simulator was used to analyse the rectifiers due to the presence of the nonlinear diodes. The circuit contains a series transmission line, shorted stub and open circuited stub between the super cell and the diode. A series HSMS 2860 Schottky diode was used for its low turn on voltage of 0.28 V and fast switching speed at the frequency of operation of 2.4 GHz. In addition, two open circuited stubs and two series transmission lines were used between the diode and the RC circuit to ensure a good match between the diode and the load resistance and to filter out all the higher order components of the waveform before reaching the load. A shunt capacitor of 120 pF was selected to appear as a short circuit for higher frequencies and an open circuit for the rectified DC power. The rectifier was designed to have an impedance conjugate to that of the super cell for each polarization in order to maximize the power transfer between the energy collector and the rectifier. The Large Signal S-Parameters (LSSP) simulator was used in ADS to analyse the reflection coefficient of the rectifier for each polarization as shown in Fig. In addition, the AC to DC power conversion of the rectifier was analysed for each polarization as shown in Fig. The effect of the input power level for both rectifiers on the AC to DC efficiency was also analysed to ensure that the rectifiers perform at their maximum efficiency. The rectifier was fed by a sweep of input power to analyse the magnitude of the AC to DC power conversion as a function of the input power. The simulated input power sweep as a function of AC to DC efficiency is shown in Fig. In light of the results obtained from the full-wave simulation for the radiation to AC analysis and the results obtained from ADS for the AC to DC analysis, a full rectenna system was built as shown in the photos of Fig. 9:2. In addition, In the measurement, a 10 dBi gain horn antenna was used as a transmitting antenna. The horn antenna was fed with an E4438C keysight ESG Vector Signal Generator having a maximum power and frequency of 25 dBm and 6 GHz. To control the amount of power fed to the horn antenna, a Mini Circuits High Power Amplifier ZHL-16W-43-S is connected between the horn antenna and the signal generator. The metasurface was placed 1 m away from the transmitting horn antenna. The voltage across each variable resistor for each polarization was measured separately using a multi-meter. The radiation to DC power conversion efficiency of the super cell was calculated by the following equationThe incident power was then swept as a function of efficiency while both rectifiers are terminated by the optimal resistance of 250 The efficiency of the rectenna system is then analysed as a function of frequency. In this measurement step, the incident power and the load resistance were fixed at the optimal values obtained above. In addition to the two incident polarizations proposed in Fig. mentclass2pt{miniment Fig.  comparedent Fig. .Figure 1The resonance frequency is strongly affected by the length of the sub-cell, L, and most importantly by the separation distance between the cells, S. To understand how a small deviation in the fabrication of the metasurface can cause a frequency shift as experienced in the measurement, a sweep of different values of L and S as a function of the total efficiency of the super cell was performed numerically. Figure 2 (deep blue) to the largest of 1 mW/m2 (deep red). When the plane wave hits the metasurface at the resonance frequency of 2.4 GHz  absorb all the energy from the incoming wave, (2) deliver all the absorbed energy to the load, and (3) replace the load with a rectification circuitry and convert the collected AC energy to DC. From Fig. Although the designed metasurface at the resonance frequency experiences full absorption, this does not necessarily qualify it as an energy harvester. This is due to the fact that the absorbed energy can be lost within the dielectric substrate as the case in previous metasurface absorbers presented in the literature22, patches23, bowties24, loops25 and spirals26. The AC power is then fed to a rectifier which can be half wave series27 or parallel diode28, or full wave rectifier29. The total efficiency of a single rectenna is typically higher than an array of rectennas. This is mainly due to the energy lost by the AC or DC channeling circuit, which combines the power collected by all the elements in the rectenna system and channels it to a single load. In addition, the effective aperture of a single antenna is typically much larger than its physical footprint. A number of rectenna arrays were presented in the literature for linear and circular polarization. In30 a rectenna array made of three elements semicircular slotted antennas operating at 9.3 GHz was presented. The array achieved 21% radiation to DC efficiency when illuminated by a field with a power level density of 245 31. A maximum efficiency of 44% was obtained with an input power level of −11 dBm. A dual band rectenna consisting of 1 × 4 quasi-Yagi antenna array was used in32 to harvest the microwave energy at 1.85 GHz and 2.15 GHz. The array captured the incoming electromagnetic energy with an efficiency of 40%. In33, a four element circularly polarized patch antenna array was used as a rectenna system operating at 24 GHz. The total radiation to DC efficiency was 24% at a power level of 10 34, a large scale rectenna system consisting of 2304 rectennas was tested experimentally. The array was able to convert and channel 50% of 1.2 kW input power to a load resistance of 358 35. A measured efficiency of 41% was realized with an input power of 10 dBm. A broadband rectenna array made of spiral antennas with diodes mounted at the feed of each antenna was studied in36. The energy was collected over the frequency range of 6–15 GHz with efficiencies varying between 5 and 45%. A rectenna array made of dipole antennas integrated with fullwave rectification was presented in29 with a reported radiation to DC efficiency of 52%. For brevity and clarity, a number of papers presented in the literature in terms of efficiency, polarization, bandwidth, power level and operating frequency are summarized in Table In previous works, rectennas were presented as a single element or an array. Various antenna types were used to receive the microwave energy and convert it to AC power such as dipolesThe radiation-to-AC efficiency simulation of the super cell was performed using the full-wave numerical simulation tool HFSS. In the simulation the super cell was placed inside a waveguide with periodic boundary condition assignment on the lateral walls. Master and slave periodic boundary conditions were used for the four lateral walls to simulate the super cell in the presence of an infinite array as shown in Fig. 38. The rectifier was analysed using the LSSP and HB simulators to account for the nonlinearity effect of the diode. Then two different rectifiers were designed accordingly and the traces for the rectifier were added after the feed location for each polarization (see Fig. The AC to DC simulation of the rectifier was performed using the circuit simulator ADS. First, the impedance matrix of the super cell obtained for each polarization in the transmitting mode analysis from the full-wave simulation was extracted and saved in a citi file format. Here the Z matrix is refereed to as the directional impedance at the feed location circled in Fig. see Fig.  before tIn the fabrication stage, a We demonstrated the design of a microwave energy harvester that is capable of scavenging energy from multiple polarizations. A super cell consisting of


To estimate the timing of key events in the natural history of Zika virus infection.Zika. By pooling data, we estimated the incubation period, the time to seroconversion and the duration of viral shedding. We estimated the risk of Zika virus contaminated blood donations.In February 2016, we searched PubMed, Scopus and the Web of Science for publications containing the term We identified 20 articles on 25 patients with Zika virus infection. The median incubation period for the infection was estimated to be 5.9 days , with 95% of people who developed symptoms doing so within 11.2 days (95% CrI: 7.6–18.0) after infection. On average, seroconversion occurred 9.1 days (95% CrI: 7.0–11.6) after infection. The virus was detectable in blood for 9.9 days (95% CrI: 6.9–21.4) on average. Without screening, the estimated risk that a blood donation would come from an infected individual increased by approximately 1 in 10 000 for every 1 per 100 000 person–days increase in the incidence of Zika virus infection. Symptom-based screening may reduce this rate by 7%  and antibody screening, by 29% .Neither symptom- nor antibody-based screening for Zika virus infection substantially reduced the risk that blood donations would be contaminated by the virus. Polymerase chain reaction testing should be considered for identifying blood safe for use in pregnant women in high-incidence areas. There are concerns about potential transmission through blood transfusion because a large proportion of people infected with the virus remain asymptomatic,,,,–As temporary deferral or the banning of blood donations could result in severe shortages in blood supplies, research on the duration of viraemia and the time to antibody seroconversion is vital for quantifying the risk to blood supplies and for developing strategies for protecting them. Furthermore, better knowledge of the natural history of Zika virus infection, including the incubation period and infectious period, is essential for designing evidence-based surveillance systems and informing public health policy.The aim of this study was to better characterize the natural history of Zika virus infection and to inform disease prevention, surveillance and blood supply safety strategies by applying an extension of this analytical approach to case reports collected through a systematic review of the literature. Using pooled data, we estimated the incubation period, the time to seroconversion and the duration of viral shedding from Zika virus infection.Zika in any field. For our analysis, we included publications that provided information on: (i) the time of exposure to the Zika virus; (ii) the time of symptom onset; and (iii) the time of sample collection for, and the result (i.e. positive or negative) of, virological (e.g. by polymerase chain reaction or culture) or antibody Zika virus testing or both. Each publication was randomly assigned to two reviewers who independently screened titles and abstracts for relevance. We excluded publications that: (i) were not about the Zika virus; (ii) contained no data from humans; (iii) did not provide sufficient information to determine a bounded time of exposure; (iv) reported only perinatal viral transmission; or (v) were not in English. However, papers in French, Portuguese or Spanish that would have passed abstract screening had they been in English (i.e. 55 of 78 non-English articles) were also reviewed  for publications containing the term reviewed . Then, tWe abstracted the data necessary to estimate: (i) the incubation period of the Zika virus; (ii) the timing and duration of viral shedding; and (iii) the time to a positive serum antibody test result. In particular, we obtained information that enabled us to determine upper and lower bounds on the time of: (i) exposure to the Zika virus; (ii) symptom onset; and (iii) sample collection for virological or antibody testing. The exact timing of events was used when possible; otherwise bounds on the timing of an event were derived from the information available (e.g. the dates of travel to an endemic region). For virological and serological tests, the test result was recorded and specific immunoglobulin-M serological test results were noted, when available. We also recorded basic demographic details, the type of sample collected (e.g. blood or urine) and, when available, the mode of viral transmission.The bounds for the time of Zika virus infection were the earliest and latest possible times of exposure consistent with the case report. When no latest exposure time could be determined – for example, the patient developed symptoms in an endemic area – it was assumed to be the latest possible time of symptom onset – the time of symptom onset was specified to the nearest day in most case reports. The earliest possible time of seroconversion was considered to be immediately after the last negative serological test and the latest possible time was immediately before the first positive test. If only a positive serological test was reported, the earliest possible time of seroconversion was considered to be the same as the earliest possible time of exposure; when only a negative test was reported, seroconversion was considered to have occurred after the time of testing. Similarly, the earliest possible time of viral clearance, which was defined as no detectable virus in blood, was the time of the last positive virological test and the latest was the time of the first negative test. Missing virological test results were treated in the same way as missing serological test results.,For each observation of a time to a key event in the course of Zika virus infection , we used the observed data to derive upper and lower bounds for the time of exposure and for the event. These censored observations were then used to fit separate distributions for each key event using an adaptation of previously described techniques.,We estimated the impact of the distributions of key variables on the safety of blood supplies for a constant incidence rate. The number of blood donors with a possible Zika virus infection in every 100 000 in the absence of screening was calculated as the daily incidence of infection per 100 000 multiplied by the mean time to viral clearance. This estimate was adjusted for symptom-based screening using the mean time to symptom onset and by assuming that 80% of those infected remain asymptomatic.Zika, of which 118 were selected for full text review , with a dispersion of 1.5 days (95% CrI: 1.2–1.9). Hence, 5% of symptomatic cases would be expected to develop symptoms within 3.2 days of infection (95% CrI: 1.7–4.6), 25% within 4.6 days (95% CrI: 3.1–6.0), 75% within 7.6 days (95% CrI: 5.8–10.4) and 95% within 11.2 days  if no screening were performed. Refusing donations from people with recent symptoms of a possible infection would decrease this risk by only 7% , assuming that 80% of individuals with Zika virus infections are asymptomatic and given that those who develop symptoms are infectious but asymptomatic for an average of 5.9 days – here it is assumed that the Zika virus can be transmitted via blood from the moment of infection. Serological screening would reduce the risk by 29%  but improve the safety of blood supplies only marginally. In settings where the risk is solely from imported Zika cases, ensuring blood supply safety is easier. We estimated that, by 23.4 days (95% CrI: 14.3–154.3) after infection, 99% of cases would no longer have detectable virus in their blood. For these estimates, we assumed that a blood donation would be safe if there was no detectable virus in the donor’s blood. However, in four reported cases, a saliva, nasal or urine sample tested positive for the virus even though it was no longer detectable in blood . Blood d,In June 2016, WHO reported that the incubation period of the Zika virus was uncertain but likely to be “a few days”.,,In practice, many countries and organizations recommend deferring blood donation until 28 days after the resolution of symptoms or after the time of a positive serological or virological test result for an asymptomatic individual, as recommended by WHOOur study highlights the need for a highly specific, simple and rapid Zika virus antigen test. As well as for screening donated blood, an antigen test could be used to monitor the incidence of Zika virus infection, to help provide advice for women considering becoming pregnant and to identify pregnant women at risk of a poor clinical outcome. In addition, saliva or urine could be used in diagnostic tests and research into the relationship between the presence of the virus in bodily fluids and the risk of disease transmission is also needed. Knowledge of the time between infection and the virus becoming detectable in various fluids is essential for ascertaining the ability of antigen testing to ensure the safety of blood and organ donations. Moreover, knowledge of the incubation period can help clinicians determine whether Zika virus infection should be considered in the differential diagnosis of febrile patients who have recently travelled abroad and a good estimate of the time to seroconversion can help optimize the timing of confirmatory testing. Knowing the time to viral clearance after a potential infection or exposure can indicate when it may again be safe to become pregnant. However, the time to clearance from seminal fluid remains unknown. Our analysis provides only a first step in determining the values of key variables in Zika virus infection as the small number of cases included means that there are substantial uncertainties and a potential for bias. Investigators should continue to collect data to refine and update our estimates and to provide information on other key variables in the disease’s natural history, such as the latent period (i.e. the time between being infected and becoming infectious). To assist that process, all our data and the analysis software we used are freely available to enable other investigators to contribute to this work or apply our methods to their own data.Our analysis necessarily involved several assumptions because the published data were not collected to assess key variables in Zika virus infection. First, we assumed that virological testing of blood or sera had a sensitivity of 100% for detecting a Zika virus infection – however there is evidence that viral shedding can continue longer in urine and other bodily fluids and the virus may persist in the blood below the limit of detection. We also assumed that the time to seropositivity for the Zika virus was independent of previous infections – however it is probable that people who have had a prior flavivirus infection may seroconvert more quickly. Consequently, it is possible we overestimated the time to seroconversion because the majority of cases in our analysis were travellers returning to countries where flaviviruses were not endemic. Another limitation is that the majority of our data were from people presumed to have been infected through mosquito bites. The timing of key events may differ for other routes of infection . Furthermore, all our cases were symptomatic – the time to seroconversion or viral clearance may be different in asymptomatic individuals and it is possible that cases reported in the literature may have been more severe than usual. Nevertheless, the principle limitation of our analysis was the small number of cases.Despite these limitations, our analysis provides the most detailed, quantitative estimates to date of the timing of key events in the natural history of Zika virus infection. Our findings can help guide disease surveillance in both endemic areas and in returning travellers and can underpin research into the basic features of this pathogen.


The IPv6 Routing Protocol for Low Power and Lossy Networks (RPL) was proposed for various applications of IPv6 low power wireless networks. While RPL supports various routing metrics and is designed to be suitable for wireless sensor network environments, it does not consider the mobility of nodes. Therefore, there is a need for a method that is energy efficient and that provides stable and reliable data transmission by considering the mobility of nodes in RPL networks. This paper proposes an algorithm to support node mobility in RPL in an energy-efficient manner and describes its operating principle based on different scenarios. The proposed algorithm supports the mobility of nodes by dynamically adjusting the transmission interval of the messages that request the route based on the speed and direction of the motion of mobile nodes, as well as the costs between neighboring nodes. The performance of the proposed algorithm and previous algorithms for supporting node mobility were examined experimentally. From the experiment, it was observed that the proposed algorithm requires fewer messages per unit time for selecting a new parent node following the movement of a mobile node. Since fewer messages are used to select a parent node, the energy consumption is also less than that of previous algorithms. RPL is a routing protocol devised for low power and lossy networks (LLN) that consist of resource-limited devices. As a routing protocol that operates among IoT (Internet of Things) devices, RPL was designed to be suitable for wireless sensor network environments, and it supports various routing metrics to accommodate the requirements of various applications . The RPLMobility support is a fundamental issue in RPL. Previous works on mobility support in RPL mostly aimed to achieve rapid detection of the movement of mobile nodes and the provision of better links through an efficient selection of parent nodes. In other words, mobility support in RPL is directly related to a fast search for appropriate nodes to become the parent node when a mobile node makes a movement. Moreover, previous works on mobility support in RPL focused on improving the trickle algorithm used in RPL ,9,10,11.This paper proposes an algorithm for the timely transmission of solicitation messages for node mobility support in IoT environments that require the movement of the nodes or things. The proposed algorithm provides mobility support by dynamically adjusting the transmission period of the messages for selecting the parent node. This is based on the speed and direction of the movement of a mobile node.The rest of this paper is organized as follows. The RPL standard  defines In RPL, the creation and management of a DODAG starting from the DODAG root are achieved through the transmission of DIO messages. The DODAG root creates a DODAG and spreads the DODAG information to the nodes in the network through the transmission of DIO messages. Nodes that receive a DIO message participate in the DODAG and generate an upward path toward the DODAG root. The routers in the network that are capable of broadcasting allow for the other nodes to participate in the DODAG by transmitting DIO messages. The nodes that are currently participating in DODAG generate a downward path using DAO messages. DIS is used to solicit DIO messages from router nodes in RPL. DIS may be used to probe neighbor nodes in adjacent DODAGs. After receiving the DIO messages, the new node then selects one or more parent nodes using the objective function (OF).The trickle algorithm in RPL is used to maintain consistency in a network by using control messages . The triA trickle timer governs the transmission of control messages for adjusting the network to a consistent state. The timer controls the inconsistencies in an RPL network and prevents duplicate transmissions of DIO messages. If an RPL network is in an inconsistent state, the interval of the trickle timer becomes shorter, and control messages are transmitted more frequently in order to stabilize the network. By contrast, if an RPL network is in a consistent state, the number of control message transmissions is reduced by increasing the trickle timer interval in order to reduce the overhead in the network incurred owing to control messages.If there is a node that moves frequently in an RPL network, a route that is suitable for movement must be selected for this node ,10. For There have been several studies to improve the trickle algorithm with the support of node mobility in RPL. Ghaleb et al.  proposedThe algorithms of ,10 are tIn this paper, we propose an algorithm that dynamically allocates the time interval of selecting the parent node by considering the speed and the moving distance of a mobile node. We also present a scenario for selecting parent nodes considering the situation of moving based on the dynamic time interval.In this section, we propose an algorithm to support node mobility in RPL and describe its operating processes based on several scenarios. The operation procedure of the proposed algorithm is described in The proposed algorithm is identical to the RPL standard in that DIS and DIO messages are used to search for routes, and DAO messages are used to select a path. However, the proposed algorithm supports the mobility of nodes by dynamically adjusting the DIS message transmission period based on Doppler frequency and signal strength between a mobile node and its neighboring router nodes.Moreover, the proposed algorithm considers a network environment where both fixed and mobile nodes exist, and the mobile nodes are assumed to operate as leaf nodes without broadcasting owing to limitations in power supply. When a mobile node attempts to participate in a network by configuring the DODAG information, a DIS message is transmitted to neighboring router nodes to find its new parent node. As soon as the neighboring router nodes receive the DIS message, the nodes transmit a DIO message to the mobile node as shown in Then, the mobile node extracts the values of the Doppler frequency and signal strength from the DIO message. The Doppler frequency is used to measure the moving speed of a mobile node, and the signal strength is calculated to measure the distance between a mobile node and router nodes ,14,15,16The proposed algorithm, which is executed on the mobile node, is composed of five phases as follows. The pseudocode for the proposed algorithm is described in the table in Algorithm 1.k. Instead, it has a parent list table. When the algorithm is first executed, Initialization phase: While the proposed algorithm is similar to the trickle algorithm in that Receiving information of neighboring router nodes: When the algorithm is started, DIS messages are transmitted to the neighboring router nodes, and DIO messages required for parent selection are received from the neighboring nodes until Scenario-based parent selection: Afterward, if the current time reaches Adjusting the time interval: A DAO message is sent to the router node selected as the parent, and the interval used for the selection of the next parent is dynamically adjusted based on Equation  describeReinitialization of parameters: Next, the current time of the mobile node and the PP attributes in the parent list table are initialized. If there are no values for the PP attributes in the parent list table when the current time reaches Algorithm 1 Proposed algorithm1:2:3:4: 5:6:define 7:define 8:struct 9: 10:11:12:struct 13:struct 14: 15:16:loop17:ifthen 18:  send DIS to Router Nodes by one-hop broadcasting19:end if 20: 21:while cTime ≤do 22:if received DIO then  23:   24:   25:end if  26:end while 27: 28: 29:ifthen 30:ifthen  31:ifthen   32:    33:else if parent node ID in then   34:if parent node OF in then    35:     36:end if   37:else  38:    39:end if   40: 41:   send DAO to a selected router node42: 43:   44:   45: 46:ifthen   47:    48:else ifthen   49:    50:end if   51: 52:else   53:    54:end if   55: 56:   57:   58: 59:end if 60:end loopAs a mobile node moves from one location to another, a frequency difference occurs in the received signal owing to the Doppler effect. This frequency difference is referred to as Doppler frequency. The maximum Doppler frequency in the received signal is proportional to the speed of motion of the mobile node. The relative speed of the mobile node is related to the signal sent from the neighboring router node. The signal can be used to find the speed and direction of the mobile node ,16If a neighboring router node is in motion relative to a mobile node, the frequency of the signal received by the router node is different from that of source signal. If a mobile node moves closer to a router node, the received signal has a higher frequency than the transmitted signal. When a mobile node moves farther away from a router node, the received frequency decreases.c, If the speed of motion of a mobile node is Equation :(1)fd=frTo find the dynamic time interval proposed in this paper, we first need to know the speed of the mobile node. Using Equation (1), the speed of a mobile node can be estimated as shown in Equation :(2)Vm=fdAs shown in ter node ,17. TherL) in the transmitted signal is calculated as the difference between the two signals and can be found using the Friis free space propagation model [The current method estimates the distance based on the fact that the RSSI varies with distance. By transmitting a signal of fixed strength from the router node, the distance can be estimated using the strength of the attenuated signal received by the mobile node. Therefore, the transmission loss , r and the angle r is the transmission range of the router node. By calculating the Equation τ=de/x is a value randomly selected from [Here, In this section, we describe the case of a mobile node participating in an LLN for the first time. In The mobile node can measure the Doppler frequency upon receiving a DIO message. The speed of the mobile node is estimated based on Equation  and is uIn this section, we describe the case where the parent node information is renewed while the mobile node is moving. The same process as described in During this process, if there is a router node with the same ID as the parent node selected at In the example shown in In this section, we describe the case where the information of the previous parent node is not found at the new location of the mobile node. The mobile node stores the information of neighboring router nodes received at This section describes the case where the mobile node escapes the LLN while moving freely. After transmitting a DIS message, the mobile node receives a DIO message for the duration of The absence of information in the parent list table of a mobile node implies that there are no router nodes nearby. Therefore, the mobile node must collect the information of the neighboring router nodes as soon as possible and thus select a parent node. During this process, k value must be configured with a default value in order to exclude the duplicate information from neighboring router nodes. Therefore, in this paper, a k value of two was used for the original trickle algorithm and the E-trickle algorithm during the experiment.The proposed algorithm finds the time interval used by the mobile nodes to select the parent node in a dynamic manner. An experiment was conducted using MATLAB to compare and evaluate the proposed algorithm, the original trickle algorithm , the E-tIn order to compare the performance of our proposed algorithm with existing methods, three criteria were evaluated using different network topologies, as shown in To establish a grid network topology as shown in In the first experiment, we measured the number of DIS messages transmitted from the mobile node to select a parent node. The number of DIS message transmissions is related to the energy consumption in the mobile node. This is because even if a single DIS message is transmitted, the mobile node receives multiple DIO messages from each neighboring router node. Therefore, the number of DIS message transmissions with respect to time using each algorithm was obtained and compared.In the second experiment, the packet loss rate of the transmissions from the mobile node was obtained. The packet loss can happen as a mobile node moves to a location that is not covered by the current parent node of the mobile node. Then, the mobile node cannot transmit a DIS message to a new parent node because the predefined time interval on a previous parent node is not expired yet. When a mobile node makes a movement, the optimal parent node for the mobile node at the new location must be selected. However, owing to the interval time defined by each algorithm, there are cases where the parent node is not selected in a timely manner. Moreover, there are cases where the mobile node escapes the transmission range of the previous parent node. If the parent node information possessed by the mobile node is not renewed at this point, losses may occur in the packet transmitted from the mobile node. Therefore, for each algorithm, the loss rate of the packets transmitted from the mobile node with respect to time was obtained and compared.In the last experiment, the energy consumed by the mobile node in selecting a parent node was measured. Since mobile devices in most practical environments operate on batteries, the lifetime of a device is increased by reducing energy consumption. In this paper, the mobile node is also assumed to be a device operating on a battery. Energy consumption was measured based on the number of transmissions and receptions of messages used to select a parent node. The energy model for the measurement of energy consumption was based on Equation  in Sectiecreased .m-bit message a distance d using the communication energy consumption model in each time interval of the mobile node. More details are represented in Equation  between a mobile node and neighbor router nodes. Another component is the energy consumption value for receiving DIO messages between a mobile node and neighbor router nodes (between one and n). In Equation  environments, focusing on stable and energy-efficient methods for supporting mobile node-based services.