In social robotics, especially with regard to direct interactions between robots and humans, the robotic movements of the body, arms and head must make an adequate displacement to guarantee an adequate interaction, both from a functional and social point of view. To achieve this, the use of closed-loop control techniques that consider the complex nonlinear dynamics and disturbances inherent in these systems is required. In this paper, an implementation of a nonlinear controller for the tracking of trajectories and a profile of speeds that execute the movements of the arms and head of a humanoid robot based on the mathematical model is proposed. First, the design and implementation of the arms and head are initially presented, then the mathematical model via kinematic and dynamic analysis was performed. With the above, the design of nonlinear controllers such as nonlinear proportional derivative control with gravity compensation, Backstepping control, Sliding Mode control and the application of each of them to the robotic system are presented. A comparative analysis based on a frequency analysis, the efficiency in polynomial trajectories and the implementation requirements allowed selecting the non-linear Backstepping control technique to be implemented. Then, for the implementation, a centralized control architecture is considered, which uses a central microcontroller in the external loop and an internal microcontroller  for each of the actuators. With the above, the selected controller was validated through experiments performed in real time on the implemented humanoid robot, demonstrating proper path tracking of established trajectories for performing body language movements. Body language  is a key component of human communication ,2. ExpreCurrent literature suggests that movements performed by robots are able to influence attitudes and perceptions toward them ,6,7. It In the context of service robots there have been developments of common gestures that could be applicable in different social scenarios  . ExampleThe mechatronic implementation of all these movements requires the use of automatic control techniques that consider the complex dynamics and disturbances inherent in these systems ,14. The Specifically, in some studies ,24, lineAt Pontificia Universidad Católica del Perú (PUCP), the Qhali robot is under development. Qhali is an assistance robot designed to perform telepsychological interventions. Its design considered a humanoid appearance with two (02) articulated 4DOF arms and one (01) 2DOF head with an LDC display. Both elements allow the robot to perform gesture expressions with arms and head movements, aiming to improve the human–robot interaction during the interventions. The robot also has a navigation system that allows it to move automatically from one point to another. To communicate verbally and non-verbally, the robot has audio and video systems to achieve the ability to express emotions, gestures and body language whose purpose is to improve human–robot interaction . The robIn this article, the design and implementation of the arms and head of Qhali are initially presented, then the mathematical model of two arms with 4DOF and the head with 2DOF will be obtained by applying the physical principles. It is verified that with the increase in equations for the different necessary operating points, a highly non-linear model is obtained.Then, the control design for this highly non-linear system is selected from the comparison of three non-linear controllers, such as non-linear PD control, Backstepping and Sliding Mode control, validating the results in simulation. Once the controller has been selected, the controller is implemented in ARM microcontrollers communicated with each of the servomotors through the CAN BUS protocol. Moreover, programming methods are presented which allow the use of these microcontrollers for centralized control in real time. In the implementation, first the validation of the obtained mathematical model is carried out and the control algorithm will be developed in the external loop that sends the necessary torque references to each motor where there will be an internal PI control loop.Finally, the validations of the control strategies are performed from a generation of spline and polynomial trajectories. These experiments are analyzed in real time, obtaining all the information to MATLAB through a serial communication protocol to the PC. The experimental results allow verifying the effectiveness of a purely non-linear controller such as Backstepping compared to a partially adapted linear controller such as PD control with gravity compensation. The results are documented and discussed with which we will be able to obtain the conclusions of the work developed. Finally, the programming of these controllers and the generation of trajectories improve the movements performed by the arms and the head of the robot.The design of the arms and head of the humanoid robot was performed following the methodology VDI 2206  used forAs a first step of the methodology, the design requirements were defined as shown in Following the design methodology, three (03) conceptual designs were developed and implemented to evaluate their performance. V1: four High torque servo motors, pulley and belt mechanism for 4th DOF, LED Matrix for eyes. V2: two High torque servo motors and two smaller, lower torque, pulley and belt mechanisms for 4th DOF, three small screens for eyes and mouth and V3: Joints directly driven by two high torque servo motors and two smaller, lower torque. Two screens for eyes and mouth.Based on a technical-economical evaluation, the third alternative was selected as the optimal conceptual design due to its performance and simplicity. Using this design, the upper body of the robot was included to the mobile robot platform, including the external structure. The electronic and mechanical design was carried out. The actuators for the arms were selected according to the torque requirements of each joint. The maximum torque was calculated through a static analysis at the critical position of a horizontally extended arm, as shown in According to the requirements, the PLA 3D-printed structural pieces were designed to support the motor loads and to be as lightweight as possible, making each arm of a total weight of 2.31 kg. The critical elements, which required an structural analysis due to the forces generated with motion, are located in the arms. A total of four (04) different pieces were required in order to assemble the arms and head, as shown in The chest piece, which was also 3D printed and contains the electronic boards to control and power the arms and head. It includes an audio subsystem (mp3 module and amplifier) and three (03) STM microcontrollers to interconnect different CAN buses and UART ports for communication with the actuators and other processors of the robot. The main chest piece also supports the head and the first arm joints, and connects the column with the upper body of the robot. The head has two (02) actuators, where their axes are perpendicular to allow 2DOF. The head has speakers on both sides, as well as two (02) screens of 5 and 3.5 inches, to emulate facial expressions, connected to a raspberry pi 4. Based on the specific-domain design, a prototype was implemented to continue with the control design for the arms. The final design of the robot arms and head possess the capacities to perform movements such as the ones represented in The modeling of mechanical systems is obtained from the physical relationships that govern movement such as gravity, inertia, and effects such as Coriolis and friction. All these motion parameters are mathematically related in the Lagrange equation, which can become very complicated as the degrees of freedom of the system are larger than two. In Fu et al. , we obseFrom the design of the prototype presented in When carrying out this analysis we obtain the homogeneous transform matrix arrays (4 × 4), that provide us with the information of the translation and rotation of a specific point of the system. In addition, this analysis will allow applying the inverse kinematics that allows the linking of an The application of the recursive algorithm explained in  gives usressions :(4)D=d11On the other hand, After obtaining all the system parameters of the robotic equation, several simulated tests have been performed to verify and validate the mathematical model found. In This is how we can verify that the system obtained is stable. The procedure is similar for both arms. In this way, we obtain the mathematical models of the arms and even for the head, considering the latter as a 2 × 2 matrix system. These models will be used to design and implement the control system.The control architecture of the system is composed of a main controller in the external loop that has as references the position In the case of internal PI control for each motor, the controller provided by the motor through its own software will be used, to which tuning tests will be applied to establish the most appropriate proportional and integrative parameters for each degree of freedom. In the case of the external loop, there is a nonlinear control that has been selected based on simulation tests in MATLAB according to the mathematical model obtained. Below is the comparison of the controllers.It is known that PID controllers are quite simple in their application to various systems since prior knowledge of the system is not required. In the case of robotic systems, applying an integrator could cause the control to limit the system to slower movements than required. A solution to this problem is to use a gravity compensator that provides the system with a variable bias in each move to obtain zero stationary error. The gravity compensator is added to the previous PD control law and forms a non-linear controller. It is possible to demonstrate the convergence of this controller if we apply the controller that has the following form:Then replacing Equation  in the rConsidering the following expression as a Lyapunov function:Its time derivative:Furthermore, considering the properties of the matrixes of the robotic equation, the following result can be reached:With which it is verified that the origin is stable and using the Lasalle invariance principle, the global asymptotic stability can be demonstrated using the following omega function:Since for Equation  it folloThen Similarly,  shows meIt is a controller based on the mathematical model of the system shown in Equation (3). Its main disadvantage is repeating the differentiation of virtual inputs, which increases the complexity of the controller . The litThe efficiency of this controller lies mainly in the choice of a successful system model. This controller, as in other nonlinear controllers, bases its design on the stability and convergence criteria of the closed-loop system from Lyapunov functions. The procedure to find the control law starts from the remodeling of the robotic Equation (3) to a state space system of vector form as follows:Then the state space equations would be:w has been used to represent the entire expression of Please note that the variable For this system, the first Lyapunov function and its following derivative are considered:To show that Then the stability of the system must be demonstrated to ensure that our virtual variable complies with what is required. This new system is given by:From Equation  the follBy deriving Equation  and consBy replacing Equation  in EquatTo achieve the stability of this system, the following Lyapunov function and its derivative are considered:To show that quations  and 24)V˙<0, thequations  obtaininRearranging the last expression:It is evident that to obtain that In this way, it is obtained:Thus, this last result allows us to prove that w with its original expression given in Equation  controllers designed and implemented using the MATLAB simulation software, it is possible to perform the tests that facilitate the comparison and the necessary conclusions for the choice of the controller that will be implemented in hardware.The first test is the comparison of the responses of each controller to a step input  CAN BUS ports for communication with the motors at each end of the robot and serial UART port for communication between all the ends of the ROBOT and the transmitted data to an analyzer such as MATLAB. To optimize the communication times of the CAN BUS protocol, it has been decided to use the two (02) CAN BUS ports of each STM32 card, connecting up to two (02) motors in each port. In this way, it has been possible to achieve a communication time of less than 20 ms. This time was used as the sampling time for the closed-loop controls. The STM32 cards share a serial bus one after the other through the UART protocol where they receive the selection of the actions to be performed by the limbs from the central navigation system. An additional UART port has also been implemented in each STM32 for the output of data in real time that will be used for the presentation of the results obtained in the experiments performed using the MATLAB software.The next step in the implementation is to verify that the mathematical model of the system is correct. As mentioned, most of the model parameters have been obtained from the CAD design of the worked prototype. However, only heuristic values were used for the proposed friction model. In , an expeIn this case, it was necessary to implement the PD controller with gravity compensation applied to a generation of trajectories with a trapezoidal profile that maintains constant speed. In Algorithm 1 Non-Linear Controller ExecutionResult: Torque signals to be applied by GYEMS motorsEach loop is timed per interruption at 10 mswhile doif “writing” is equal to 0 then            Generate position and velocity profiles        Compute control law and obtain torques in N/m        Scale the torque signals from N/m to Amp        Transform torques to communication CAN BUS signal        Set “writing” to 1else            Request position and speed information by CAN BUS        Perform scaling of position and velocity signals        Apply filter to the speed reference        Set “writing” to 0end if        end whileThe algorithm applied for the non-linear control of one of the arms was the following Algorithm 1:This algorithm was the same as applied for the Backstepping controller for both the arms and the head. A first experiment was performed using only the PD controller applying gains obtained by the Ziegler-Nichols method for each motor and then with the PD controller with gravity compensator, obtaining the results shown in Thus, we can see that gravity compensation solves the problem of the error in steady state and in this way, it is possible to apply it in with the generation of trajectories with trapezoidal profiles to obtain the frictions as can be seen in In this way, we obtain in At this point in the experiments, it can be observed that motors 1 and 2 maintain a very similar speed profile and the same for motors 3 and 4. This is because the first two motors are of the same GYEMS RMD motor model -X8 Pro with 6:1 reducer while motors 3 and 4 are GYEMS motors of the RMD L-70 model with lower torque capacity.Now that we have all the parameters validated for the mathematical model and with the comparison tests performed in the design and simulation stage (according to the discussion in the previous section), backstepping control is implemented. To verify the effectiveness of the implemented control, a first test performed out with changes in angles with a step input and with a disturbance applied to the system. It is observed that the arm reaches the desired position, and seconds later an external force is applied that changes the position and the Backstepping algorithm is responsible, after the disturbance, for repositioning the arm to the requested position. In When verifying the effectiveness of the Backstepping control in the regulation of the position, the generation of trajectories with trapezoidal profiles have been applied to take the wrist of the arm to a new different point in the cartesian space and return it to the ZERO position. This second test was performed by applying a disturbance during the resting state at the desired point of the movement. In In the same way as the first experiment, a better control can be observed for motors 1 and 2, which correspond to the motors with gearbox, which present better follow-up of the torque requested by the main Backstepping control, while in the case of motors 3 and 4, which do not have a reducer, the torque presents noise and therefore a more complicated follow-up, but still with regulation of position and speed. The disturbance applied in steady state also allows us to confirm that the regulation for all the motors of the arm is always achieved successfully.By performing the experiment at another cartesian point, we are verifying a controller expansion in a workspace with a slight change in controller gains. This test is motivated to perform a new experiment for a different point but this time applying softer movements through the use of polynomial trajectories of degree three to the right arm. With this, a smoother movement of the arm could be observed to reach the desired point. Additionally, the same control has been tested for the head system. In With the design, implementation, and testing of the proposed control scheme, it has been possible to provide a basis for the technological development of nonlinear controllers for complex multivariable systems. In addition, the analysis of different controllers used in this work provides us with a comparative reference for its implementation to other types of mechanical systems.As a result of the different experiments performed in the prototype of this project, it has been possible to verify the effectiveness of a purely non-linear controller such as Backstepping compared to a partially adapted linear controller such as PD control with gravity compensation. For this point, in addition to the results already presented, In the case of PD control with gravity compensation, it has been possible to observe that a minimum change in the values of the gains causes very different movement responses for the same conditions of the experiment, to the point of leading the system, in some cases, to instability. This further complicates the selection of gains for this controller which must change often depending on the desired motion. This allows us to think of an adaptive solution for the automatic change of these gains and in this way generalize the controller for a workspace.In the case of the Backstepping control, the selected initial gains have been generalized for all the movements tested in the arm, having to make a minimum adjustment.In this way, the present research is a starting point for the implementation of adaptive control laws or as a combination of the controllers used here with other controllers based on sliding modes and adaptive control.The programming of these controllers and the generation of trajectories provide us with the necessary tools to improve the movements performed by the arms and the head of the robot, even currently working on a combination of the generation of trajectories implemented for the formation of movements. composed and brought to a stage where the robot performs a complex presentation of its functions as part of the robot’s social interaction routine with people.The presented work performs the implemented tests of a Backstepping control for the arms and head of a teleoperated robot. The details of the movements made during the tests with the initial prototype are available to any researcher at the link specified in .A control scheme for the tracking of trajectories and a profile of speeds that execute the movements of the arms and head of a robot with natural motion similar to people was presented. Thus, it was possible to demonstrate the effectiveness both in simulation and experimentation in real time. The control strategy used is based on the information provided by an encoder of the position and speed of each motor with internal torque regulation with PI control through the CAN BUS protocol to the central Backstepping control that ensures the positioning of the motors for both arms and head of the robot. The work presented also made a comparison of the main nonlinear controllers on which it has been possible to distinguish the Backstepping control as the most appropriate regulator for the implementation presented, as well as some additional features as a result of this comparison. During the development of the non-linear controller algorithm, a procedure was performed that allows real-time communication of up to four (04) GYEMS motors with a single STM32 microcontroller and additional simultaneous communication of three (03) STM32 microcontrollers with a central navigation system through serial protocols. The results obtained for each movement were satisfactory since the control objectives were achieved, obtaining a precise control system that allows the freedom to regulate the way in which the robot arms and head reach the points that the robot routine requires.As future work, the Backsteeping control will be implemented to execute several routines, for which an automated calibration process will be developed to reduce the required time to optimize the parameters of the controller for different routines. Additionally, variations of the speed of the arms will be evaluated during the interaction with survey participants to determine the perception of the robot gestures based on their speed.


In this scenario, compact antennas on flexible substrates represent a strategical technological step to pave the way to a new class of wearable systems. A crucial issue to overcome is represented by the poor radiation properties of compact antennas, especially in the case of flexible and thin substrates. In this paper, we propose an innovative design of a miniaturized evolved patch antenna whose radiation properties have been enhanced with a Split Ring Resonator (SRR) placed between the top and the ground plane. The antenna has been realized on a flexible and biocompatible substrate polyethylene naphthalate (PEN) of 250 μm by means of a new fabrication protocol that involves a three-layer 3D-inkjet printing and an alignment step. The antenna has been characterized in terms of the scattering parameter S In this regard, the conception of wearable and bendable antennas is a crucial issue to overcome4. Scientific efforts concerned the design of miniature flexible antennas to cope with modern requirements such as wearability.With the advent of 5G and new 6G network infrastructures, flexible and bendable IoT devices are becoming increasingly popular5. However, the higher is the transmission frequency the more probable is the insurgence of disturbing phenomena such as multipath fading and attenuation6. The second alternative is antenna miniaturization. This technique aims to decrease the resonance of antennas by increasing its electrical length, so with the same geometrical dimension antennas can radiate at a lower frequency. The main drawbacks of this strategy are the degrading of the radiation properties and bandwidth reduction. In addition to compact footprints, optimal radiation properties are needed. These requirements increase the difficulty of the design procedure since the geometry of the antenna must be efficiently optimized, typically and especially on very thin substrates.Due to the high demand coming from the market, rapid prototyping and cost-effective technologies for antenna fabrication are becoming crucial and, hence, multiple technologies have to be combined to achieve the very strict goals required by antenna design. From one side, the footprint of the antenna can be reduced increasing the operating frequency7 and antennas11.In this context, artificial intelligence (AI) comes to aid. AI algorithms have been used for years to solve a huge variety of optimization problems, including antennas design. Among other methods, the genetic algorithm (GA) is one of the most used approaches regarding different electromagnetic problems such as photonics12. Miitra13 was one of the first authors to exploit this line of research. Reference8 reports a tutorial about GA applied to this kind of applications while reference9 details the design of antennas employing GA and the Method of Moments (MoM). In10, the GA is applied to miniaturize a patch antenna for cardiac pacemakers operating at 402–405 MHz. The coding scheme used to treat the problem consists of subdividing the patch into smaller sub-patches. Each sub-patch can be either metal or air. The same approach has also been used in11, where the genetic algorithm has been applied to a patch antenna shifting its resonance from 4.8 GHz to 2.16 GHz.The genetic algorithm generates a set of trivial solutions, i.e. antenna geometries, which evolves step by step until the best solution is reached. Antennas generated according to this approach are said to be evolvedIt has been demonstrated that the design of antennas by means of genetic algorithms is a good choice; however, only the miniaturization cannot be pushed far without suffering from low radiation efficiencies.An approach used for improving this feature is the introduction of metamaterials. Each material in nature is composed of atoms and their properties and spatial orientations affect its electrical behavior. The idea behind the metamaterials is the logical expansion of this concept at a macroscopic scale. By creating an array of single cell having specific properties it is possible to generate tailored electrical and magnetic characteristics of the entire structure.Metamaterials are applied to a huge variety of fields and one of the most promising regards the enhancement of radiation properties of small antennas.14. In particular, SRRs can be used to realized Artificial Magnetic Conductor (AMC) layers having effective permeability near to zero, i.e. Zero Index metamaterials (ZIMs). Recent studies employ ZIMs to improve the radiation properties of antennas by placing such supermaterials between the top layer of the antenna and the ground plane22. In this case, the ZIM acts as a very precise mirror that does not introduce phase variations in the reflected electromagnetic waves, improving the radiation characteristics of the ground plane on the bottom of the antenna. A problem arising from the use of metamaterials is that the inclusion of a superstrate adds a metallic layer to the stack composing the antenna, hence an alignment process must be performed.Split Ring Resonators (SRRs) represent an optimal solution since their planar geometry and easy integration simplifies the fabrication process24, is the ink-jet printing25, as it is the most economical, the fastest, and the cleanest solution. By this technique, the antennas are realized by depositing conductive inks through hundreds of nozzles which are mechanically controlled. Despite its optimal characteristics, this method does face some issues: the quality of the prints depends on the viscosity and the size of the droplet of the conductive ink25.A very attractive technological process for the fabrication of flexible antennas even of multilayers stacksIn addition, in the case of multilayers antennas fabricated on commercial substrates not direct printable, the alignment step becomes difficult. This happens because it is necessary to perform two different printing processes on both faces of the same dielectric. This last case can be the case of metamaterial antennas designed on stretchable substrates.26 an example of a flexible antenna enhanced with a metamaterial has been reported. The antenna is composed of a polyimide substrate with a top radiating element placed on a second substrate with a 3 × 3 array of metamaterial structures and a ground plane at the bottom. However, in this case, a precise alignment is not strictly necessary since the superstate needs only the metallization of its bottom surface. Moreover, the two layers are not fully integrated but are just placed on each other.InAs a consequence, even though in literature there exist a huge number of antennas realized using GA, metamaterials and inkjet printing, to the best of our knowledge, an antenna that exploits these three technologies jointly has not been reported yet.The biggest issue to overcome is the lack of the rapid prototyping fabrication techniques on flexible substrates of a process characterized by multilayer printing with an optimal alignment between all the parts composing the antenna. In this work, we propose a flexible multilayer ink-jet printed evolved antenna. The stack is composed of five layers . The radiative layer (i.e. top layer) is designed by using a genetic algorithm in order to miniaturize its footprint. The gain is enhanced by a split ring resonator which acts as a metamaterial and, at the bottom, the ground plane is placed to minimize the back radiation. The working frequency is in the sub-6 GHz band of the 5G spectrum, in particular, around 4 GHz.The metallic layers are fabricated by means of a multi-material 3D printer which requires a precise alignment process on a 250 μm Polyethilene Naphtalate (PEN) substrate. The dielectric layers are attached to each other by a Polydimethylsiloxane (PDMS) adhesive interlayer of 40 μm.11 parameter and 2D radiation patterns by means of VNA. The paper is organized as follows: in “Finally, the antenna has been characterized in terms of the S27 is a robust global optimization method based on Darwinian laws. The process starts from an initial random binary population (parents) that evolves iteratively towards the optimal solution under the selective influence of a cost function. The genetic algorithm works through eight main steps, as shown in Fig. The Genetic Algorithm first formalized inEncoding the problem is schematized as a function of general parameters. A single parameter is treated as a gene. Generally, binary values are preferable to be used for the genes. Their arrangement  forms the chromosome which describes the partial solution.(1) Initialization the initial population is generated. The set of trivial solution is composed of random chromosomes.(2) Evaluation of the population at this step, the fitness function is applied to all the elements of the population. At the end of this process, a direct correspondence between each chromosome and its relative fitness value is obtained, which quantifies the proximity of the trivial to the real solution of the problem.(3) Chromosomes rank and selection process the chromosomes are grouped two by two. The selection can be performed randomly or by considering their fitness values.(4) Crossover from each couple of chromosomes, the offsprings are generated. The descendants are created by mutual recombination of the genes of the initial chromosomes forming a new set of gene values starting from the parents.(5) Mutation the set of trivial solutions is perturbated by the insertion of random variations which can speed up the convergence of the algorithm. Mutations can be applied to a single gene or multiple chromosomes and are strictly dependent on the nature of the problem. In general, the presence of mutations avoids stalling the solver in local minimum, however, a rate too high can degrade the performance.(6) Reordering the fitness function is evaluated as in step 3, on the new offspring. The population is then rearranged by eliminating the chromosomes with the worst fitness values.(7) Loop statement the best fitness value is compared to the threshold value and if the condition is matched the algorithm stops, while otherwise the entire process is repeated from step 3.(8) Figure The antenna is composed of 5 layers: from the top, the patch radiating element (level 1) which is on a dielectric substrate (level 2), then the metamaterial split ring resonator (level 3) placed on a second dielectric substrate (level 4) and the ground plane (level 5).29.The dielectric substrates, made of PEN, have a thickness of 125 µm, a dielectric constant of 2.9 and a loss tangent equal to 0.005. PEN presents very good properties as a substrate for flexible electronics: it is a transparent and low-cost material. It is also characterized by a very high heat shrinkage coefficient and good resistance to acids and basis30. However, it is not possible to control and engineer the bandwidth or the gain of the device but only the geometrical parameters. Conversely, our optimization problem can be treated using a binary coding scheme, hence, the genetic algorithm is the most straightforward to be implemented. The geometrical parameters of the antenna , 0 if it made of air (blue), as shown in Fig. 1)  EncodingInitialization the starting elements are generated randomly. The population size is strictly linked to the nature of the problem and its degrees of freedom. By considering a huge population, it could be possible to obtain better results but at the cost of higher computational times; on the contrary, by using a small size for the population the execution speeds up but the optimizer may get stacked in local minima. To minimize the convergence time avoiding the insurgence of partial solutions, the possible elements of the population can be restricted to delete pointless individuals. In this case, since the radiation efficiency is directly linked to the size of the radiating area, each element of the population must be made of metal in a percentage greater than 60%.(2) Evaluation of the population the value of the cost function , by means of a finite difference time domain (FDTD) solver using the Eq.  is the value of the impedance assumed by the patch at its resonance. The exponential term assumes lower values when the resonance fR is near to the objective frequency. In addition, this function takes into account the impedance of the resonant peaks in order to discard antennas having a value of the real part of the impedance far from 50 Ω.(3) mentclass2pt{minimChromosomes rank and selection process the elements of the population are then grouped two by two using a roulette selection process. The probability associated with the selection of the single element πi follows a Boltzmann distribution, hence is evaluated by means of Eq.  s of Eq. :2\documeElements characterized by a lower cost function, hence nearer to the final solution, result more attractive than the others; however, it is worth stressing that by using this selection process the probability of selecting the worse elements is not deprecated at all.Crossover two offsprings are then generated from each group by a single point cross-over.(5) Mutation occasionally, a mutation event has occurred with a probability equal to 1%. The mutation corresponds to a variation of a single gene of an element of the population.(6) Reordering the cost function is evaluated for each element of the new population. The elements are then reordered in an ascendent order with respect to their costs. The latest elements are discarded, and the best value is compared with the threshold value of the algorithm to decide on the convergence of the solution.(7) Loop statement the process is repeated starting from step 3 until the condition on the threshold is reached.(8) 2 resonating at around 3.89 GHz with an S11 dip of − 24.47 dB and a bandwidth of about 14 MHz.In our implementation, the algorithm converged after 12 iterations giving as result an evolved patch antenna with a footprint of 16.88 × 13.76 mm31.The realized gain at the resonant frequency is equal to -0.647 dBi. The reduction of the dimensions of the antenna and, more important, of the ground plane always leads to worse radiation properties; to improve the antenna radiation pattern a mu-negative metamaterial composed of a square split ring resonator has been added between the top and the ground planeThe square split ring resonator is composed of two concentric etched split rings separated by a gap and having their apertures placed in the opposite direction Fig. a.Figure 32. The value of the inductance The SRR behaves like an LC circuit as shown in Fig. t is the thickness of the ring and G the aperture of the ring.As regards the capacitance, ion, Eq. 4\documenFinally, s in Eq. :5\documeA is an equilibrium constant.By considering the geometrical parameters of the SRR, the resonant frequency In this work, the geometry of the square split ring resonator has been properly designed to increase the gain at the working frequency of the antenna.The geometrical dimensions of the square SRR are listed in Table After this procedure, the entire structure is composed of 5 layers as shown in Fig. The results of the simulations are shown in Fig. 11 parameter is shown; there is a dip of − 14.2 dB at 3.984 GHz with a bandwidth of about 15 MHz. The narrow-band could be increased by redesigning the cost-function of our algorithm or considering a circular patch33. In Fig. In Fig. In Fig. It is worth stressing that with the insertion of the dielectric layer with an SRR, it is possible to observe an increase of the gain from –0.647 dBi to 1.89 dBi without modifying the footprint of the patch antenna. The directivity is equal to 6.48 dBi at the resonant frequency.Table 2) at a lower working frequency of 3.96 GHz. In comparison with a classical patch antenna at the same frequency , we got a reduction in size of 60%. Besides, the evolved patch antenna presents a reduction in terms of gain and bandwidth, in line with the behaviour of miniaturized and electrically small antennas34.The Genetic Algorithm allows to retain the starting patch antenna footprint .11.Figure 35. Both curves present a dip around 4 GHz, the desired operating frequency, where the realized gain is equal to -0.8 dBi for the simulated antenna and -1.5 dBi for the fabricated one, when the losses are taken into account. Figure In particular, it is possible to see a dip of − 14.2 dB at 3.984 GHz and a dip of -13.41 dB at 3.962 GHz for the simulated and the measured evolved patch antenna, respectively. There is a shift of few tens of MHz due to the introduction of a SMA connector which introduces a static capacitance, therefore increasing the electrical length of the device11 parameter and the radiation patterns are in agreement with the simulations. The main resonance of the fabricated prototype is in the sub-6 GHz of 5G spectrum, showing a dip of S11 parameter of − 27.41 dB at 3.962 GHz, with a bandwidth of 14.7 MHz. In case directivity and gain need to be enhanced, an array configuration of this patch can be implemented. We believe that the proposed approach could be a valid choice for the realization of compact, flexible and wearable IoT devices.A multi-layer 3D-printed metamaterial-based evolved patch antenna has been presented. The genetic algorithm has proven to be a powerful method to optimize antenna miniaturization and the radiation properties have been improved with the insertion of the split-ring resonator. The fabrication protocol turns out to be very fast and capable of realizing antennas with a precise alignment step between the layers. The measurements of the S


We present a model useful for interpretation of indentation experiments on animal cells. We use finite element modeling for a thorough representation of the complex structure of an animal cell. In our model, the crucial constituent is the cell cortex—a rigid layer of cytoplasmic proteins present on the inner side of the cell membrane. It plays a vital role in the mechanical interactions between cells. The cell cortex is modeled by a three-dimensional solid to reflect its bending stiffness. This approach allows us to interpret the results of the indentation measurements and extract the mechanical properties of the individual elements of the cell structure. During the simulations, we scan a broad range of parameters such as cortex thickness and Young’s modulus, cytoplasm Young’s modulus, and indenter radius, which define cell properties and experimental conditions. Finally, we propose a simple closed-form formula that approximates the simulated results with satisfactory accuracy. Our formula is as easy to use as Hertz's function to extract cell properties from the measurement, yet it considers the cell’s inner structure, including cell cortex, cytoplasm, and nucleus.The online version contains supplementary material available at 10.1007/s10237-022-01639-5. Despite the improvements in the available equipment, measuring the mechanical properties of animal cells is challenging. There are several measurement techniques precise enough to deform a single cell in a controlled way and read out the force used in the process. They include atomic force spectroscopy, optical traps, micropipette aspiration, among other techniques. , is characterized by relatively low stiffness. Therefore, it was omitted due to a negligibly small contribution to the overall elastic response. To ensure this approach was correct, we examined the influence of a 10 nm thick bilipid layer on cell stiffness. The results confirmed that neglecting the cell membrane did not alter the simulation noticeably.. Bursa et al. .All these approaches have been exploited in the literature. Bursa and Fuis  presenteThe experiments suggest that the elasticity of cells depends on their shape  using the method of micropipette aspiration  and poroelastic at higher speeds , but at shorter timescales the cytoplasm is viscoelastic  with the ANSYS Workbench/Mechanical environment. All simulations were performed using a static solver. Such an approach is valid for short time scales and small indentation depth when the cell behaves poroelastically , as well as their sizes, varied in a credible range taken from the literature. The choice of range is justified in the previous section and in the supplementary tables. A set of average parameters was used as a reference for a typical setup  inside the nucleus does not change the results noticeably. Changing Young’s modulus of the nucleus from 1 kPa to 0.45 kPa does not change the result either. Ultimately, the nucleolus was omitted and the Young’s modulus of the nucleus was kept constant at 1 kPa.This section presents the results of the simulations performed using the model described in Sect. In the following sections, we investigate how the character of the cortex influences the measurements, we take under consideration different cell shapes and sizes, various nucleus sizes, different probe sizes, and we examine off-center load and friction. Finally, we propose a closed-form formula for the indentation force in the presence of the cortex and conduct a parametric study of its applicability.First, the results of our cell model were confronted with the simple Hertz model. As the Hertz model describes only homogeneous and isotropic materials, the cell model was simplified and the cell was made entirely of cytoplasm. The difference between the Hertz formula and the FEM model of such a cell was below 1% at every indentation depth. Therefore, we can assume that the Hertz model approximates the simple FEM model well. The modifications to the cell structure will be proposed in the following sections, and they will be confronted with the control Hertz model.As mentioned previously in this paper, we treat the cortex as a solid 3D body. In this way, we can account for the influence of its bending stiffness in the results. To estimate the influence of bending stiffness on cell behavior, we compared the results obtained using two approaches to approximating the cortex. The first is the above-mentioned full 3D cortex with its real thickness; the second-modeling it as a thin 2-dimensional body with no bending stiffness. To mimic the 2D behavior, the cortex was actually modeled as an extremely thin 3D object so that the bending stiffness could be easily neglected. In this case, Young’s modulus was elevated to preserve the stretching stiffness of the cortex. The results are presented in Fig. Figure entclass1pt{miniman of the indentation  is treated as a free parameter:A Hertz-like function was fitted to results obtained for various cortex thicknesses and indenter sizes to study how the cortex modifies the shape of the force-indent curve. By a Hertz-like function, we mean a function where the exponent n independently for all simulation parameter combinations. The dependence on the geometrical parameters for a typical cortex Young’s modulus is given in Fig. In this series of fits, the constant n=1.5 is the most appropriate for certain sets of cortex thicknesses and indenter radius. For all of the simulation runs exponent values Finite element modeling shows that the standard exponent Another factor that was taken into consideration is the cell size. The results presented so far were obtained using our typical cell dimensions. Figure That way we can assume that formula  encapsulApart from the cell size, we also investigate the cell shape. The thickness of the cytoplasm varies in different parts of the cell, so the nucleus and cortex are not concentric spheres. To estimate the influence of the cytoplasm layer and the curvature of the cell cortex, two simulations were compared. One was our typical cell, and the other was a cell with the same height only with a 50% larger radius of curvature that maintained the same overall height of the cell. The cortex thickness and nucleus were the same for both cases Fig. .Fig. 5a The effects of friction and non-central indentation are discussed in this section. To investigate this effect, a set of simulations was performed. The coefficient of friction and horizontal distance between the center of the cell and the center of the indenter were varied Fig. b. The fri ‘ is the effective indentation, i—indentation in the y direction , R, r—cell and indenter radii, respectively, and a—horizontal distance between the center of the cell and the center of the indenter (offset). The formula is derived in the appendix.where The nucleus size is a factor that varies between different cell types. Therefore, to check the influence of that parameter on the indentation, additional series of simulations were performed. In the simulations, the nucleus diameter was swept over the range from 10,5 µm to 2 µm. It appears that the nucleus size has a significant influence on the reaction force for a large nucleus. For diameters smaller than 9 μm, the dependence flattens Fig. . This deAs there is little dependence on nucleus size smaller than 4.5 µm, this analysis is valid for any smaller nucleus size.Calculations for the special case of the big nucleus were also performed. The chosen size was 10.5 µm. The result is presented in Sect. In Sect. entclass1pt{minimaThe original Hertz function has a square-root dependence on the indenter radius. As can be seen in Fig. All of the above-mentioned observations allow us to write down the dependence of the reaction force on all geometrical factors. We have shown in the previous section that the dependence on the indentation depth Here tion Eq.  has a siIn this subsection, we determine the range of cell properties in which our modified Hertz function is accurate. The proposed function Eq.  was fittAssessment of the value of fit quality using R-squared allows one to determine the parameter range for which the proposed parametrizing function is valid. The function generally fits quite well, especially for the lower half of cytoplasm Young’s moduli range. The direct comparison of the global resulting formulas  and 5 toFigure d as Eq. . After bd as Eq. , these rwhere As mentioned earlier, a similar analysis was conducted for the case of a large nucleus. Another ca. 750 simulations runs were performed, scanning the same range of parameters as previously. The difference was that the diameter of the nucleus was now considerably larger (10.5 μm). The results were analyzed in the same manner as described in Sects. In this section, the accuracy of the proposed formula is tested. Figures Previously, no closed-form formula was proposed to include the properties of the cortex in an animal cell indentation experiment. The proposed formula  has someThe proposed formula does not contain any free parameters, thus it can be used to extract material parameters . This does not allow us to fully characterize all mechanical properties of the cell, but gives a much better insight into the cell structure than using the Hertz formula. The Hertz formula yields only apparent Young’s modulus, which is not directly associated with any of the fundamental properties of the cell material or structure.This work focuses on modeling the indentation of the animal cell, while treating the cortex as a full three-dimensional body with its real bending stiffness. It shows that the dependence of the reaction force on the indenter radius is similar to the one from the Hertzian contact, only shifted vertically by a term proportional to the squared thickness of the cortex. In other words, the dependence of the reaction force on the cortex thickness is a square function. One can imagine that during indentation, when the cortex ‘surrounds the probe’, it changes the size of the probe. By adding an extra term, we managed to regain Hertz-like behavior with much better convergence of the model to the experimental data, and we maintained the simplicity of the proposed equations. It is also important to emphasize that the proposed model modification is not based on simply increasing complexity by adding a few free parameters, but on introducing corrections related to material data.Moreover, there is a significant difference in response when treating the cortex as 3D in contrast to the 2D body without bending stiffness. The difference is more pronounced for smaller indentation depths. For our typical cell, there was a twofold relative difference in the applied force at a small indentation depth.On the other hand, the influence of friction and off-center load is less significant. It turns out that the friction of the order of magnitude measured in the experiment does not contribute much to the force-indentation curve. Similarly, the maximal force measured under constant vertical indentation depth changes little between the center and the side of the cell. We presented the formula for computing the effective indentation depth, knowing the distance from the center and the vertical indentation.Supplementary file1 (DOCX 93 kb)Below is the link to the electronic supplementary material.


Head posture is a balance of several positions and therefore shows inherent variation. Most methods available to quantify this are however instantaneous, not providing information about its variation over time. A dynamic recording of head posture would thus be beneficial.The purpose of this study was to evaluate the variation in natural head position (NHP) over 5 min using an inertial measurement unit (IMU).Fifteen healthy young volunteers were asked to sit on a chair and keep their head in the self‐balanced position for 5 min. A mirror was then revealed in front of them, and they were asked to look at their eyes for 20 s. This procedure was undertaken on two separate occasions with a one‐week interval. This was compared to an instantaneous measurement of head position at a specific time point corresponding to the 15th second of the recording.During the 5 min of recording, the participants tended to elevate their head progressively by a mean of 1.5°, which is then corrected by looking at oneself in the mirror. Most participants tended to rotate their head to the left and continued that progressive rotation despite looking in the mirror. The roll axis had no systematic changes observed between the self‐balanced position and the mirror‐guided position and was the most reproducible axis. Moderate to good correlations were found comparing both sessions for each axis.The comparison between the five‐minute analysis and the instantaneous measurement showed a systematic difference on the pitch axis but no differences for the yaw and roll. These results suggest that the variation in the NHP during a period of 5 min is generally specific to each participant with a head elevation and rotation to the left in most cases. Natural Head Posture (NHP) is a balance of several positions and therefore has inherent variation. However, most measurement methods available are instantaneous, not providing information about variation over time. A continuous (dynamic) recording could allow a better evaluation of head posture. The objective of this study was to evaluate the variation in NHP over 5 min using an Inertial Measurement Unit. We found that NHP variations are generally specific to each participant. And Systematic differences on the pitch axis were observed when comparing continuous and instantaneous measurements. We also found that the evolution of the head posture was generally similar among the participants.  The self‐balanced position is adopted when a person looks at an imaginary point in front of him/her, from an infinite distance at the eye level.Evaluation of the NHP is performed on three axes namely pitch, roll, and yaw. The pitch is the angle between the horizontal plane and the Frankfort plane. The roll is the angle between the horizontal plane and the bipupillary plane. Finally, the yaw is the angle between the acromial process and the median sagittal plane. Figure .Compare the instantaneous analysis to a five‐minute analysis of the head position.Analyse the evolution of the NHP in a self‐balanced position for 5 min and compare it to the mirror‐guided head position for the three axes.Evaluate the reproducibility of the self‐balanced head posture and the mirror‐guided head position for the three axes in a group of healthy young adults.The aims of this study were to22.1The present study was approved by the Swiss Association of Research Ethics Committee. The experimental procedures were conducted in conformity with the Declaration of Helsinki. Informed consent for participation in the study and publication in an open‐access format was obtained from the participants, with regard to their recordings and personal information. The procedures of the study were fully explained to the participants, and they provided their informed written consent prior to being enrolled in the study.2.2Fifteen healthy young adult volunteers (eight women and seven men) at the University Clinics of Dental Medicine in Geneva, Switzerland, aged from 20–30 years (mean age of 28.4 years) were recruited for this study.Wearable sensors or inertial measurement units (IMU)s were used to measure head position. These are electronic devices allowing movements to be tracked in three dimensions (3D).The participants were asked to sit on a chair in the 90–90–90 position The IMU system used was the MetaMotionR (Mbientlab lnc.). This system is composed of two sensors. Before measuring the head position, this system needs to be calibrated to assess the neutral position (corresponding to 0° on each axis). This was done by placing the first sensor on the ground in front of the participant and the second one behind them. Both have to be parallel, on the same plane, and perpendicular to the ground axis. After calibration, the first sensor was placed on the forehead of the participant.In order to minimize the error due to the positioning of the sensor, one front face photograph was taken to make sure that the sensor was parallel to the bipupillary line. A second profile photograph was taken to eliminate the slope of the forehead from the IMU recordings. The postprocessing calibration was performed with Pixelstick . This calibration method was the same as that used by Billiaert et al.2.3All statistical analyses were performed using SPSS . The data were separated into four different segments. The initial segment (I) represents the mean of the first 20 s, the finishing segment (F) the mean of the last 20 s before the mirror‐guided position. The self‐guided position (S) is the mean of the full segment from initial to finish. Finally, the mirror‐guided position segment (M) represents the mean of the 20 s when the mirror was revealed in front of the participants . The meaFor the instantaneous measurement, recorded data were taken at the 15th second with the IMU system. As there are no clear instructions in previous studies regarding the time at which the photograph for the head position measurement was taken, the 15th second was chosen because it represents approximatively the time required to take a photograph.The differences between the instantaneous measurement and the five‐minute recordings were analysed. The instantaneous measurement was taken and compared to the mean of the recordings for the self‐balanced head position (S). The difference between I–F, F–M, and I–M was analysed to better understand the evolution and tendency of the head position. The self‐guided head position (S) was also compared to the mirror‐guided head position (M), and the two sessions were compared to assess whether the variation within the five‐minute recording period was random or if it followed a specific and reproducible pattern.p values inferior to .05 considered statistically significant. Pearson's correlations and intraclass correlation (ICC)*SEM=StandardDeviation×1‐ICC).For each set of measurements, the difference between the means was calculated, with 3The data show a greater interindividual variation in the pitch axis with a negative value corresponding to an elevated Frankfort plane than the horizontal plane. The roll axis had the least amount of interindividual variation and a slight deviation to the right compared to the median plane. The yaw axis had comparable interindividual variation to the roll axis and had a slight deviation to the left compared to the plane that passes by the acromial process (shoulders) Table .3.1p = .04), whereby the mean pitch from the five‐minute procedure was elevated by 0.9 degrees compared to the instantaneous procedure. For the roll and yaw axes, no systematic differences (p > .05) were found. However, a good correlation and good to excellent reliability was found for all the three axes , which was then corrected by the mirror‐guided position . The roll axis has the least amount variation with the standard deviation ranging from 0.9° to 2.3°. On the yaw axis, the participants tend to progressively increase the deviation, generally to the left by 2.3° ±4.7° (p = .13), and the mirror‐guided position does not seem to correct this.During the self‐balanced position, the participants tend to elevate their head by 1.5° ±3.8° , and for the yaw axis moderate to excellent reliability was found (ranging from 0.55 to 0.96).3.3p > .05). When comparing the same segments for the two different sessions . The participants that tended to rotate their head kept their rotation and continued in the same direction.The variation of head position seems to be influenced by different factors. The rotation of the head may be related to the dominant eye, which is often the right eye. This observation is described by Pradham et al. who found a strong relationship between eye dominance and direction of head rotations.When comparing the two sessions, a stronger correlation was found for the self‐balanced head position than the mirror‐guided head position on each axis. The correlations of the mirror‐guided head position found in this study were similar to the ones found by Billiaert et al.For the mirror‐guided head position, a good correlation was observed on the pitch axis since the mirror affects it. However, the mirror‐guided position does not seem to influence the roll and yaw axes, which is why the correlation was much lower for these axes. For the self‐balanced head position, good correlation was found even for the roll and the yaw axes. This indicates a similar pattern between the two sessions, meaning that the variation in head position may be specific to each participant.The limitations in the present study include the potential lack of generalizability as all the included participants were healthy young adults and, thus, represent only a small part of the population. However, the use of this system can be interesting for every population including children, the elderly, and patients with a handicap or other pathological conditions since it is easy to use and allows a recording of the variations of head position over a certain period of time.The reproducibility found in this study is based on a one‐week interval, and on two sessions. A longer period between the recordings and multiple sessions would be necessary to evaluate the long‐term reproducibility. Finally, different elements influence the head position, such as fatigue and ocular and respiratory factors, and thus the recordings of each participant should be evaluated when these factors are the same for the two sessions.5Good‐to‐excellent correlations were found between the instantaneous analysis of head position and the five‐minute head position recordings. However, on the pitch axis, the head position was systematically more elevated in the five‐minute analysis than the instantaneous procedure, whereas no difference was observed for the roll and yaw axes.Most participants have the same pattern of evolution of their head position over a five‐minute recording. An elevation of the head and a rotation to the left were observed as general patterns. Only the elevation of the head, however, is corrected by the mirror‐guided position.The pattern of evolution of the head position and its variation are generally specific to each participant with moderate‐to‐good correlation between the two sessions. Overall, the means of the five‐minute recordings were more reproducible than those of the mirror‐guided head position. The roll axis had the least amount of variation, followed by the pitch and finally the yaw axes, respectively.The authors declare no competing interests.K.B. and M.A., contributed to the data collection and data analysis, G.S.A. and S.K. contributed to the study design and drafting of the manuscript.https://publons.com/publon/10.1111/joor.13297.The peer review history for this article is available at


The formation and growth of ice layers in fractured rock masses is one of the main causes of frost weathering in bedrock in cold regions. The mechanism of ice layer formation in fractured rock masses was simulated in this study by conducting frost weathering tests on a simulated rock mass with a vertical through fracture, which was fabricated by splicing two cement blocks. The test results were used to propose a novel mechanism for ice layer formation in terms of the initial crack-frost effect in which moisture mainly migrates in vapor form. The continuous accumulation and growth of these frosts eventually forms an ice layer that expands the crack, and the fractured rock simulation model undergoes frost-heaving damage. The frost layer on the rock wall in the negative temperature region is similar to the frosting process on the cold surface of thermodynamic studies. The relative humidity (RH) gradient and temperature gradient were shown to be the factors affecting water vapor migration, where the former plays a direct and dominant role, and the temperature gradient has a very limited direct effect on vapor migration. Frost weathering consists of two physical processes, freezing and melting, in which the formation and growth of ice layers during freezing leads to cracking of bedrock or expansion of existing fissures, making the rock mass develop toward fragmentation. On the one hand, this may greatly increase bedrock’s permeability to groundwater recharge, drinking water supply and contaminant transport, and on the other hand, present significant safety hazards to the construction of projects on bedrock of cold regions. The formation and development process of these ice layers are key to understanding the frost weathering process and bedrock characteristics in permafrost areas. These results can be used to predict the long-term evolution of bedrock in cold regions and guide the design, construction and maintenance of related projects.Frost weathering is a fundamental geomorphic process operating from Polar region to tropical high mountains, wherever rocks experience a temperature fluctuation across the freezing point and moisture is present (Matsuoka and Murton1): if water completely fills the spaces in rock and freezes in situ, ice growth at – 22 °C can, in principle, generate pressures up to 207 MPa inside cracks in rock (Tsytovich2) that is strong enough to fracture any rock, because the maximum tensile strength of rock is one to two orders of magnitude lower than 207 MPa. However, precisely defined conditions are required for frost weathering by volumetric expansion: the rock must be nearly or completely water-saturated and freeze rapidly from all sides. Another mechanism is ice segregation: Walder and Hallet4 developed a mathematical model (W–H Model) for the breakdown of porous rock via the growth of ice lenses within cracks. Laboratory experiments have demonstrated that ice segregation can fracture porous, moist rock . Ice segregation does not require specific environmental conditions for in situ volumetric expansion, and the applicability of this theory to porous rocks has been demonstrated by field investigations .Two mechanisms have been proposed, in literature, for the formation of an ice layer in rock. One mechanism is in situ volumetric expansion  are the two major driving forces for vapor transport in a medium.2·s) in the medium caused by temperature and vapor pressure (relative humidity) gradients is (Lu and Likos15)2/s) is the diffusion coefficient for water vapor transport in the medium, 3) is the saturated vapor density, RH (%) is the relative humidity, T (K) is the temperature, The diffusive vapor flux The negative signs of the first and third terms on the right-hand side of Eq.  show thaThe second term on the right-hand side of Eq.  is negliIce segregation occurs when temperature gradient-induced suction in freezing or frozen ground (or rock) drives unfrozen water through a porous media towards a freezing site, where lenses or layers of ice grow. Some typical ice segregation experiments and phenomenon is listed in Table 16; Tao et al.17), where the diffusion of water vapor leads to thickening and densification of the frost layer. Figure 17).The frosting process on the negative temperature region of a single rock wall is equivalent to the frosting process on the cold surface of thermodynamic studies. The growth of the frost layer at a general cold surface consists of a formation period (Stage I), growth (Stage II) and stable growth (Stage III). The frost layer can be considered to be a porous medium during the frost growth period (Stage II)  is the local convective mass transfer coefficient; v/kgdry air) is the humidity ratio of air evaluated at v/kgdry air) is the humidity ratio of air evaluated at The total heat, Q, through the frost layer is the sum of contributions from convection and phase change:2s) is the average convective mass transfer coefficient, 3) is the local frost density, The water vapor transferred from the humid air stream partially deposits as frost on the cold surface and partially diffuses into the porous frost sublayers as follows:Natural fractured rock masses are the most suitable test samples. However, the fractures in these samples are often irregularly developed, and the rock matrix is anisotropic. Numerous conditions can affect the test results, making it difficult to identify the main influencing factors. Therefore, cement blocks were prefabricated and spliced into a sample with a vertical through fracture to simulate the simplest type of rock mass: a rock mass with a vertical through fracture. The cement blocks were made of P.O42.5 cement and water with w/c ratio of 0.5 and a block size of 12 The blocks were saturated by immersion for 7 days. After the blocks are saturated, there was negligible water migration within the blocks over the entire test process. Two cement blocks were spliced into a fractured rock simulation model with a vertical through fracture. The surface of the fracture is basically flat and smooth.As shown in Fig. A circular hole was prefabricated every 5 cm on the sides of the 5 cm The terminals of the temperature sensors and the pressure sensor were connected to an automatic data acquisition device (model number BGK-MICRO-40), whereby changes in the temperature and water level were automatically collected and recorded during the test. The study was conducted in a Xutemp freeze–thaw cycle box (Model Number XT5405FSC).(1) Installation of temperature sensors: the PT100 temperature sensors were placed in the prefabricated holes of blocks A and B and sealed with cement mortar.(2) Saturation of test blocks: the blocks were saturated by immersion for 7 days.(3) Splicing of test block: the 12 cm 4) Sample installation: The sample was placed on the temperature control bottom plate in the freeze–thaw cycle box, the top plate was installed, and rubber sponge (thickness 20 mm) was used to wrap the rectangular plexiglass enclosure, the top and bottom plates, and the connection rubber hoses. Transparent tape was used to seal the gap between the top of the specimen and the plexiglass baffle, as shown in Fig.  Sample i(5) Preparation of temperature and moisture migration measurement: the temperature sensors and the pressure sensor were connected to the automated data acquisition device. The Mariotte’s bottle was connected to the bottom of the sample using a rubber hose, the constant water level was 3 cm from the bottom plate, and the initial position of the liquid surface in the Mariotte’s bottle was 76 cm.(6) Initiation of temperature control system: in order to simulate the frost weathering effect of surface cooling on the internal bedrock, the top and bottom plate temperatures were set to − 5 °C and + 2 °C, respectively, and the temperature in the freeze–thaw cycle box was set to + 2 °C, as shown in Fig. (7) Date recording: the data acquisition system, including the temperature measuring elements and pressure sensors in the Mariotte’s bottle, was set to automatically collect data at 0.5–1 h time intervals.The frost weathering test was conducted for a total of 260 h, during which the temperature in the sample and the water level in the Mariotte’s bottle were continuously monitored. The frost weathering test was carried out following 7 steps, as shown in Fig. Removal of the temperature control top plate revealed approximately 5 ~ 10 mm of frost distributed on the inside of the tape used to seal the top of the sample, as shown in Fig. As shown in Fig. Opening block A along cracks A-1 and A-2 revealed ice crystals on the surface, with some large pores on the crack surface, as shown in Fig. The temperatures recorded by the temperature sensors were analyzed. Large data loss occurred during reading and recording at temperature sensors 1, 2, and 3, and dramatic and clearly unrealistic temperature changes were observed at temperature sensor 12. Therefore, temperature sensors 1, 2, 3 and 12 were excluded from the temperature analysis. The data obtained at temperature sensors 6, 11, 10, 9, 8 and 7 were used to represent the temperature changes in the sample from the top down to 2, 7, 12, 17, 22 and 27 cm, respectively.Figure Figure Figure In Fig. The corresponding water level at 260 h was 5.67 cm; considering the initial water level of 76 cm, the water migration during the test was (76−5.67)5) and siliceous chalk  in the freezing test, it took a long time for a significant segregated ice layer to appear (> 1000 h), and for the relatively dense cement blocks, it should take even longer to produce the segregated ice layer, while this test lasted only 260 h. On the other hand, the segregated ice layer is generally perpendicular to the temperature gradient, while Crack-2  volumetric expansion produced a weak cross section in the negative temperature zone (because of pore development or the deterioration of the section strength by the prefabricated temperature measurement holes), resulting in initial cracks; (2) as the sample cooled, the water in the lower portion of the sample continuously migrated upward in vapor form to the negative temperature zone and condensed in the initial cracks; the subsequent expansion of the continuously growing ice crystals further expanded the crack; and (3) vapor migration stopped when the equilibrium condition was reached, and the ice crystals in the crack stopped growing.Results from field research and the experiments presented above are used to propose a novel mechanism of ice layer formation in fractured rock masses, where the initial crack-frost effect can be described as follows: in rock masses with through fractures whose bottom is connected to the groundwater level, a drop in the surface temperature causes groundwater to migrate in vapor form through the fractures to the negative temperature zone and condense into frost in initial cracks (pre-existing or produced by in situ freezing). These frosts continuously accumulate and grow into an ice layer that expands the crack, resulting in frost-heaving damage to the rock mass. The entire process is shown in Fig. Thus, there are three conditions for ice layer formation in a fractured rock mass: the positive temperature zone is replenished by water, the penetrating fractures serve as water vapor migration channels, and the negative temperature zone contains cracks (that are preexisting or generated during frost heave). These conditions are relatively common in bedrock in cold regions, which supports the initial crack-frost effect as a mechanism for ice layer formation in a fractured rock mass.Assume that the water vapor in the rectangular plexiglass enclosure is in steady flow. Calculate the vapor migration due to the temperature gradient according to Eq.  in sectiv = D0 holds approximately, where D0 is the free air diffusion coefficient, with a value of 10-7m2/s; considering that the temperature in the freeze–thaw cycle chamber is 2 °C, the saturated vapor density is 6.5 g/m3; 2, such that the total vapor migration induced by the temperature gradient is For vapor migration in a rectangular plexiglass enclosure, the relation DTherefore, the RH gradient is the main driving force for vapor migration in the rectangular plexiglass enclosure. In the approximately closed environment, the condensation of supersaturated water vapor into frost at the top of the sample where it was cold caused the RH of the air at the top of the sample to drop; thus, water vapor continuously migrated from the bottom to the top under the vapor pressure gradient, until the RH of the air at the top of the sample reached 100% again. The frost layer on the cold wall became increasingly thick during this cycle. The water vapor remained in a dynamic equilibrium until the frost layer stopped growing and then ceased migrating.The formation process of frost layer on the wall in the negative temperature region of the specimen is similar to the frosting process on the cold surface of thermodynamic studies, as shown in section “(1) A novel mechanism for ice layer formation in a fractured rock mass is proposed in terms of an initial crack-frost effect: in a rock mass with through fractures with groundwater at the bottom, a drop in the surface temperature causes water to migrate, mainly in gaseous form, through the fractures to the negative temperature zone and condense into frost in initial cracks (which may be preexisting or generated during frost heave). These frosts continuously accumulate and grow into an ice layer that expands the crack, inflicting frost-heaving damage to the rock mass. The mechanism of the initial crack-frost effect may be more applicable to the formation of ice layers in fractured rock masses than the mechanisms reported in the literature. This effect does not require specific environmental conditions unlike volumetric expansion and ice segregation: the conditions required for the initial crack-frost effect are through fractures with groundwater at the bottom and initial cracks in the negative temperature zone.(2) Moisture mainly migrates in vapor form in through fractures. Water in rock fractures migrates in both liquid and vapor forms, where liquid water migration is driven by capillary suction but has a very limited climb height. The vast majority of water migrates in vapor form to condense into frost in cracks in the negative temperature zone.(3) Relative humidity (RH) gradients are the main driving force for water vapor migration. Supersaturated water vapor condenses into frost at the top of the sample where it is cold, and the drop in the RH in the air at the top of the sample creates a vapor pressure gradient that drives the continuous migration of water vapor from the bottom to the top of the sample. Temperature gradients have a very limited effect on water vapor migration.(4) The formation process of frost layer on the rock wall in the negative temperature region is similar to the frosting process on the cold surface of thermodynamic studies, therefore, this can be described by referring to the mechanism of frost on cold surfaces. However, the frosting mechanism in cracks is somewhat different from this and needs further study.(5) The late stage of frost growth in cracks involves the complex process of frost-ice transformation, and many microscopic tests and theoretical studies are required to elucidate this mechanism.The formation mechanism of an ice layer in a fractured rock mass was investigated by splicing two prefabricated blocks into a sample with a vertical through fracture and a constant water level at the bottom. A temperature control plate was placed at the top of the sample to simulate the unidirectional cooling of a rock mass. The following conclusions were drawn from the experimental results and a correlation analysis.


Overall, the use of the newly designed collimator will allow for a more comfortable treatment of the head and neck region, reduce the treatment time, and reduce the dose delivered to the surrounding healthy tissue.In June 2020, the Japanese government approved boron neutron capture therapy for the treatment of head and neck cancer. The treatment is usually performed in a single fraction, with the neutron irradiation time being approximately 30–60 min. As neutrons scatter in air and loses its intensity, it is preferable to bring the patient as close to the beam port as possible to shorten the irradiation time. However, this can be a challenge, especially for patients with head and neck cancer, as the shoulders are an obstacle to a clean positioning. In this study, a novel neutron collimation system for an accelerator based neutron source was designed to allow for a more comfortable treatment, without compromising the irradiation time. Experimental measurements confirmed the simulation results and showed the new collimator can reduce the irradiation time by approximately 60% (under the same condition where the distance between the source and the patient surface was kept the same). The dose delivered to the surrounding healthy tissue was reduced with the new collimator, showing a 25% decrease in the D These high-LET particles  have ranges that are roughly equal to the size of a human cell. Clinical trials of BNCT that utilised 10B-para-boronphenylalanine (L-BPA) as the boron delivery agent have been reported for the treatment of recurrent head and neck cancers4. Historically, BNCT was performed using neutrons generated from nuclear reactors. Accelerator-based neutron sources are becoming more popular, as they offer several proven advantages over a nuclear reactor. The world’s first accelerator based neutron source for clinical BNCT was designed and developed by Sumitomo Heavy Industries, in collaboration with Kyoto University BNCT research group6. This accelerator was used in a clinical trial treating recurrent or locally advanced head and neck cancer between 2016 and 20187. The same type of accelerator system was installed in September 2016 at the Kansai BNCT Medical Center of Osaka Medical and Pharmaceutical University. On March 11, 2020, the Japanese Ministry of Health, Labor and Welfare approved the BNCT system (NeuCure® System) as a novel medical device that can be manufactured and sold for clinical use, together with the dose calculation program (NeuCure® Dose Engine). The NeuCure® Dose Engine utilises the general-purpose Monte Carlo particle transport simulation code system called Particle and Heavy Ion Transport code System (PHITS) version 3.2 to simulate both the neutron and photon transport8. BNCT has been approved for coverage under the national health insurance system for unresectable, locally advanced, and recurring cancer of the head and neck region as of June 2020. Currently, the center has treated over 60 head and neck patients using the NeuCure® System (with the standard type of collimator) along with Steboronine®  produced by STELLA PHARMA corporation.Boron neutron capture therapy (BNCT) is a binary treatment modality that selectively kills cancer cells. It is based on the nuclear reaction that occurs when a thermal neutron is captured by a For BNCT, it is preferable to bring the patient as close to the beam port as possible to keep the treatment time short, since neutrons scatter through the air and the intensity drops. This is important as the Steboronine® is only approved for infusion for a total of 3 h (the infusion rate for the first two hours is 200 mg/kg/h and the last hour is 100 mg/kg/h). The neutron irradiation is performed when the infusion rate is dropped to 100 mg/kg/h, so the maximum irradiation time (while the BPA is being infused) is limited to 1 h. However, bringing the patient close to the beam port is not easy. This is because the current system only has a single fixed horizontal beam line, and the patient needs to move toward the neutron beam port . This is troublesome, particularly for patients with cancer near the hypopharynx area, as the shoulders are an obstacle that prevents bringing the tumour area close to the beam port. Inevitably, this produces an air gap of the order of several centimeters between the beam port and the patient surface, and in some cases greater than 10 cm. This air gap increases the treatment time and an unnecessary exposure to healthy parts of the body.This paper investigates an improvement in the beam collimator design that can be easily adapted to the current system to address the issues mentioned above.A computer aided design software was used to design the collimator Fig. . Two des9. A proton charge of 0.3 C was delivered for both the thermal neutron and gamma ray measurements. Detail on the methodology of thermal neutron flux and gamma ray dose rate determination and can be found elsewhere10.Thermal neutron and gamma ray distribution inside a water phantom was measured using gold foil activation method and thermo-luminescent dosimeters (TLDs), respectively. Thin gold wires  were placed inside the water phantom ) along the central beam axis to measure the central axis thermal neutron flux and perpendicular to the beam axis to measure the off-axis thermal neutron flux. After neutron irradiation, the activated gold wires were cut into small pieces (approximately 5 mm length) and the 412 keV prompt gamma rays were measured using a high purity germanium detector. As gold reacts to both thermal and epithermal neutrons, cadmium covers were used to differentiate between the two. For the measurement of gamma ray dose rate, neutron insensitive TLDs were placed inside the water phantom to measure the depth dose distribution due to gamma radiation, along the central axis. A custom made BeO TLD enclosed in a quartz glass was usedGold foils and TLDs were placed free-in-air along the surface of each collimator at 1–2 cm intervals to measure the collimator leakage. The data analysis was the same as above.10. The extended collimators were modelled in detail according to the design mentioned above. The thermal neutron and gamma ray dose rate inside the water phantom was simulated using the T-Track tally. The number of primary particles run was set to obtain a relative error lower than 0.5% for the thermal neutron flux and less than 1% for the photon dose rate at a depth of 10 cm along the central beam axis.The neutron and gamma ray spectrum of the NeuCure® system has been modelled and verified previously3 with a weight fraction of 0.1, 0.1, 0.03, 0.77 for hydrogen, carbon, nitrogen, and oxygen atom, respectively)) assuming a uniform distribution of 10B with a concentration of 25 µg/g was simulated. The total dose was determined by summing each of the four main dose components 7Li, nitrogen dose 14 N14C, hydrogen dose 1Hp, and the gamma ray dose originating from both the primary beam and the 1H2H reaction). Parameters summarised in Table 10. The irradiation time required to deliver a maximum dose of 12 Gyw to the mucosal membrane was calculated  along with the advantage depth, which is a parameter used to evaluate the performance of a neutron beam. It is defined as the depth where the biologically weighted dose in the tumour region equals the peak value of the biologically weighted dose in the healthy tissue region . Furthermore, the off-axis dose distribution at a depth of 2 cm was calculated and the 80% and 50% isodose width was determined to investigate the effect an air gap has on the lateral beam profile.The effect of an air gap between the beam exit (collimator surface) and the phantom surface on the dose distribution was investigated for the three different collimators. The dose distribution inside a 30 cm × 30 cm × 30 cm cubic phantom .A cancer of the left nasopharynx was simulated using a dummy patient dataset. A hypothetical 1 cm3 spherical tumour was placed below the thyroid, in front of the esophagus, midline of the patient. Simulation was performed using both the standard collimator and the 5 cm extended collimator  the thermal neutron flux along the central beam axis approximately doubled with the extended collimator. The measured and simulated central axis gamma ray dose distribution for each collimator is shown in Fig. The advantage depth and irradiation time as a function of the distance between the wall and the phantom surface for the different collimators are shown in Fig. w) for the standard collimator, the 10 cm extended collimator and the dose difference between the two collimators. The dose distribution of the standard collimator was more spread out, with the effect being more prominent near the neck and shoulder region. Table w to the mucosa membrane for the standard collimator was calculated to be 86.5 min and 46.1 min with the 10 cm extended collimator.Figure w) for the standard collimator, the 5 cm extended collimator and the dose difference between the two collimators. The dose distribution of the standard collimator is more spread out, with the effect being more prominent near the oral cavity and chest region. Table w to the mucosa membrane for the standard collimator was calculated to be 58.5 min and 32.4 min with the 5 cm extended collimator.Figure In both cases, when the dose was normalised to the mucosal membrane and the source to skin distance was kept the same, the irradiation time was significantly shorter with the extended collimator when compared to the standard collimator. The dose to the organs outside the irradiation field were reduced and the dose delivered to the tumour was improved for case 1.w to the mucosal membrane), the total number of neutrons leaking from the collimator was found to be less than or approximately the same as the standard collimator. Also, the spread of neutron beam was reduced with the extended collimator in comparison with the standard collimator with an air gap present. Overall, the use of the extended collimator reduced the out-of-field dose. Unlike conventional X-ray or proton therapy, where the particles mostly travel in a straight line before reaching the patient, epithermal neutrons scatter in air before reaching the patient, resulting in a gaussian like shaped dose profile. Therefore, the physical collimator size (12 cm diameter for this study) does not indicate the dose profile width inside the patient. The profile width changes with the air gap and the depth inside the patient. So, care must be taken when selecting the collimator size to make sure the target is covered by the desired isodose line. In this study, a fixed RBE/CBE factor was used to determine the total weighted dose. There are other calculation models (for e.g. the photon-isoeffective dose17), which may produce a different total dose distribution in contrast to the fixed RBE/CBE method.The experimental measurements of the thermal neutron flux and the gamma ray dose rate inside the water phantom closely matched the simulation results. By extending the collimator, the distance from the BSA to the collimator exit was increased, which decreased the neutron intensity as neutrons scatter in air. However, the decrease in the neutron intensity was compensated by increasing the volume inside the collimator. The neutron leakage rate (per second) measured at the surface of the collimator was found to be higher for the extended collimator when compared with the standard collimator. However, the irradiation time was significantly reduced with the extended collimator (under the same condition). Therefore, when the irradiation time was normalised to the mucosal membrane , which is usually the organ where the dose is prescribed to for head and neck BNCT. The treatment time was significantly reduced (approximately up to 60% reduction) with the use of the extended collimators. This is important not only from the patient comfort point of view, but it may also reduce the patient motion during treatment. However, for case 1, it was found the maximum dose of the brain, brainstem, and left parotid slightly increased with the extended collimator. This may be due to the increase in the thermal neutron distribution, particularly along the central beam axis, as the direction of neutrons become more forward directed with the use of the extended collimator. Although the dose to the tumour increased, the dose to the OAR’s near the center of the field also increased and this needs to be considered when generating the treatment plan.For a slightly deep-seated tumour (5–6 cm), the use of the extended collimator increased the tumour dose by approximately 7%. The advantage depth marginally increased with increasing air gap. No significant difference in the tumour dose between the extended collimator and the standard collimator was observed for a shallow tumour. For the organs at risk, a significant reduction was observed with the use of the extended collimator, particularly for the mucosal membrane , and the treatment would be performed in a much comfortable position. For BNCT, the dose profile width inside the patient is not determined by the physical collimator size. The profile width varies depending on the collimator shape, air gap, and depth inside the patient. Therefore, when selecting the collimator size, it is important to ensure the target is covered by the specified isodose line. The simulation results showed the dose delivered to the organs at risk out of field were significantly reduced with the use of the extended collimators and the dose delivered to deep-seated tumours slightly increased for the same prescription dose of 12 Gy-eq to the mucosal membrane. The application of the extended collimators may increase the indication of head and neck BNCT.