This research paper presents a step by step conceptual design and life prediction approach for the design, modeling and simulation of head shaft of a belt bucket elevator, to be used for conveying grains to a height of 33.5 m and at the rate of 200 tons/h. output. For this elevator system, the force and torque acting on the head shaft as well as the bending moment were calculated. Furthermore, the diameter of each cross section of the shaft was determined taking into consideration the geometric and fatigue stress concentration factors, due to shoulders which contribute significantly to most fatigue failures of shafts. The stress induced on the shaft by the force and the factor of safety for each cross section of the shaft was calculated using the DE-Goodman criterion. The model of the shaft was created from the calculated diameters and subjected to static and fatigue analysis using SolidWorks FEA. The results were validated by comparing the values from the FEA and the calculated values for stress and factor of safety of the critical section of the shaft, which showed an equivalent value. The FEA gave a fatigue load factor greater than one, which signifies that the shaft will not go into failure mode within the infinite life cycle of the shaft. The value of the fatigue strength obtained from FEA was higher than the value for the maximum von misses stress of the shaft, this result shows that the head shaft will sustain the loading stresses over a finite life prediction. This research is significant because the stress induced forces on the head shaft from each component of the elevator system were properly identified and analyzed so as to obtain precise results for life prediction. A broken head shaft can be devastating with consequences such as loss production time with its associated downtime cost, drop in quality of grains and wastage (due to moisture and weevils’ infestation). Also of safety concern, the procedure for replacement of the failed shaft is very difficult, most especially for very tall and heavy elevators, where the belts and cups will have to be suspended to remove the fractured shaft, this poses a significant safety risk to the maintenance engineers. Thus considering the load, the shaft will be subjected to and the consequences of any failure, a proper design of the head shaft of the elevator is critical and a generous safety factor for an infinite life is recommended to ensure safe and reliable operation of a developed elevator system4. The head shaft should be designed to sustain both static and cyclic loading in its service life. The cyclic load carried by the shaft causes bending which produces stresses within the shaft and results in fatigue failure when the cyclic loading over a period of time leads to the failure of the shaft even when the magnitude of the stress is below the material yield strength. Since it is on record that majority of engineering shaft failures are caused by fatigue, it is recommended that at the conceptual design stage, shafts should be correctly sized to prevent fatigue failure within the expected period of usage by the industry5.Grains such as corn and wheat produced from farms and processed in industry are first stored in silo facility to ensure all year round availability of food for human consumption. These grains are usually discharged into the silo by means of a belt bucket elevator system, which is one of the important material handling equipment used in industries to convey bulk materials from the ground level to a required height. The belt bucket elevator system Fig.  consists6 investigated the failure of an elevator drive shaft due to torsion-bending fatigue and found out that failure occurred at the keyway of the shaft due to faulty design of the keyway, which resulted to a high notch effect at the keyway section. Brijesh et al. optimized the weight and discharge capacity as well as the stress and deformation of the bucket and shaft of a modeled belt driven elevator for material transport using SolidWorks7. Chavhan et al.8 studied the load carrying capacity of an elevator bucket, the strain in the bucket edges and the clamp bolts using CATIA V5 3D model and ANSYS software and concluded that failure of elevator shaft was the main cause of the bucket failure. Gililland et al. reported that the loads imposed on the boot shaft are very low when compared to the head shaft. This establishes the critical nature of the head shaft of an elevator system9. Snehal et al.10 reviewed that failure on shaft takes place due to high stress on the keyway and areas where there are abrupt changes in cross sectional area. Yin et al.11 investigated the failure of a bucket elevator chain link and reported that the failure was due to propagation of crack embedded within the material during loading. This signifies that the elevator shaft was equally affected by such loading. The drive shaft of a system was examined and reported to have failed under fatigue due to design error of the fillet radius of the shaft12. Ariwibowo et al.13 equally investigated the failure of a shaft and reported that the failure was due to crack propagation initiated from fatigue loading.There are many literature which have dealt with problems relating to elevator shaft system. Goksenli et al.14. Baig et al.15 investigated a shaft for failure and reported that failure always occurs at the areas of high stress concentration. Pelaseyed et al.16 studied the failure of the shaft of a unit and concluded that the failure was as a result of fatigue loading. Gurudath et al.17 investigated the failure of a bucket elevator shaft and reported that the failure was due to crack initiated at the heat affected zone of tack-welded spot on the shaft which propagated transversely by fatigue due to cyclic loading. Butlovic et al.18 study on design of machine parts such as shaft inferred that the use of CAD softwares provides simple and exact values of stress and deformation distribution on the shaft. It was also reported that the Goodman theory was widely used and adjudged to be a safe design approach in case of combined static and cyclic stress. Adekunle et al.19 developed a software for shaft design that satisfactorily handled design based on strength and safety. Sathishkumar et al.20 created a shaft model using CREO software, performed static analysis of the model to determine the stress and deformation under load using ANSYS software, it was concluded that the result obtained in good agreement and is within the safe limit. Ofolabi et al. investigated the parameters of fatigue life of a shaft and produced a 3D model of the shaft using Inventor software. It was reported that the results of the finite element analysis when compared with calculate values were satisfactory21. Engel et al. studied the failure mode of a shaft, analytic method was carried out to determine the stress and deformation of the shaft under combined torsion and bending loads, the results where then compared with that of finite element analysis method. It was concluded that the shaft needs some surface treatment to increase its fatigue life22. Rasovic et al. analyzed a SolidWorks-modeled drive shaft using finite element analysis and reported unsatisfactory result from the analysis as a result of the shaft geometrical change and low yield strength of the shaft material23. Robothan et al.24 analyzed a shaft and concluded that the behavior of shaft under combined loads can be accurately predicted using finite element analysis.Osakue developed a reliable model for a probabilistic design approach for shafts under combined bending and torsional loading, it also reported that for conditions of combined torsional and bending stress, distortion energy (DE) theory of failure was appropriate for the design analysis of the component26. With model-based design approach, shaft design engineers can make accurate prediction of the system performance as well as its service life, and make corrections of potential failure points of the shaft at the conceptual design stage. In this study, the limitations to obtaining safe shaft design for infinite life, such as the presence of stress risers and the centrifugal force action were analyzed using standard shaft design calculation procedure. The model of the head shaft was produced and simulated, so as to make accurate prediction of the service life of the designed head shaft.With the level of advancement in mechanical design in this era, shaft prototypes with optimal performance are developed through modeling of the physical system, as this helps to eliminate failure which comes with costly consequencesHence, this research work provides a comprehensive approach for design and modeling of the head shaft of a belt bucket elevator system which will not fail under fatigue as well as in predicting the service life of the shaft, using DE-Goodman criterion and SolidWorks engineering software.The assembly model of the bucket elevator head as shown in Fig. 29.For the design, AISI 1020 steel was selected for the pulley because of its high ductility, machinability, strength, polished finished property and good weldability. AISI 1018 steel was selected for the elevator cups because of it great ductility, malleability, toughness, ease of welding and cheaper cost. AISI 1045 cold drawn steel was selected for the shaft because of its high tensile strength, hardness, excellent size accuracy, straightness and good surface conditionDuring operation of the belt bucket elevator system, the head shaft is subjected to torque from the gear drive motor and bending moment from the weight of the belt, cups filled with wheat grains and pulley, these generates torsional shear stress and bending stresses on the shaft, because of these reasons, the shaft was designed for combined stress using distortion energy theory of failure. The shaft design involves the determination of the preliminary diameter of the shaft. The graphical representation of the methodology is shown in Fig. For the model based design, it was considered that there was no resisting friction from the bearing and the weight of the shaft was negligible. It was also considered that both the pulley and the gear drive were mounted to the shaft using shrink disc, hence, the need for welding and keyway which act as stress risers was eliminated. It was also considered that the gear drive was well suspended by external clamp, hence its weight was not on the shaft. The grain product used was wheat.The design analysis covers some areas which includes:. To determine the volume of the pulley, we split the pulley into two sections as shown in Figs. The head pulley of the elevator is a crowned type which uses flat beltP—Volume of pulley, W—Width of pulley, dO—External diameter of pulley(drum), d1—Internal diameter of pulley, d3—External diameter of pulley side cover plate, d4—Internal diameter of pulley side cover plate, t1—Thickness of pulley plate, t2—Thickness of side cover plate.The hollow cylinder and the two side plates of the pulley were considered. The volume of the pulley was determined using Eq. 1\documenP—Weight of the head pulley, The weight(N) of the head pulley was determined from Eq. ,2\documeThe elevator operates on an open belt drive system as shown in Fig. B—length of belt, Dd1—Diameter of the head pulley (Drive pulley), Dd2—Diameter of the bottom pulley (Driven pulley), SD—Centre to centre shaft distance,The length of the open belt drive was determined from Eq.  given asθ1, θ2—Angel of contact (or wrap) for the head and bottom pulleys successively31.tB—Width of the belt, tB—Thickness of belt, LB—Length of Belt.The mass of the elevator belt was determined from Eq.  given asBL—mass of belt per metre length.The density of the belt was also determined from Eq.  as:5\docB) was determined using Eq. .Similarly, the radius(r) of the semi-ellipse section of Fig. C) was determined as the difference between the volume of external cup dimension and the volume of the internal cup dimension; this is equivalent to the difference of the sum of the area of the triangle and area of the semi-ellipse multiplied by length for external section and that of the sum of the area of the triangle and area of semi-ellipse multiply by length for the internal section of the cup. Thus, the volume of the cup material was determined using derived Eq.  of cup, tc—Thickness (gauge) of cup material.Thus, considering the hollow section of the elevator cup, the volume of the cup . Thus, the actual mass of wheat (excluding the cup weight) only transported by each cup was given in Eq.  as:13\do34The designed capacity of the elevator cup is equivalent to the volume of internal cup dimension, hence, the designed capacity of the elevator cup was determined from Eq. 33,3414\dThe mass of each elevator cup carrying wheat was determined using Eq. 15\documeThe forces acting on the shaft are the weights of the head pulley, elevator cups, grain (wheat) and the belt. This was resolved using the free body diagram shown in Fig. 91—Tension(force) on tight side of belt, F2—Tension(force) on the slack side of belt, WP—weight of the head pulley, T—Torque.Where F1) of the belt was determined using Eq.  tension(force), FCE—Tension due to centrifugal force,Taking centrifugal force into consideration, the force/tension on the tight side  of the belt on the pulley interface (i.e. FF ≈ FC).For the elevator belt to rotate, the circumferential force must be equal to the frictional force (FF) was given in Eq.  into the chute at the head pulley, a speed in the range of 1–2 m/s is recommended for centrifugal bucket elevator. Also, it has been reported that rubber coated flat belts running over pulleys in practice displays friction coefficient between 0.3 and 0.8. Thus, these criteria were used as validation values during the analysisThe Initial tension or preload force of the belt on the shaft was determined using Eq. 20\docume1) in radians was determined from Eq. (38:The angle of contact for the head (θfrom Eq.  given asce) was determined from the derived Eq.  was determined from the Eq.  + Torque to rotate the head pulley (THP) + Torque to rotate the bottom pulley (TBP).The total torque(T) required to operate the elevator system was determined from Eq.  given as1—Mass moment of Inertia of the head pulley, J2—Mass moment of Inertia of the bottom pulley, This is represented thus:1) was derived from Eq.  was developed as shown in Fig. 5, d6, d3, d7—diameter of each shoulder section of shaft in mm. Also, the length of the shaft cross sections is in mm.Where dThe shaft design was based on determining the safe design diameters for each section of the shaft to carry loads efficiently without failure. Thus, the areas of the design analysis covered are:This was determined from bending moment diagram. The free body diagram was first developed as from the schematic diagram in Fig. From the design, the two sections of the pulley side plates are fixed to the shaft. For this reason,S1 is equal to FS2 (i.e. FS1–FS2). Thus, FS1 is determined using Eq. 36)35\docTaking sections of the beam,The bending moment at E from Fig. E), we have Eq. , is MA = 0.Thus, the bending moment at A  was determined from Eq. (Bending moment at G (Mfrom Eq. :39\documH) was determined from Eq. (Bending moment at H (Mfrom Eq. :40\documB) was determined from Eq. (Bending moment at B (Mfrom Eq. :41\documJ) was determined from Eq. . Assuming generous fillet radius, the standard 1st pass, we assume KtT = KFATT1 = 2.7, KtB = KFATB1 = 2.2Also, for quick conservative 1FATT—Fatigue stress concentration factor for torsion in 1st estimate, KFATB—Fatigue stress concentration factor for bending in 1st estimate.Where K5) at the shoulder at H was determined using DE-Goodman criterion as shown in Eq. , n1—Safety factor for 1st pass, MH—Alternating bending moment at H, Tm—midrange torque.The diameter  for 1st pass was determined from Eq.  was determined from Eq. (The surface factor (Kfrom Eq.  given asb1) = 1 (for 1st estimate), Load factor (Kc) = 1(for combined loading), temperature factor (Kd) = 1(Assumed room temperature), Reliability factor (Ke) = 1, Miscellaneous factor (Kf) = 1.The size factor (KThe uncorrected endurance limit was determined from Eq. 46\docume1) of 5 (for the 1st pass) was used48Furthermore, considering that the stress type and material condition is uncertain, a safety factor (n5 = 90 mm) was analyzed to determine its fatigue and yielding factors of safety.From Eq. , the sta5—endurance limit correction factor for d5,5, 5.From DE-Goodman equation, the fatigue factor safety was determined from Eq.  given as5 (Se5) was determined from Eq. (The endurance limit correction factor for dfrom Eq.  given as5 (Kb5) was calculated from Eq.  H and was determined using Eq.  and the standard shaft size (d5 = 90 mm), the fillet radius and shoulder height for the shaft from bearing catalogue are 50.Considering the bearing placement at section H and was determined from Eq.  was determined from Eq. (5) determined from Eq.  was determined from Eq. (The endurance limit correction factor for dfrom Eq.  given as6 (Kb6) was calculated from Eq.  G and was determined using Eq.  and was determined from Eq.  was determined from Eq. (6), it was determined from Eq.  where determined from Eqs. (FATTI is the fatigue stress concentration factor for torsion at section I (d7) and was determined from Eq. 70\documetTI is the theoretical stress concentration factor for torsion at point I and its value was determined from chart of theoretical stress concentration for shaft with shoulder fillet in torsion for 49.KI is the fillet radius at I and was determined from Eq.  curve which is one of the fatigue life methods to predict the number of cycles to failure for specific load level the shaft will be subjected to was constructed. A well-defined stress-life (S–N) characteristic of the shaft material will aid in obtaining precise fatigue life prediction for the shaft. The simulation analysis of the shaft model for both static and fatigue loading was done using Solidworks engineering software. The software uses finite element analysis (FEA) in predicting real world physical behavior of modeled mechanical componentsThe step-by-step procedure for the simulation on solidworks are as follows:AISI 1045 cold drawn steel was selected as the shaft material. The material properties of the shaft material are given in Table The shaft has a bearing on the left and right hand of the shaft, for this reason, bearing fixture was applied at the left and right hand end of the shaft as shown in Fig. Equal forces of 8157.5 N were applied at the slit sections of the shaft where the pulley is fixed. A torque of 2316 Nm was also applied to the shaft end at a position the gear drive motor will be coupled, as also shown in Fig. This is a crucial step in design analysis which involves subdividing the model into small pieces. A good mesh increases the accuracy of the simulation result. Mesh setting was first carried out before the meshed model of the shaft was produced. The mesh setting was done in steps as shown in Fig. The meshed model and a complete mesh information as shown in Fig. Criterion MAX Von Misses StressComputing alternating stress Equivalent stress (Von misses)Mean stress correction GoodmanThe parameter setting used for fatigue are as follows.The simulation results for the maximum von misses stress and that of the yielding factor of safety were determined from the static analysis. Following that, fatigue analysis was carried out with the same software and the value for the fatigue life, fatigue load and S–N curve were equally obtained from the simulation results.At this conceptual design stage, the performance of the head shaft was tested and compared with value obtained from the analytic design calculations. The results Figs. , 27, 28 See Figs. 7 N/m2 which was equivalent to the value (4.852 × 107 ≈ 48.52 N/mm2) obtained from the design calculation. The value of the maximum von misses stress was less than the yield strength value of the shaft material, this signifies that the shaft will operate in the elastic region, this means that the designed diameters calculated for the shaft are safe for the elevator system operation. From the plots in Figs. 6 cycles. The plots of Figs. 6 cycles, this result signifies infinite life for the shaft. This was validated from the result of the S–N curve of Fig. 8 N/m2, this value was higher than the value of the maximum von misses stress (4.817 × 107 N/m2), thus signifying that the shaft will not fail but will survive indefinitely in operation. The closeness of the calculated values with the values from the analysis show that FEA is a very useful and effective tool for design of mechanical components that will be subjected to combined loading as well as for predicting the service life of the component.From the plots Figs.  and 21, Also, this research used the DE-Goodman criterion because of the need for accurate prediction of failure for the ductile shaft material and also due to the combined load of bending and torsion on the head shaft. The analysis also showed the difficulty of getting optimized numerical values for some design parameters such as the material variation and shaft weight, this point may surely be future research work for a more accurate and optimized head shaft model analysis. Also, fatigue test of the developed model should be performed in future research to confirm the theoretical data.This study presented a detailed approach for the design, modeling and simulation analysis of the head shaft of a belt bucket elevator for transporting grains (wheat). As a critical component of the elevator system, the forces acting on the shaft were first determined, the load type and the stresses at potential critical locations were considered in the design calculations. To ensure a proper design, modeling and simulation analysis were performed on the designed shaft so as to determine the fatigue strength and to make accurate prediction of the fatigue life of the head shaft. The result from the simulation analysis shows that the designed diameters for the shaft were safe for operation considering the 200 tons/h design capacity of this bucket elevator system.This study can be used in industry as a reference for predicting the service life of shaft designed for different capacity of elevator systems. It will also help industrial engineers to have better understanding of the behavior of elevator shaft as well as to gain advanced knowledge on how to improve the fatigue life of shafts in manufacturing machines using FEA tools; this will directly reduce cost associated to downtime.Note also that the complexity of the model is such that authors where not able to show and discuss all the details of their work. The authors stay away with pleasure to the disposal of the interested readers for any further discussion on the approach followed here.


A vast number of drug molecules are unable to cross the blood-brain barrier, which results in a loss of therapeutic opportunities when these molecules are administered by intravenous infusion. To circumvent the blood-brain barrier, local drug delivery devices have been developed over the past few decades such as reverse microdialysis. Reverse microdialysis  offers many advantages, such as a lack of net volume influx to the intracranial cavity and the ability to sample the tumour’s micro-environment. However, the translation of this technique to efficient drug delivery has not been systematically studied. In this work, we present an experimental platform to evaluate the performance of microdialysis devices in reverse mode in a brain tissue phantom. The mass of model drug delivered is measured by computing absorbance fields from optical images. Concentration maps are reconstructed using a modern and open-source implementation of the inverse Abel transform. To illustrate our method, we assess the capability of a commercial probe in delivering methylene blue to a gel phantom. We find that the delivery rate can be described by classical microdialysis theory, except at low dialysate flow rates where it is impacted by gravity, and high flow rates where significant convection to the gel occurs. We also show that the flow rate has an important impact not only on the overall size of the drug plume, but also on its shape. The numerical tools developed for this study have been made freely available to ensure that the method presented can be used to rapidly and inexpensively optimise probe design and protocol parameters before proceeding to more in-depth studies. For non-resectable tumours in particular, the possibility to insert catheters or implants, analogously to standard biopsy procedures, has been explored in a variety of ways, for example in Convection-Enhanced Delivery (CED)6, electrokinetic7 or electrophoretic8 delivery, gel implants10, or retrodialysis18.Bioavailability in the brain of systemically-administered drugs is generally poor due to the blood-brain barrier. This has largely hindered the development of new therapeutic options, especially for the treatment of brain cancers. Many targeted drug delivery techniques have been proposed to overcome this challenge19. By contrast, when using a microdialysis probe in reverse mode the drug solution  flows through a closed channel and leaves at an outlet, as depicted in Fig. 20. However microdialysis probes and accessories have been designed and optimised to measure solute concentrations and their translation to efficient drug delivery devices has not been systematically studied. In particular, a system to measure the release of a dye as a drug model to a brain tissue phantom would be beneficial for the rapid optimisation of the design and operating conditions of microdialysis probes in reverse mode.CED, the leading experimental treatment among these techniques, consists of injecting drug solutions with a catheter directly to the tumour site. A major challenge is to reach a reasonable infusion rate while avoiding over-pressure in the intracranial space and reflux along the catheter port21 developed an instrument to study the delivery and reflux of a dye solution to an agarose gel. Their methodology relies on carefully controlled absorbance images and a tailored concentration reconstruction algorithm. Since it is entirely based on optical imaging it does not require the use of expensive equipment such as X-ray or MRI scanners. We show further improvements to this technique, such as the use of a band-pass optical filter which extends the applicability of Beer-Lambert law of absorbance and increases the versatility of the system by being able to quickly adapt to different dyes. We also employ a telecentric lens which is beneficial for reconstructing concentration maps of wider areas. Importantly, we use a Python environment and open-source packages for the entire data analysis pipeline. Both the data used to support this study and the analysis scripts are freely available and will support the rapid development of the field.In the context of CED, Sindhwani et al.The paper is organised as follows: first we reexamine the theory of microdialysis mass transfer, and the developments needed from the perspective of drug delivery. Then we present an experimental instrument to measure the release of a dye in a brain phantom and provide a detailed description of the data processing framework. Finally we illustrate and discuss our methodology by performing a series of experiments on a commercially-available probe.22. It has been discussed in the context of microdialysis by many authors28, therefore we only report here the main assumptions and scaling laws. However, before doing so, we shall emphasise the points specific to a reverse mode of operation which are not straightforward from previous analyses. First, in probing mode, the quantity of interest is likely a concentration in the vicinity of the probe. In reverse mode the concentration of the drug (bioavailability) is important but we can argue that we are also interested in the total mass delivered to the tissue, and at which rate this is achieved. Second, in probing mode we expect concentration gradients not to extend too far from the membrane. In reverse mode we would like to target a larger volume in order to reach tumour edges. Therefore we will discuss the impact of transient concentration gradients in the gel. Finally, we highlight the role of the flow rate  in the channel. Not only does it drive the overall delivery rate, but it also affects the shape of the drug plume, as we will see in the “Solute transfer from a low Reynolds number capillary flow through porous walls is an archetypal problem in life sciencesL (length of the membrane in the direction of the flow), and an outer diameter d. We consider a probe with a large aspect ratio L/d. Although we are dealing here with a concentric cylinder design with an annular flow along the membrane, the following scaling analysis also applies to other geometries such as linear capillaries or rectangular channels, so long as the aspect ratio of the probe is large. Other parameters are the channel depth, h, the membrane thickness, V. The drug is supplied at concentration The geometry of the probe is sketched in Fig. x along axis, the radial mass flux per unit area, 25:x, V and time t have been emphasised in this equation and shall be discussed now.Considering a thin slab at position mentclass2pt{minimFirst, in the flow, it is assumed that the concentration gradient (and therefore mass transfer by diffusion) is mainly radial. This is valid provided that the Péclet number relative to the active length is large:In practice, this sets a minimal flow rate for the flow to have any effect on the delivery mechanism, compared for example to drug diffusion from a gel implant. Regarding the mass transfer from the bulk flow to the membrane inner surface, we can distinguish two regimes of flow: a moderate flow where the radial concentration gradient spans the entire depth of the channel along the majority of the active length. In other words, the mass transfer boundary layer see Fig. b is as l25. The flow-averaged concentration x because the drug is depleted as it flows past the membrane. Conversely, the mass transfer resistance of the flow is constant and scales as:This is the typical assumption in previous microdialysis analyses29:The second regime is a strong flow with Therefore:25. Finally we consider the resistance of the external gel, d is the probe outer diameter, and d and outer diameter t. Then the resistance of this cylindrical shell scales as:The resistance of the membrane, Consequently at short times , 60 mg, is dissolved in 10 mL Dulbecco’s phosphate-buffered saline (DPBS) by heating to 100+ °C on a hotplate for 10 min. Once the polymer has dissolved (the solution turns from cloudy to clear), the hot solution is poured into a transparent plastic cuvette  and allowed to cool and gel for at least 30 min.The experimental setup is sketched in Fig. After the gel is set and at room temperature, a hole is made using a pointy metallic rod (outer diameter 0.65 mm). The rod is removed and the micro-dialysis probe  is inserted. The probe is flushed with 0.5 mL of DPBS at 15 μL/min. This priming step removes bubbles and impurities from previous storage. Then frame capture is started and 1 mL of a methylene blue solution at a concentration of 0.2 mg/mL in DPBS is infused, first at 15 μL/min during 5 min, then at a fixed flow rate depending on the experiment. The first 5 min at high flow rate ensures that each experiment starts with the entire device filled with the same concentrated solution. It is also the manufacturer’s recommanded procedure. After the experiment, the probe is flushed with 0.5 mL of DPBS at 15 μL/min and stored in buffer until reused for another run. All experiments are done at 20 °C.A collimated light source  shines parallel beams through the brain phantom. A telecentric objective lens  is mounted on a digital camera . The use of telecentric objective eliminates geometric distortion and therefore allows a better 3D reconstruction from the image. A pass-band filter  centred around 500 nm, with a bandwidth of 40 nm is mounted at the back of the lens. The aim of this filter is to extend the linearity of Beer-Lambert law when absorbance is computed from pixel intensity values, as it will be discussed below. It also gives better versatility of the system by being able to quickly adapt to different dyes depending on their respective absorption characteristics.Images are recorded at 1 frame per minute with a fixed exposure time for each series (in the range 9 ms to 11 ms). Images are processed using a Python environment and open-source packages. The next subsection describes how concentration or mass information can be extracted from images.A is the absorbance due to the dye and B is the absorbance due to the blank gel and the cuvette walls. To get rid of the unknown B and At a specified wavelength, 21) is the use of a band-pass filter which enables the identification of spectral light intensity ratio with pixel value ratios, assuming sensor linearity. Another option could be the use of a monochromatic light source. Under such conditions, we can measure absorbance at time t for each pixel referenced by position  in the image:I and I are the pixel intensities at time t and at An important feature of our setup . Formally, the concentration field can be found from measuring the absorbance and applying the inverse Abel transform, Let us now assume that the concentration field has a symmetry axis, here the entclass1pt{minimagain Eq.  along th21 proposed their own reconstruction algorithm without explicitly referring to the Abel transform. However we see from the above analysis that we can benefit from recent advances in the broader field of computational Abel transform and use robust and validated algorithms. Here we employ the BASEX algorithm34 provided with the open-source PyAbel package35.Sindhwani et al.The data processing workflow is illustrated in Fig. PyWavelets Python module. The result can been seen in Fig. We found that noise filtering is not necessary if one is only interested in measuring the mass captured in an area of the image that has many pixels and is away from the probe shadow. However, noise reduction is highly beneficial prior to applying the inverse Abel transform. Images suffer from two main sources of noise: electronic noise of the sensor and light scattering in the gel. The sensor noise is responsible for non-linearity of the dark values (impossibility to have pure black images even with a shutter on) and uncorrelated variability over time in a series of frames capturing the exact same scene. The former is reduced by using short aperture time (here in the order of 10 ms). To reduce time fluctuation, we consider each pixel independently as a time series and apply a wavelet filtering using the scikit-image Python module)  Fig. k,l. The le) Fig. m. We useFinally, the absorbance inside the probe shadow is computed using the forward Abel transform of the concentration field. This produces an absorbance image Fig. n we woulThe importance of properly accounting for the probe shadow is illustrated in Fig. In conclusion, we have described a method to monitor the delivery of a drug (or model drug) to a gel phantom. Images captured by a carefully designed optical system are processed to compute a time series of absorbance fields. The mass of drug visible in each image can be derived, and concentration maps are reconstructed using a modern algorithmic implementation of the inverse Abel transform, also providing an estimate of the mass occluded by the probe.We employed the method described above to assess the performance of a microdialysis probe in delivering methylene blue to a brain tissue phantom. The probe has an axial symmetry design, and a membrane length of 1 cm and external diameter of 0.6 mm. Results are reported in Fig. The delivery rate computed by finite difference is plotted in Fig. The average steady-state delivery rate  is measured in each experimental curve, and the delivery efficiency Eq.  is deriv36. The cross-section area and channel depth, assessed using X-ray tomography, are Q in μL/min). Therefore the Péclet number in the experiments is ranging from 2 to 200, and we can expect a reduced if not negligible contribution of the flow resistance to the overall mass transfer resistance at 10 μL/min. To assess the reduction in resistance, we can calculate the order of magnitude of the low Péclet channel flow resistance  have ruled out geometry effects such as axial concentration gradient in the gel or eccentric cylinders positions. On the other hand, occasionally we were able to observe a strong stratification of methylene blue in the waste cuvette, with concentrated solution sinking down the bottom during the initial flushing step. To check the influence of gravity, we carried out an additional experiment at 0.1 μL/min but having the cuvette and the probe positioned upside down. The result, reported in Fig. More puzzling is the discrepancy at 0.1 μL/min. Unexplained lower-than-expected performance at low flow rates has been reported in other microdialysis studiesA major advantage of the method presented here compared to a standard microdialysis setting is the ability to investigate concentration profiles in the brain phantom. Examples of concentration maps are shown in Fig. Starting with the concentration profiles after 20 min Fig. a,b, the Finally, we compare the maps at the instant when 10 μg have been released to the gel Fig. e,f. At 0By recalling from Fig. Here we have presented a workflow which benefits from the axial symmetry of the probe in two ways: first, to accurately measure the delivered mass by accounting for the probe shadow, and second, to reconstruct concentration fields from absorbance using the inverse Abel transform. Although the theoretical analysis holds regardless of the detailed design of the probe, measuring the delivered mass accurately or reconstructing the concentration fields can become problematic with the lack of axial symmetry. If the probe is flat, neglecting the shadow might not produce a significant error, however reconstructing concentration would need additional means.One approach would be to follow a standard computational tomography (CT) method with capturing multiple angles of the scene. The availability of open-source CT libraries makes this approach workable. Nevertheless this would require significant hardware modifications, with a rotating stage and synchronised capture. The delivery process would also need to be slow enough so that variation of concentration field would be negligible during the full rotation time of the cuvette. It may be more beneficial although expensive to use a commercial X-ray CT scanner with a contrast agent matching the properties of the drug under investigation. This would have the additional advantage of exposing the inside of the probe and potential defects such as bubbles which are not visible with our approach.Another option to deal with non axially-symmetric designs could be to rely on 3D diffusion simulations and solve the inverse problem of finding concentration by matching absorbance fields.Finally, one can argue that a microdialysis probe can perform rather differently in a real brain than in a phantom. This is true especially if the mass transfer resistance of the brain is much larger than the resistance of the membrane. We can expect that to happen for large vehicles such as nanoparticles. Although we can match diffusion properties of the brain phantom with that of real brains and tumours, it would be still difficult to account for other transport processes such as drug intake or degradation, and interstitial fluid flow. Also, absorbance images rely on the fact that the phantom is transparent, or produces very limited scattering, a property which could be difficult to obtain with more elaborate tissue phantoms. Nevertheless, the method presented here can be used as a part of a quick design optimisation loop before proceeding to more expensive and elaborate in vitro and in vivo experiments.In this study we presented a method to measure the retrodialysis delivery of a dye to a brain phantom. Optical images are used to compute absorbance fields and a modern implementation of the inverse Abel transform is employed to compute concentration maps and missing absorbance pixels due to microdialysis probe shadow. The method was used to measure the delivery of methylene blue to an agarose gel with the dye solution flowing through the probe in a range of flow rates. The resulting delivery rate and efficiency can be interpreted using a simple model from the microdialysis literature. Deviations from the model occur for both the lowest and the highest flow rates investigated here. The former is explained by an effect of buoyancy while the latter is due to a net fluid convection to the gel. Reconstructed concentration fields were also compared in different scenarios, showing that the flow rate in the probe affects not only the overall size of the drug plume, but also its shape. The method presented here can be used for quick and inexpensive probe design and protocol iterations before proceeding to more in-depth in vitro and in vivo experiments.


To enhance the efficiency of tractor operation, the longitudinal and lateral dynamic control of a self-driving tractor is studied in this paper, and a control system that decouples control of the longitudinal and lateral movement of the tractor is proposed. The trajectory controller calculates the desired speed and desired yaw rate signals of each subsystem, and a PID controller regulates the longitudinal speed of the tractor. A pure pursuit algorithm calculates the desired front wheel angle of the tractor. To decrease the system time delay in the automatic steering system, an automatic steering scheme based on improved Smith predictive control is proposed. Through decoupling control of the longitudinal and lateral controllers, the tractor’s path tracking performance is assured. According to the tracking direction, path tracking can be split into lateral tracking and longitudinal tracking. At present, the most used lateral tracking algorithms are PID, fuzzy control, optimal control and preview point control.The loss of young labour and the aggravation of the energy crisis have promoted the development of high efficiency and energy saving agricultural production. To enhance the efficiency of tractor operation, this paper studies the path tracking problem of autonomous driving tractors that many scholars have researched in this field. At present, methods commonly used for tractor path tracking are split into two categories: one is to control through mathematical models, and the other is to regulate methods that do not rely on mathematical models. According to the type of mathematical model used, they are divided into control methods based on a vehicle kinematics model and control methods based on a vehicle dynamics model2 used a PID control method for trajectory tracking, which has better tracking performance in lateral trajectory tracking, but has poor adaptability to complex situations. Kang et al.3 used a PID method to obtain steering input values. The model uses two PID controllers to control the lateral deviation and the heading deviation and calculates the steering input value through the output of the deviation controller. Luo et al.4 used a PID algorithm to design a path tracking controller for Dongfanghong X-804 tractor straight tracking, which uses the front wheel angle as the input and the lateral tracking deviation is the output. Bodur et al.5 proposed a double look-ahead reference point vehicle path tracking method, which uses only simple arithmetic operations. The adopted preview reference point can compensate for the centrifugal force and reduce the lateral deviation caused by the change in the path curvature. Zhang et al.6 used the fuzzy adaptive PID control method to control a transplanter’s steering operation. The deviation between the actual heading angle and the target heading angle was the difference from the actual front wheel angle, and the desired front wheel angle was calculated together with the driving speed. Plessen and Bemporad7 proposed a trajectory tracking method based on linear time-varying model predictive control theory for high-precision closed-loop offline path tracking in agricultural scenes. Wang and Hsu8 proposed an improved pure pursuit algorithm, which reduces lateral tracking deviation by regulating the heading angle and steering angle and improves the tracking accuracy compared with traditional methods. Li et al.9 proposed a path tracking method based on a fuzzy adaptive pure pursuit model, which improves the path tracking accuracy through adaptive adjustment of the forward-looking distance. Chen et al.10 designed an auxiliary driving system for a high-gap plant protection machine based on the preview algorithm and verified the driving stability and operation accuracy of the auxiliary driving system through simulation and real vehicle tests. A composite controller for wheeled mobile robots with external disturbances and parameter uncertainties was studied by Liu11. A disturbance observer based on an adaptive sliding mode dynamic controller was introduced to estimate disturbance online, adjust control gain automatically and eliminate the chattering phenomenon. Zhang et al.12 proposed a sliding mode method based on the integrated control algorithm of deviations of lateral position and heading angle. This strategy generates the corresponding steering angle by modifying the proportional coefficients of the lateral position controller and the heading angle controller. A comparison of the various lateral tracking control strategies is shown in Table In terms of lateral tracking, some researchers have conducted correlated studies. Netto et al.13 studied high-level unmanned vehicles, designed for speed tracking, and verified the input and output linearization of a sliding mode controller through a test for variable speed on a straight path to propose a sliding mode control strategy. Erdal14 studied the path tracking control of tractors, proposed a PD + T2FNN  yaw-angle dynamics controller and PID controller for longitudinal speed control, and tested the effectiveness of the algorithm through actual vehicle tests.Longitudinal tracking regulates the longitudinal speed or acceleration as the target. Because a tractor’s operating environment is relatively simple and the requirement for longitudinal motion tracking is relatively low, traditional PID control can satisfy the operation requirements. Researchers have conducted studies in the field of autonomous vehicle longitudinal motion control. CaoAmong the above methods, methods using kinematic and dynamic models largely depend on the accuracy of the mathematical model. In addition, a tractor is a complex nonlinear system in actual operation. It is difficult to establish a high-precision mathematical model, so the accuracy of the established model directly affects the efficiency of tractor path tracking. PID control and pure pursuit algorithms neither rely on complex mathematical models nor require complex control theory. They are widely used in the field of agricultural vehicle navigation control. At present, most researchers use the tractor steering angle as the control variable, and speed control research mainly focuses on the development of cruise control systems. There are few studies that combine longitudinal speed control and lateral motion control. The combined control of the longitudinal and lateral movement of a tractor can not only improve the efficiency of the tractor and reduce the labour intensity, but will also be more practical. Meanwhile, there is a lack of relevant research on steering time delay in the literature on steering subsystem research. When a tractor operates in a straight line in the field, it must maintain a steady speed to ensure the operation effect. When the head turns, the driving speed should be reduced during the turning process to ensure the smooth running of the tractor while achieving the smallest turning radius. To provide a technical reference for the realization of higher efficiency and higher precision unmanned driving, based on the inverse kinematics model, this study analyses the longitudinal and lateral control of a tractor and uses a pure pursuit algorithm to couple the longitudinal and lateral motion of the tractor. To improve the time delay of an automatic steering system, an improved Smith predictive control strategy is established, and the effectiveness of the improved control strategy is verified through simulation comparison.This paper is organized as follows. The experimental plant is described in “The hardware system structure of an automatic driving tractor is shown in Fig. When the satellite signal is lost, the data calculated by the inertial navigation system can be used to locate the tractor through corresponding calculation. The inertial navigation system can also measure the tractor’s attitude angle information.The navigation computer calculates the deviation value between the current trajectory and the reference trajectory based on the data transmitted by the integrated navigation system to provide the steering angle information for the automatic steering system to execute. The steering computer calculates the steering deviation value according to the steering angle instruction received and the real-time detection value obtained by the front wheel angle sensor and controls the hydraulic steering system to complete the steering operation. The pressure sensor in the figure is used to detect the oil pressure and prevent the operation of the automatic hydraulic steering system from overloading. The yaw rate and front wheel angle of the tractor are measured by a gyroscope and front wheel angle sensor, respectively.When a tractor is operating, it usually works with farm tools. Different farm tools need different traction forces during operation, and some farm tools need to be driven by the tractor’s power output to achieve the operation effect. Therefore, the tractor motion is simplified in this study, only the motion of the tractor itself is considered, and all the power of the tractor is used for its own driving.Tractors are low-speed four-wheel vehicles. When considering errors such as tire and soil characteristics, tire slip, actuator transmission, installation and other errors, it is difficult to describe the system motion through an accurate mathematical model. Simplified mathematical models are usually used to describe the control system. This study uses the model shown in Fig. Vy = ωlr:In the decoupling control of the longitudinal and lateral motion of a tractor, it is necessary to research the longitudinal speed and the yaw rate. The above tractor kinematic model can be further written as follows according to PCG = [x y]T, the above formula can be expressed as:Because the coordinate of the CG is The inverse kinematics model shown below is established.The desired longitudinal velocity and the desired yaw rate are expressed as:ωd is the desired yaw rate, and Vxd is the desired longitudinal speed. Martins et al.15 further expressed the above inverse kinematics formula as follows:ex = xd − x and ey = yd − y are the current position errors in the X and Y axes, respectively. ks represents the saturation constant, ke represents the gain of the controller,and both ks and ke > 0. The coordinates  and  are the current and the desired coordinates, respectively.In the above formula, The air resistance of the tractor when driving is ignored.Considering that the moments of the tires are small, they can be ignored.When a tractor actually operates, the driving speed is slow. It can be considered that the sideslip forces acting on the left and right wheels are equal. A three-degrees-of-freedom vehicle model is used to research the yaw, lateral and longitudinal motion of the tractor. The tractor’s speed, slip angle, and external force on the vehicle body are shown in Fig. The lateral movement of the tractor can be obtained according to the force balance:J represents the moment of inertia of a rigid body and β represents the angular acceleration of a rigid body. According to the definition of the moment of inertiaHere, The yaw motion of the tractor at the CG is written as Eq.  accordin16 approximated the moment of inertia as:To decrease the calculation strength of the tractor’s moment of inertia, Garrott17.ki, i = {f,r} represents the cornering stiffness of the tires.Considering that a tire is a complex nonlinear system in actual operations, to facilitate the calculation of the tire lateral force, a linear model is used to simplify it. The lateral tire force has a linear relationship with the slip angle according to Gartley and BevlyThe side-slip angle of the front and rear wheels is calculated with the following formula:Equation  can be wThe equation of tractor yaw dynamics can be written in a state space formWhen a tractor is running on sloping ground, assuming that the air resistance is ignored, the force analysis diagram of the tractor can be simplified into Fig. According to Newton’s second law of motion, the force balance along the slope direction can be expressed in the following form:18 defines the slip rate as:uw represents the speed of the wheel centre, ωw represents the wheel angular velocity, and rr0 represents the wheel radius when the tractor is not braking.Rajamanis is small, Ftf and Ftr have a linear relationship with s, which can be approximately expressed as:When the slip ratio k represents the rolling resistance coefficient.The rolling resistance of the front and rear wheels is approximated by the following formula:Mtire-r = 0, the moment equation is:When the rear wheel is the moment balance point ΣFrom the above equation, we can obtain:In the same wayFz.We can see that the acceleration of the vehicle U(s) as input and a steering angle δ(s) as output (Shinji and Tsugiharu19). When considering the actual delay in the system, the open-loop transfer function of the hydraulic steering system can be expressed asThe electronically controlled hydraulic steering system of a tractor can be regarded as a mathematical model with a reversing valve control voltage K = 22.7, τ = 0.05, and L = 0.12.The parameters are determined through tests to be When an autonomous tractor is operating, the current position and motion state are determined in real time through satellites and compared with the target point on the set path. The steering angle of the front wheels and the longitudinal speed are controlled through correlated algorithms so that the tractor can drive along the set path. The tractor’s automatic navigation system corrects the front wheel steering angle and longitudinal speed to make the vehicle drive along the set path. The overall control block diagram of a tractor is shown in Fig. As shown in Fig. To control the longitudinal and lateral motion of a tractor, it is necessary to study the longitudinal speed and the steering angle of the front wheels and determine the desired longitudinal speed and the desired yaw rate from the tractor inverse kinematics model obtained above.For longitudinal speed control, this study uses a PID control strategy, and for the control of the front wheel steering angle, this study uses a pure pursuit algorithm to determine the desired front wheel angle according to the desired longitudinal speed and the desired yaw rate. Finally, path tracking is completed by decoupling the control of longitudinal movement and the lateral movement.20. The navigation controller calculates the lateral deviation and heading angle deviation based on the position information and path information and generates the expected front wheel steering angle, as shown in Fig. To enhance the positioning accuracy of tractors, inertial navigation is usually used to assist satellite positioning22.In the path tracking algorithm, the pure pursuit algorithm does not rely on complex mathematical models. It is used to calculate the arc required by the vehicle to track the target path. The test vehicle must follow the calculated arc to move from its current position to a target position at the next moment, and the target point is selected from the set path. The pure pursuit algorithm continuously iterates, and the preview point P continuously updates the position along the path so that the vehicle travel path forms a smooth tracking trajectory and finally makes the vehicle travel trajectory completely coincide with the path A–B, completing the tracking controlThe geometric relationship of the pure pursuit algorithm is shown in Fig. Llook, and θ is the heading deviation. Then, the following formula can be obtained from the geometric relationship in the above figure:In Fig. From the above equationk, k = 1/r. Then, the above equation can be written as:The path curvature when turning is The following geometric relationship is obtained from Fig. θ is small e−Ls = G0(s)e−L0s. The tracking response transfer function from reference signal U(s) to system output δ(s) can be obtained from Fig. When the actual steering system and the steering system model match each other , the actual object is equal to the object model, that is, q(s) to the system output δ(s) isThe transfer function from the input interference signal It can be seen from the above formula that the input response and interference response in the control structure are completely decoupled, and the parameters of the controller can be obtained according to the internal model control method. Therefore, the IMC-PID controller is adopted to design the tracking controller and disturbance suppression controller. D(s) does not affect the input response, and it is used to stabilize time-delay unstable objects. The stability of the system is related to the characteristic equation Figures Through the structure of the internal model control principle, the following formula can be obtained:The internal model controller and feedback controller are27, the integral link is approximated by the first-order link, and when α is taken as a large enough numberAccording to the relevant theory of internal model controlThe process model is expressed asAccording to the design conditions of the internal model controller.Q(s); Q(s)G(s) is stable; (1 − Q(s)G(s)) G(s) is stable.There is no unstable pole in Therefore, the filter design isC(s) is represented by Eq.  is designed to beThe filter When the actual steering system and the steering system model match each other, the compensation sensitivity function of the load interference suppression closed-loop is expressed asY(s) formula, so D(s) is designed with reference to the knowledge related to internal model control theory, similar to C(s).The form of the above formula is similar to that of the Q(s) is used to represent the internal model controller. Then, referring to the relevant knowledge of the internal model controller27, Q(s) is expressed asIn the above formula, From Eq. , the folThe disturbance rejection controller formula is further approximated by first-order Taylor to obtain the following PID form:K = 22.7, τ = 0.05, and L = 0.12 of the hydraulic steering system determined in the previous section, the values of the two controllers C(s) and D(s) are established. Since the process is not clear and unknown, take According to the model parameter, Step signal input simulation. When the time is 0 s, a unit step signal is added to the input of the set point. When the time is 6 s and 13 s, the step interference signals with the amplitudes of 0.2 and 0.1 are added to the input and output of the controlled object, respectively. The output waveform shown in Fig. Sinusoidal signal simulation. When the time is 0 s, the unit sine signal is added to the input of the set point. When the time is 6 s and 13 s, the input and output of the controlled object, respectively, are added with step interference signals with amplitudes of 0.2 and 0.1 in the opposite direction. Finally, the output waveform shown in Fig. To test the effect of improving Smith’s predictive control, the model shown in the Fig. The results shown in Fig. The green dotted line in Fig. It can be seen from the above simulation diagram that the hydraulic steering control method used in this paper not only improves the anti-interference ability of the system but also makes the system have strong robust stability. In the hydraulic steering system control scheme proposed based on the improved Smith predictive control theory, the disturbance suppression response and tracking response of the steering system are independent of each other. The two controllers are designed in IMC-PID form, and they can be independently adjusted and optimized through a single parameter. Based on ensuring the performance of the setpoint tracking response, the system has good anti-interference ability and can fully meet the requirements of the actual work of the autonomous tractor.29. Therefore, the longitudinal motion system model of the tractor is represented by “Vxd represents the desired speed of the tractor, Vx represents the actual speed of the tractor, and the parameters of K and T were estimated as K = 1.04 and T = 2.06, respectively, by related experiments.Considering the operation situation of a tractor, the longitudinal dynamics model can be simplified to a first-order systemKp = 6, Ki = 3, Kd = 1.5In the longitudinal motion, a PID controller is used to control the speed of the vehicle. PID parameters are selected according to the longitudinal motion system model, and finally 30. Simulink was used in the simulation to build the model. The time step was fixed-step: 0.025 s, and auto (Automatic Solver Selection) was set by Solver. The time step of CarSim was 0.001 s, and the output file time step was 0.025 s with the integration method: AM-2 (2 updates per step).In this section, a system simulation was executed on the vehicle dynamics simulation software CarSim, in connection with MATLAB/Simulink to test the performance of the proposed control method−1, and the constant value of the tire-road friction coefficient (u) was 0.85. The simulation was path tracking on a Moose test track (Fig. The tractor model was selected from CarSim. The tractor parameters are given in Table ack Fig. . The refThe overall CarSim and Simulink simulation model was run, and the relevant simulation results are shown in Figs. −1, and the blue line is the actual speed change curve of the tractor. When the expected speed information is sent to the longitudinal motion controller, the tractor can quickly respond to it, and finally the actual vehicle speed is consistent with the expected speed, indicating that the tracking effect of longitudinal speed meets the demand.In Fig. In Fig. It can be seen from Figs. It can be seen from Fig. −1. The test results are as follows.To verify the path tracking effect of the tractor, the test was carried out at a speed of 30 km hIt can be seen from Fig. −1 at ordinary times, which can meet the actual operating requirements.Figures From Figs. The above test data are based on the road environment, as shown in Fig. When considering the influence of the road friction coefficient, the corresponding results are shown in Fig. Vx of 8 and 10 km h−1 was studied, and the results are shown in Figs. Compared with Figs. As shown in Fig. −1, there is little deviation on a straight road. There will be some deviations in path tracking during the turn, but these deviations are small and have little impact on the actual operation. At the same time, it can be seen from Figs. As shown in Fig. In this paper, a path tracking control strategy for a tractor was designed based on the inverse kinematics model of the longitudinal and lateral dynamic decoupling control. The goal of controlling a tractor is to make it automatically track the desired trajectory and ensure that the tracking accuracy meets the actual agricultural production requirements. In this paper, the improved Smith predictor controller proposed for the hydraulic steering time delay verified the effectiveness of the control algorithm through simulation and comparison.To test the overall control strategy, a joint simulation with CarSim and MATLAB/Simulink software was carried out. The experimental results show that the control strategy proposed in this paper can maintain a good tracking effect, and the driving speed can meet the actual operation requirements of the tractor. At the same time, the yaw rate, lateral acceleration, and other information when the tractor is travelling are analysed. The proposed path tracking control strategy can ensure the comfort and driving stability of the driver while ensuring the accuracy of path tracking. Considering that suspended farm tools are not considered in the vehicle dynamics modelling in this study, an overall tractor-farm tool dynamics model will be built in future research, and the tractor will be controlled according to the overall dynamics model so that the tractor can reach a better operation effect and maintain good fuel economy.


Discover the associations of force of applanation on the eye with the plunging depth of the cornea and quantify them. The results will be utilized as the feedback parameter in the new prototype development of eye care instruments as additional force may damage the internal structure of the eye or may result in erroneous output.A finite element-based eye model is designed utilizing the actual dimensions of the human eye. A standardized tonometer is designed and the simulation is carried out at predetermined deformation of the cornea to find the force of applanation on the cornea during tonometry. Adding on, the influence of IOP during tonometry is analyzed for a range of plunging depths of the cornea. The graphical results inferred the linear relation between the force of applanation with the deformation of the cornea and the results are quantified. The resulting deformation and stress plot of FEM based simulation approach is analyzed and observations regarding deformations and stress are made.The human eye is successfully developed and also computed force on the cornea during tonometry is validated. The inference drawn from the deformation plot and stress plot is that the junction of cornea–sclera along with cornea-tonometer periphery undergo maximum deformation and experiences the highest stress compared to other areas of the eye while during tonometry. Glaucoma refers to a group of diseases that damages the optic nerve. It is a pathological condition that causes optic nerve neuropathy and structural damage to the eye. This finally culminates in permanent vision loss . There iThe present study is focused on the biomechanical FEM (finite element model) simulation of an asymmetrical 3-D model of the human eye constructed consisting of cornea and sclera under tonometry. The study is also evolved with the design of a standard tonometer which consists of a probe to applanate the cornea. Currently, Pneumotonometer, tonopen, Mackay Marg tonometer, and Icare tonometer are the existing tonometers that utilize the plunger or probe to measure the IOP of the eye. A plunger with a 5 mm diameter inside the Pneumotonometer placed on the eye for 5–10 s will measure the pressure inside the eye for the given displacement . TonopenC1 = 1530 m/s, s1 = 2.1057 and vitreous humor as viscoelastic G0 = 10 Pa, G∞ = 0.3 Pa, β = 14.26 1/s, k = 2.0 GPa, sclera and cornea were modeled as the nonlinear stress–strain as material properties [The explicit dynamic analysis was conducted for the blunt impact of foreign bodies on the eye . The eyeoperties . The visoperties . The eyeoperties .In the present research, FEM-based evaluation is used to calculate the amount of force exerted by the tonometer on the cornea during tonometry with a standard tonometer. The FEM study incorporates a tonometer cylindrical probe of 1.7 mm diameter . PredeteThe tabulated results from this study such as force, stress, and deformation can be implemented in the new technology development of eye care instruments such as a tonometer, goniolens, pachymeter and hence can be utilized in the eye care industry.The designed model of the human eye is close to the actual dimensions of the eye and hence the model is close to the actual human eye. The investigation of the force on the cornea during eye care testing procedure is not addressed in clinical and industrial side and hence the study about the applanation force during eye care testing procedure is unique.The eye model was made with the loft protrusion method. The dimensions of different parts of the eye model are listed in Table The eye model was divided into nine different parts as 4 parts of the sclera, 1 part of the cornea, and 4 parts of the corneoscleral junction for the simplification of the meshing. The average element size of the complete eye model is 1.9816 mm. The mesh model resulted in a total node count of 58,999 and a total element count of 11,613.The main aim of the simulation is to determine the force applied by the tonometer over the eye. The tonometer will apply force over the surface of the cornea to provide a predetermined deformation or plunging depth on the surface of the cornea. In the previous simulation in the literature, the main concentration was impact analysis. Since the tonometer is not impacted on the eye, analysis was carried out in ANSYS static structural to find the reaction force or applanation force responsible for deformation of the cornea for a given fixed set of displacement of the tonometer. This is simulated by moving the tonometer probe onto the eye in direction towards the retina or of the apex of the orbit and calculating the reaction force on the tonometer. The tonometer was taken as a cylinder with a diameter of 1.7 mm . The tonHuman ocular tissues are generally viscoelastic and exhibit nonlinear material properties . But it The sclera was given the condition of the remote displacement zero. This boundary condition allows the deformation to occur on the mesh elements of the eye but constraints the movement in the space. This simulates the eye held in place by the eye socket which is similar to the research done in , 15 but The human eye is modeled using FEM-based simulation software that is more close to the actual size. The model consists of the human cornea, sclera (4 components), and the junction between cornea and sclera. The tonometer probe designed is 1.7 mm in diameter. The simulation is carried out on the designed model of the eye, by placing the standardized designed tonometer at the center of the cornea. The deformation of the cornea takes place when external pressure exceeds the internal pressure , and a sThe FEM-based investigation has resulted in a deformation chart of the eye and also stress distribution of the eye during tonometry. Figure The eye model with dimensions obtained from –26 constThe deformation chart of the human eye during tonometry is indicated in Fig. Figure The simulation is carried out for determining the amount of force applied on the cornea for the predetermined displacement of the cornea during the tonometry test. Plot 1 demonstrates that the force applied on the cornea is small at lower deformation of the cornea and further steeply increases at larger deformation of cornea. Hence, the force increases from 0.02 to 0.045 N for an increase in the plunging depth of the cornea from 0.3 to 0.7 mm. The force on the cornea increases with increasing the IOP of the eye from 10 to 20 mmHg during tonometry. Plot 1 concludes that force on the cornea is increased by approximately 0.004 N for every 5 mmHg increase in IOP of the eye.The research work is carried out with a design of a standard tonometer of size 1.7 mm diameter and also by considering the standard tonometer such as Goldmann applanation tonometer. The simulation is repeated with Goldmann Applanation tonometer of 3.06 mm diameter, at 20 mmHg IOP of eye and by varying the plunging depth of the cornea from 0.3 to 0.7 mm in the steps of 0.1 mm along the direction towards retina. The reaction force experienced by the Goldmann applanation tonometer for providing the plunging depth of cornea from 0.3 to 0.7 mm in steps of 0.1 mm was found out to be 0.028956 N, 0.031776 N, 0.034597 N, 0.037417 N and 0.040237 N, respectively. The results are very close to the observations obtained with the tonometer of 1.7 mm diameter. The results prove that the force of applanation on cornea depends on the IOP of eye and the area under the influence of force of applanation and is independent of the dimensions of the tonometer. Also, the force of applanation on cornea varies linearly with respect to the deformation of cornea.The limitation of the study is that the simulation approach has not considered the flow of aqueous humor in the anterior chamber of the eye to develop the required pressure in the eye.For the validation of the eye model and simulation results, the experimental results from  was consThe outcome of the research is that a maximum force of up to 0.045 N will be applied on the cornea during tonometry with a standard tonometer while the IOP is in the normal range. The analysis has also resulted in quantifying the stress to be 0.2 MPa on the cornea at the junction during tonometry while IOP is in the normal range. The plot of the amount of deformation on the entire surface of the cornea and sclera are measured accurately while performing tonometry. The stress experienced by the cornea at the junction of cornea and tonometer is assessed in the course of tonometry.In the present study, the force on the cornea is evaluated based on the size of the probe and the amount of deformation of the cornea. In the future may be utilized for the design of new technology development of tonometer or can also be implemented as an additional constituent in any working tonometer. The results can also be utilized as feedback to determine the amount of force applied on the cornea in all the clinical eye testing procedures and if it is increased can act accordingly. In the future, the circulation of aqueous humor in the anterior chamber could be considered for the accurate analysis of the simulation work.


To evaluate three of the main verbal models that have been proposed to explain the relationship between fluctuating asymmetry and fitness in humans: the “good genes,” the “good development,” and the “growth” hypotheses.A formal model was generated for each verbal model following three steps. First, based on the literature, a theoretical causal model and the theoretical object of inquiry were outlined. Second, an empirical causal model and the targets of inference were defined using observational data of facial asymmetries and life‐history traits related to fitness. Third, generalized linear models and causal inference were used as the estimation strategy.The results suggest that the theoretical and empirical assumptions of the “good genes” hypothesis should be reformulated. The results were compatible with most of the empirical assumptions of “the good development” hypothesis but suggest that further discussion of its theoretical assumptions is needed. The results were less informative about the “growth” hypothesis, both theoretically and empirically. There was a positive association between facial fluctuating asymmetry and the number of offspring that was not compatible with any of the empirical causal models evaluated.Although the three hypotheses focus on different aspects of the link between asymmetry and fitness, their overlap opens the possibility of a unified theory on the subject. The results of this study make explicit which assumptions need to be updated and discussed, facilitating the advancement of this area of research. Overall, this study elucidates the potential benefit of using formal models for theory revision and development. An empirical estimand, on the other hand, defines the quantity that can be recovered from observed data only, and thus informs us about the theoretical estimand under specific assumptions . The last component of this framework is the estimation strategy or the process that will be used to learn about the empirical estimand, which includes the estimator and estimate. Among other things, it is sought . The difference between DAGs and other ways of encoding the causal relationship, such as structural equation models (SEMs), is that while the former encodes the qualitative relationship between them, the latter specifically encodes the form  of said relationship , a theoretical causal model of this relationship and establish what the theoretical object of inquiry  is. Then, from these general models, I outline the empirical causal model and the target of inference  that is the focus of the present study, and the estimation strategy used.1.2The definition of FA entails two different interpretations of what an increase in FA means , distributed in 78 extended and nuclear families, with an average of three members per family (range = 0–11). This dataset was collected in Chiapas province in Mexico. Volunteers who lived in the same geographic area throughout their lives, without previous facial surgery, craniofacial trauma, congenital anomalies, or orthodontic treatment were included in this study. Informed consent was signed by each participant before personal and phenotypic data were collected , following the standard recommendations for quality and accuracy of the software. The distance chelion‐chelion, measured directly on the individuals using a standard anthropometric caliper, was used as a scale factor.The 3D facial shape was captured using photogrammetric methods applied to a series consisting of five separate digital photographs from different angles . All photos were taken at a constant distance of 1.5 m with a standardized photographic protocol described in detail previously  were placed on the photographs trying to avoid data redundancy and following standard terminology  were used in subsequent analyses.The 3D coordinates of all landmarks were superimposed using the generalized Procrustes analysis (GPA) in the MorphoJ software . The number of offspring  was considered as a measure of fitness, and the adult height  of the individual as a proxy of their health status .Data on life history traits were only available on a subsample of female individuals  of FA, expecting values greater than 0 . Given that the estimation of this effect involves life‐history traits, all three hypotheses were evaluated using the subsample of females.Dagitty, Textor et al., The strategy to estimate the causal effect of facial FA on the number of offspring given the corresponding empirical causal model was, first, to use an automated causal modeling tool  of facial FA on the number of offspring, with possible values for this parameter that were most compatible with the data ranging from 0.244 to 0.402 . In other words, conditional on the DAG, individuals with higher asymmetries have more children. Additionally, the generalized linear mixed model provided a mean heritability of facial FA close to zero (h2 = 0.046) with possible values ranging from 0.0002 to 0.174 , which means that almost none or little of the phenotypic variation in FA is explained by genetic variation.The results for H1 show that there was a positive effect (β = 0.294) of facial FA on the number of offspring conditional on the individual's adult height, with possible values for this parameter ranging from 0.213 to 0.374 . This means that individuals with higher FA values for their height have more offspring. In addition, there was a negative effect (β = −0.275) of the adult height on the number of offspring, with possible values ranging from −0.359 to −0.191 . In other words, those individuals who are taller have fewer offspring. Finally, there was a negative effect (β = −0.13) of height on facial FA, with possible values ranging from −0.266 to 0.006 . This means that taller individuals exhibit lower facial FA.The results for H2 show that there was a positive effect (β = 0.01) with possible values for this parameter that were most compatible with the data in a relatively wide range from −0.127 to 0.148 . Finally, the results show a very low negative effect (β = −0.04) of face size on facial FA with possible values in a relatively wide range from −0.179 to 0.093 .The results for H3 show that the direct and indirect effects of facial FA on the number of offspring calculated under this model are the same as those effects obtained in the first and second hypotheses, respectively. Moreover, there was a very low positive effect of height on face size  for each hypothesis and tested them in the particular case of facial asymmetries and reproductive success.4.1The present study shows that even if the approaches are different, some of the theoretical assumptions overlap across hypotheses Figure , openingFrom the framework of signaling theory, attributes other than physiological information are recognized as signals  on the expression of phenotypic variation and, particularly, on the production of asymmetric traits. Specifically, this assumption differentiates between research on FA variation that focuses on its genetic basis (H1: symmetry reflects good genes) and research that focuses on the development pathways that lead to such within‐individual variation (H2 and H3: symmetry reflects the interplay between the organism and its circumstances). Although the former ignores the idea that has been present since the 1980s in the field of evolutionary developmental biology Müller,  that the4.2This study also shows some similarities and differences between hypotheses when the results are compared with the expectations derived from the empirical assumptions. In the case of the “good genes” hypothesis, the corresponding empirical causal model expects that individuals with greater facial FA values have less reproductive success than individuals with less asymmetry. Moreover, it expects that part of the phenotypic variance of facial FA is explained by genetic variation. In contrast, I found that individuals with greater facial FA values have more offspring and a heritability close to zero . The latter result is the first report of heritability of FA in the human face and is consistent with previous research showing very low or no heritability of other traits in humans and other species ; data curation (lead); formal analysis (lead); investigation (lead); methodology (lead); writing – original draft (lead).The author was supported by the Postdoctoral Fellowship program DGAPA‐UNAM.The author declares no conflict of interest.


Electrochemical responses were examined after different oxidation treatments, then simulated and interpreted using the Kissa 1D software and existing models. Our experiments indicate that a crude carbon fiber behaves as an assembly of sites with different electrochemical reactivities. In such case, the Butler–Volmer law is not appropriate to describe the electron transfer kinetics because of the large created overpotential. Oxidation of the fiber erases the effect by increasing the kinetics of the electron transfer probably by a homogenization and increase of the reactivity on all the fiber. Additionally, analysis of the signal shows the large influence of the convection that affects the electrochemical response even at moderate scan rates (typically below 0.1–0.2 V s Carbon electrode materials are used in numerous applications notably in redox flow batteries where electrodes are often composed of carbon felts . The mor4Fe(CN)6]. These two redox couples were chosen as they present different interactions with a carbon surface 4− that obviously justifies the treatment of the fiber before its use in an electrochemical application.Similar conditions and a simple electron transfer described with a Butler–Volmer law were then considered to simulate the voltammograms recorded with the untreated fiber (type 1) see . A reasolectrode . This moα around 0.8 that is considerably different from the 0.5 of the Butler–Volmer Law. Second, we do not observe a return current (reduction) in our experiments contrarily to the prediction of the simulation. The oxidation of [Fe(CN)6]4− occurs with a large overpotential on the fiber (0.7–0.8 V above the E°) and a quadratic activation-free energy relation as in the Marcus model is probably more appropriate for describing the electron transfer kinetics. This could explain that the apparent transfer coefficient is largely different from 0.5. Indeed, in the framework of the Marcus model, α is defined asα significantly different from 0.5 in case of large overpotential 4− on an activated fiber (−1). Considering a reasonable thickness for the natural convection layer around 100 μm, one could see that the extension of the diffusion layer will already be affected at scan rates below 0.1 V s−1 and that a voltammogram recorded at 0.01 V s−1 will be almost controlled by the natural convection. If we now consider a convection layer of 50 μm, even a scan rate of 1 V s−1 will be disturbed. Looking at the experiments of 6]4− oxidations on type 3 fiber, occurrence of convection explains that the voltammograms display a plateau-shape character at the lower scan rates. We could also derive a sort of empirical value around 50–100 μm for the convection layer thickness for a stationary solution.Using a single carbon fiber as an amperometric sensor is a simple concept that could be envisaged to measure the concentration of a redox species as a simple low-cost and miniaturized device notably in redox flow batteries . It woulon of Fc  or the oed fiber , the cured fiber  at the l4[Fe(CN)6] at different concentrations in KOH 0.1 mol L−1. We applied a constant potential at 0.65 V and measured the current as function of time. We used an oxidized fiber to ensure that the system is controlled by the mass transfer with negligible influence of the electron transfer kinetics. Variations of the current at different concentrations and measurement times (10−2 to 1 s) are shown on Because it is difficult to quantify the possible unfavorable evolution of the natural convection with the environmental conditions, we prepared some test solutions of K−1 and we have seen that this is the limit for neglecting the convection in a stationary solution. A simple experimental test consists in stirring the solution to modify the convection around the fiber. As seen on the recorded chronoamperogram of For the longer times, a good linearity was obtained. According to the previous estimation, measurement time of 1 s corresponds approximatively to a voltammogram of 1 V sIn conclusion, a carbon fiber that may be seen as a simple object displays in fact a complicated response for which a full description remains challenging. This is notably due to their inhomogeneous properties and the large interference of convection that is already present in most common conditions of use.Our experiments suggest that a crude carbon fiber behaves as an assembly of sites with different electrochemical reactivities. In such a case, Butler–Volmer law is not appropriate to describe the electron transfer kinetics because of the large created overpotential. Oxidation of the fiber erases the effect by increasing the kinetics of the electron transfer, probably by homogenization of the reactivity on all the fiber. This is accompanied by a light increase in the background current that could limit the use of the fiber in a short time.Concerning the use of a carbon fiber as a sensor, such application needs short measurement times that would require an improvement in the electrode in terms of background current and the use of a fast potentiostat. Using long (or even moderately long) time for the measurement is clearly not possible because of the cylinder geometry. In such conditions, the electrochemical response is affected by the natural convection and thus is too sensitive to the environment for a practical use.


The journal retracts the 12 February 2019 article cited above.Following publication, concerns were raised regarding the integrity of the data in the published figures. The authors failed to provide a satisfactory explanation during the investigation, which was conducted in accordance with Frontiers’ policies.This retraction was approved by the Chief Editors of Frontiers in Immunology and the Chief Executive Editor of Frontiers. The authors do not agree to this retraction.