Minimally invasive intervention surgery, as an essential means of diagnosis and treatment for various vascular diseases, has been widely applied in conditions such as vascular stenosis, arterial aneurysms, atherosclerosis, and thrombosis [1–4]. In minimally invasive medical interventions, practitioners employ tools such as guide wires, catheters, and stents to access blood vessels via the femoral or radial arteries, facilitating treatment in affected regions. For example, in cardiovascular procedures, a guide wire is navigated through vessels to establish a pathway, followed by interventions such as stent placement. Guide wires are essential for guiding, positioning, and treating specific areas, thereby enhancing surgical outcomes and minimizing patient risks. Compared with traditional open surgery, intravascular minimally invasive procedures offer advantages, including reduced hemorrhage, shorter recovery periods, lower infection rates, and decreased postoperative discomfort [5–8]. Clinically, X-ray imaging guides surgical procedures, and doctors depend on tactile feedback through interventional tools to sense forces between devices and blood vessels. This relies on the medical professional’s proficiency, posing risks like iatrogenic vascular injuries (IVIs), including dissection, hematoma, vascular perforation, and arterial aneurysms [9,10]. To minimize this influence, interventional surgical robotic systems are developed, which improve the precision of surgical operations, enable remote operation, and further eliminate the need for direct exposure of doctors to the radiation environment [11,12]. However, the use of interventional surgical robots limits direct contact between doctors and interventional instruments, making it challenging for them to intuitively sense the interaction between surgical instruments and blood vessels and tissues in the human body. To solve this problem, intravascular surgical robotic systems assisted by force feedback modules are proposed for monitoring and adjusting the position of guide wires [13,14]. Therefore, the force sensing element is crucial for ensuring the safety of the surgery and reducing complications during the procedure.

Various force sensors are proposed for the design of interventional surgery tools, which can be divided as resistive force sensors [15], capacitive force sensors [16,17], electromagnetic force sensors [18], and fiber-optic force sensors [19,20]. The resistive and capacitive sensors show high sensitivity; however, they suffer electromagnetic interference as interventional surgeries often involve real-time navigation and monitoring using technologies such as X-rays and magnetic resonance imaging (MRI). For the electromagnetic force sensors, the main principle is that pressure causes displacement of the diaphragm and then changes the distance between the permanent magnet and the magnetic sensor; consequently, the magnetic flux density changes accordingly. Unfortunately, this kind of sensor shows low sensitivity and easy influence by the surrounding environment. Additionally, it is difficult to realize triaxial force detection, as the forces acting on the tip of the guide wire are not only axial pressure but also include frictional forces and radial pressures from the vessel sidewalls, resulting in a triaxial force [as shown in Fig. 1(a)].

Compared with the mentioned sensors, fiber-optic sensors have been widely studied for force feedback during interventional surgeries due to the advantages of high sensitivity, compact size, lightweight, good biocompatibility, and resistance to electromagnetic interference [21–24]. The fiber optic force sensors applied in interventional devices mainly incorporate the principles of wavelength modulation using fiber Bragg gratings (FBGs) and phase modulation using Fabry–Perot interferometers. In comparison, FBG-based force sensors could experience lower sensitivity and resolution due to the exceptionally high Young’s modulus and stiffness of glass [25]. It should be noted that Fabry–Perot interference (FPI)-based fiber-optic force sensors exhibit lower temperature sensitivity and a narrower monitoring wavelength range, which is beneficial for reducing detection errors and lowering detection costs. Additionally, FPI-based fiber-optic force sensors, with their adjustable cavity length and diaphragm thickness, offer a relatively flexible detection limit.

Initially, the preparation of FPI cavities involved complex processes such as welding and ablation [26], which had high manufacturing costs and large processing errors, and could only be used for axial pressure monitoring. DLP-based 3D microprinting technology can be used for fabrication of FP-based cavities on the end face of standard single-mode optical fibers for sensing applications, as it can realize large printing area and high resolution [27,28]. To achieve submicrometer scale fabrication, two-photon printing (TPP) technology could be a solution for various micronano structures with a resolution of 100 nm. Various FPI cavities with novel structures on the end face of optical fibers are fabricated for microforce and ultrasonic detection [25,29,30]. However, the challenges faced by the above technologies include structural instability and limited force detection range, usually in micronewtons or below, which also limits them to the axial pressure monitoring range and cannot complete multiaxis force sensing.

In this work, a miniature triaxial force sensor is proposed to monitor the interaction force between the guidewire tip and human blood vessels and tissues in real time during minimally invasive interventional surgery. The sensor is mainly composed of a two-photon printed four-microcavity FPI force sensing structure and four optical fibers. The sensor has the advantage of small size and can be integrated with existing 0.035 in. commercial guide wires. The cross-sectional diameter is 890 μm. The sensor structure was optimized using the finite element method (FEM). The sensor characterization test was conducted for an axial force test of 0 to 0.5 N and a 45° spatial force test of 0 to 0.35 N. The results indicate that the single channel of the sensor exhibits a high sensitivity of approximately 85.16 nm/N and an excellent resolution of 0.2355 mN. The sensitivity is two orders of magnitude higher than that of previously reported FBG-based fiber force sensors. This full-fiber polymer sensor based on two-photon micronano 3D printing has miniaturization, high sensitivity, high resolution, good biocompatibility, and electromagnetic compatibility; further, triaxial force detection can be achieved. In addition, the sensor structure is highly adjustable, which greatly reduces the difficulty of integrating with the device. Therefore, this sensor will become an efficient force monitoring tool integrated on interventional devices during minimally invasive interventional surgery.

In order to facilitate the operation of guidewires within the human vascular system, tissues, and organs, the diameter of the guidewire tip force sensor should match the dimensions of commercially available medical guidewires. Therefore, the sensor’s diameter should be limited to below 1 mm. Additionally, the sensor should be capable of detecting triaxial forces to accurately determine the forces acting on the guidewire tip. Further, the sensor should achieve a high resolution, not exceeding 0.01 N in each direction, and demonstrate high sensitivity. The maximum detectable force should not be less than 0.5 N to ensure reliable and precise force measurements at the guidewire tip [31–34].

In order to achieve three-axis force detection based on the established research goals, a sensor design solution is proposed. The overall idea is to independently design flexible sensors and integrate them into the structure of the existing guidewire. The designed sensor has a symmetrically arranged flexible structure, which can achieve 3D force decoupling. And the sensor components must have good assembly performance. Figure 1(b) shows a cross-sectional view of the designed triaxial force sensor integrated on the guidewire tip. The core structure of the entire device is a four-microcavity FPI force sensing structure produced by two-photon micronano printing. The structure consists of a prepared circular base, four micropillars, four circular diaphragms, and four symmetrically arranged microcavities, all integrated in a single process via two-photon printing (TPP). Figure 1(c) shows a detailed assembly diagram of the designed triaxial force sensor integrated into the guidewire tip. Four single-mode optical fibers (SMFs) (diameter: 125 μm) and guide wire cores are inserted into the reserved demolding channel. Four optical fibers are positioned around the circumference, the angular interval between adjacent optical fibers is 90°, and the core of the guide wire is located at the center of the circumference. The specific layout of each element is shown in the A-A cross-section in Fig. 1(b). The four-microcavity force-sensing structure is secured to the optical fiber and guidewire core using UV-curable adhesive. Subsequently, the guide wire spring is pushed to the reserved position on the circular base of the four-microcavity force sensing structure and bonded. Finally, on the other side of the base, apply a dollop of adhesive to create a domed guidewire tip.

As shown in Fig. 1(d), for a single FPI microcavity, the FPI is defined by introducing the fiber end face and the bottom surface of the diaphragm. Initially, incident light passes through a single-mode fiber (SMF) to reach the fiber end face (first reflective surface S1). A portion of the incident light undergoes reflection, and another portion transmits into the air cavity. The transmitted light is reflected for the second time at the bottom surface of the diaphragm (second reflective surface S2). FPI occurs due to the two reflections, forming a reflective spectrum. When the diaphragm is not subjected to pressure, the microcavity has a fixed cavity length, resulting in the original reflective spectrum. When the diaphragm experiences pressure, deformation occurs, causing the diaphragm to shift into the microcavity. This shift leads to a change in the interference cavity length, altering the optical path difference for the two reflections and ultimately causing a wavelength shift in the reflected spectrum. The relationship between the wavelength shift (Δλr) and the reduction in cavity length (ΔD) is given by Δλr/λr=ΔD/D, where λr is the reflective wavelength, and D is the interference cavity length. Therefore, the force applied to the diaphragm can be calculated by tracking the wavelength shift in the reflective spectrum.

Applying axial force Fz at the sensor tip in the designed sensor will result in the compression of the diaphragms in the four interference microcavities. They can sense the axial force transmitted to the sensing structure and exhibit the same magnitude of strain. Applying radial force Fx will cause diaphragm 1 to stretch and diaphragm 3 to compress, experiencing strains in opposite directions but having the same magnitude due to their symmetric arrangement. Meanwhile, as the other two diaphragms are positioned at the neutral axis of the bending section, they undergo minimal strain relative to the strains experienced by diaphragms 1 and 3. Small cross-interference occurs among the forces in three directions. The flexible structure with symmetric arrangement of the sensor can decouple the radial force Fx by differentially processing the wavelength shifts corresponding to diaphragms 1 and 3. Similarly, Fy can be determined by the wavelength shifts caused by strains in diaphragms 2 and 4. The detailed principles of triaxial force measurement will be discussed in the next section.

The sensing principle of this sensor primarily involves the mechanical analysis model of deformation in planar circular diaphragms in the mechanical part and the wavelength shift analysis model of the FPI cavity in the optical part. Combining the physical models of these two parts with the three-axis force decoupling model constitutes the complete sensing principle of the entire sensor.

The flexible deformable element of the sensor is a planar circular diaphragm, and the strain model is illustrated in Fig. 1(d). When the measured pressure is transmitted to the planar diaphragm, deformation and strain occur. Through the above analysis, it can be concluded that when a circular flat diaphragm is subjected to uniform pressure on its surface, the maximum deflection of the diaphragm occurs at the center of the circular diaphragm. Moreover, when the physical and geometrical parameters of the diaphragm are determined, the maximum deflection is directly proportional to the pressure applied to the diaphragm. The maximum deflection of the circular flat diaphragm ωP can be expressed as [35] ωP=3P(1−μ2)16Eh3R4,(1)where P is the applied pressure, R is the radius of the diaphragm, μ is the Poisson’s ratio of the diaphragm, E is the elastic modulus of the diaphragm, and h is the thickness of the diaphragm.

The basic structure of the designed sensor is an FPI cavity. The schematic diagram of the thin-film FPI cavity is shown in Fig. 1(d). Incident light (In) propagates inside the SMF. When the light reaches the first reflecting surface (S1), some of the light is reflected back (I1), and the remaining light continues to propagate in the air cavity. When the light reaches the second reflecting surface (S2), the light (I2) is reflected and returns to the SMF. The interference equation for the two reflected light beams is expressed as [36] I=I1+I2+2I1I2cos(Δφ+φ0),(2)where I1 and I2 are the intensities of the reflections at the fiber end-air interface S1 and air-film interface S2, respectively. φ0 represents the initial phase, and Δφ is the optical phase difference between the two reflected light beams, described as Δφ=4πnlλ,(3)where n is the refractive index of air, l is the length of the interferometric cavity (the space between S1 and S2), and λ is the wavelength of light in a vacuum.

At the dip wavelength of the interference spectrum, the phase difference between the two reflected light beams satisfies the following condition: 4πnlλm+φ0=(2m+1)π,(4)where m is an integer, and λm is the wavelength of the mth interference trough. When the initial phase φ0 is considered as zero, λm can be expressed as λm=4nl2m+1.(5)

When subjected to an axial contact force, the FPI cavity undergoes a reduction in cavity length, thereby inducing a wavelength shift in the reflected light. The wavelength shift of the mth order interference fringe is quantified as follows: Δλ=4nΔl2m+1,(6)where Δl represents the change in interferometer cavity length.

From the above analysis, the conclusion can be drawn that, due to the constant refractive index of air within the cavity (n), an increase in the applied axial contact force will result in a wavelength shift. Furthermore, the wavelength linearly varies with the cavity length as follows: Δll=Δλmλm.(7)

The overall structure of the sensor can be divided into three parts, as shown in Fig. 2(a). When the sensor is subjected to external force, the main deformation area occurs in the second part, namely, the micropillar and the diaphragm, and their deformation is the change in the length of the interference cavity.

Due to the symmetry of the structure, the effects of Fx and Fy are similar. First, the changes in the length of different interference cavities when the sensor is subjected to radial force Fx are analyzed. As shown in Fig. 2(b), when subjected to radial force Fx, the neutral axis of the sensor deflects a certain angle relative to the y-axis direction. The angle is determined by the following formula [37]: tanθ(z)=IxyIy,(8)where Iy is the sensor cross section about the x axis, and Ixy is the product of the moment of inertia of the cross section about the x and y axes. Assuming that the diaphragm is rigid, the only deformable body at this time is the microcolumn. According to the unit load method, the deformation of microcolumn 1 is Δx1=∫0lFxzRcosθ(z)EIy(z)dz=FxKx1,(9)where Δx1 represents the deformation of micropillar 1 caused by Fx, E represents the elastic modulus of the sensor, R represents the radius of the sensor cross section, and Iy(z) represents the moment of inertia of the sensor, which varies with the y axis. l represents the height of the micropillar. Kx1 is a code used to replace the result of the integral expression. Since micropillars 1 and 3 are arranged symmetrically at 180°, the deformations of micropillars 1 and 3 are equal in magnitude and opposite in direction. Similarly, the deformation of micropillar 3 can be expressed as Δx2=∫0lFxzRsinθ(z)EIx(z)dz=FxKx2.(10)

The above equations show that, once the sensor structure size is determined, the deformation of different micropillars is proportional to the magnitude of the applied force. In order to decouple the components of force in different directions and make the micropillars better sense the force in the x direction, micropillars 1 and 3 are rotated by an angle θ relative to the initial position to maximize the deformation in the y-axis direction. The deflection angle can be calculated by the following equation: θ=arctan∫0lFxzRsinθ(z)EIx(z)dz∫0lFxzRcosθ(z)EIy(z)dz.(11)

Therefore, the modified deformation of different micropillars after being subjected to radial force Fx is {Δx1=−Δx3=∫0lFxzRcos(θ(z)−θ)EIy(z)dz≈∫0lFxzREIy(z)dzΔx2=−Δx4=∫0lFxzRsin(θ(z)−θ)EIx(z)dz≈0.(12)

Similarly, the deformation of the four micropillars when the radial force Fy is applied can be expressed as {Δy1=−Δy3≈0Δy2=−Δy4≈∫0lFyzREIx(z)dz,(13)where Δyi represents the deformation of the ith microcolumn when subjected to radial force Fy. As shown in Fig. 2(a), when the axial force Fz is applied, its effect is shared by the four microcolumns 1, 2, 3, and 4, and the forces acting on the four microcolumns are equal, so the axial deformation of each microcolumn can be expressed as Δz1=Δz2=Δz3=Δz4=∫0lFzEA(z)dz=FzKz,(14)where Δzi represents the deformation of the ith microcolumn when subjected to the axial force Fz, and A(z) represents the cross-sectional area.

The derivation process of the above model is based on the premise that the diaphragm is a rigid body. The actual diaphragm will deflect when squeezed by the microcolumn, and the effect of the deflection is described in the above plane diaphragm force deformation model. Therefore, when the force is transmitted to the bottom surface of the microcolumn, its stress magnitude can be determined by combining the following basic material mechanics formulas: $$\begin{gathered} ε=Δll, \\ σ=εE. \end{gathered}$$(15)

By combining the maximum deflection equation of the circular plane diaphragm, the deformation of each interference cavity when subjected to the radial force Fx can be obtained as follows: {ΔLx1=−ΔLx3≈∫0lFxzRlIy(z)×3(1−μ2)16Eh3r4dzΔLx2=−ΔLx4≈0,(16)where ΔLxi represents the deformation of the length of the ith interference cavity when subjected to the radial force Fx, L is the length of the interference cavity, and r is the diaphragm radius. The deformation of each interference cavity when subjected to the radial force Fy is {ΔLy1=−ΔLy3≈0ΔLy2=−ΔLy4≈∫0lFyzRlIx(z)×3(1−μ2)16Eh3r4dz.(17)

Among them, ΔLyi represents the deformation of the length of the ith interference cavity when subjected to the radial force Fy. The deformation of each interference cavity when subjected to the axial force Fz is ΔLz1=ΔLz2=ΔLz3=ΔLz4=∫0lFzlA(z)×3(1−μ2)16Eh3r4dz.(18)

Among them, ΔLzi represents the deformation of the length of the ith interference cavity when subjected to the axial force Fz.

For any complex spatial force F applied to the tip of the guidewire, we can decompose it into its three orthogonal components Fx, Fy, and Fz in the spatial coordinate system, as shown in Fig. 2(c). The relationship among them can be expressed as {Fx=FsinβcosαFy=FsinβsinαFz=Fcosβ.(19)

In the formula, α represents the angle between the applied force F and the z axis, and β is the angle between the projection of F on the xoy plane and the x axis.

Since the change in the cavity length of a single FPI cavity after being acted upon by the complex spatial force F is the superposition of the strains caused by three orthogonal components, the contribution of each component to the change ΔLi of the cavity length of a single interferometer cavity is expressed as follows: ΔLi=ΔLxi+ΔLyi+ΔLzi.(20)

According to the sensing principle of the FPI sensor, the relationship between the wavelength shift of each FPI interferometer cavity and the deformation caused by external force can be expressed as Δλiλi=ΔLiL,(21)where λi is the monitored interference peak wavelength. In fact, the wavelength shift of the FPI sensor is also affected by temperature, so the actual wavelength shift should take temperature compensation into account. The equivalent wavelength shift of the ith FPI cavity after temperature compensation can be described as Si=Δλi−ΔλT,(22)where ΔλT is the wavelength shift caused by temperature. Based on the above derivation, the force in the x direction can be measured by the difference in wavelength shifts of interferometer cavities 1 and 3 and is represented by S1−S3. Similarly, S2−S4 can measure the force in the y direction. ∑Si can measure the force in the z-axis direction. The three-axis force decoupling matrix of the designed sensor can be described as [S1−S3S2−S4∑Si]=[Kx000Ky000Kz][FxFyFz].(23)

Among them, Kx, Ky, and Kz are {Kx=2λi∫0l3Fxz(1−μ2)Rr416lEh3Iy(z)dzLKy=2λi∫0l3Fyz(1−μ2)Rr416lEh3Ix(z)dzLKz=4λi∫0l3Fz(1−μ2)r416lEh3A(z)dzL.(24)

Therefore, by observing the wavelength drift corresponding to different interferometer cavities, the specific magnitude and direction of the spatial force can be obtained by solving the equations. Due to manufacturing and assembly errors, the actual sensitivity matrix will deviate from the theoretical sensitivity matrix. This matrix should be calibrated through force characterization experiments.

The feasibility of the proposed sensor design was rigorously validated through finite element simulations using COMSOL Multiphysics software. In the mechanical simulation module, the intricate changes in cavity length under controlled pressure conditions were meticulously modeled, facilitating the identification of optimal microcolumn diameters and diaphragm thickness. Subsequently, in the optical simulation module, an in-depth analysis of reflective spectra across various cavity lengths was conducted, conclusively affirming the linear correlation between the sensor’s reflective spectral shifts and applied pressure.

To investigate the steady-state performance of the sensor structure, the COMSOL Multiphysics software was used to establish force sensor models with different diaphragm thicknesses (15, 12.5, 10, 7.5, and 5 μm) and microcolumn diameters. The material parameters of the established simulation models match the material properties of various components in the sensor manufacturing process, with specific values shown in Table 1. A 0.5 N axial force was applied to the sensor tip with varying diaphragm thicknesses, and the deformation results of the sensor diaphragm are shown in Fig. 3(a). It can be observed that, under the same axial force, the amplitude of the sensor cavity length change decreases with the increase of diaphragm thickness. When the diaphragm thickness is smaller, the interference cavity length of the sensor decreases more significantly. This indicates that reducing the diaphragm thickness can effectively improve the force sensitivity of the sensor.Table 1.

Detailed Parameters of the Components of the Sensor

In addition, the relationship between microcolumn diameter and the maximum bending deformation of the diaphragm under the influence of the same force (0.5 N) was evaluated, as shown in Fig. 3(b). The results indicate that reducing the microcolumn diameter increases the bending deformation of the diaphragm. The reason may be that the effective surface area of the diaphragm is the difference between the surface area of the diaphragm and the area of the microcolumn’s bottom surface. Therefore, the larger the effective surface area, the higher the sensitivity of the sensor.

To ensure that the sensor has high mechanical strength and high sensitivity, a microcolumn with a diameter of 50 μm is a suitable choice. In addition, the sensitivity of the sensor, defined as the ratio of the wavelength shift to the force applied to the tip of the guidewire, can be significantly improved by reducing the thickness of the diaphragm. Since the stiffness of high-polymer materials is relatively low, the thickness of the diaphragm cannot be too small. Therefore, a diaphragm thickness of 10 μm is chosen to ensure the structural stability and high sensitivity of the sensor.

After determining the critical dimensions of the sensor structure, the designed sensor’s mechanical response characteristics were simulated under the application of axial force Fz and 45° spatial force Fn. When applying axial force Fz, numerical simulations were conducted at intervals of 0.05 N from 0 to 0.5 N. The displacements of various points along the central axis of the diaphragm’s lower surface under different forces are shown in Fig. 3(c). It can be observed that the maximum displacement occurs at the center of the diaphragm, forming a platform advantageous for secondary reflection of light. The diaphragm center displacement data obtained by mechanical simulation and the diaphragm center displacement data estimated by Eq. (1) were statistically analyzed, and the relationship between them and the force is as shown in Fig. 3(d).

Note that the difference between the simulation and calculation is small, indicating that the circular flat diaphragm-based model can be guided for designing the diaphragm-based cavity sensors. Due to the symmetric arrangement of the sensor’s flexible structure, the four diaphragms exhibit highly similar deformation results in simulations. Taking diaphragm 1 as a representative, the analysis of the relationship between different forces and the maximum displacement at the center of the diaphragm after force application is as shown in Fig. 4(a). It is found that there is a linear relationship between the two, consistent with the established physical model. When applying a 45° spatial force Fn, numerical simulations were performed at intervals of 0.05 N from 0 to 0.3 N, and the simulation results matched the previously established physical model. As shown in the simulation results in Fig. 4(b), the deformation of diaphragm 1 is symmetrical to that of diaphragm 3. Diaphragm 1 is compressed, causing the interference cavity to shorten, while diaphragm 3 is stretched, leading to an elongation of the interference cavity. Diaphragms 2 and 4, located on the neutral axis, experience relatively small displacements.

To establish a linear relationship between the reflectance spectral shift of the sensor and the applied pressure, the Wave Optics module in COMSOL Multiphysics was used. The focus of this simulation is to obtain the reflection spectra of each interference cavity in the sensor under different cavity lengths. An optical simulation model of the FP cavity was established, focusing on studying the deformation of the diaphragm center point caused by the small core diameter of 9 μm. The initial cavity length of the designed sensor was set to 100 μm. The optical field simulation of the interference spectrum of a single FP cavity under the action of 0.1–0.5N axial force was investigated. Different force scenarios are simulated, the waveform is filtered, and vertical translation is accumulated to obtain the waveform translation diagram, as shown in Fig. 4(c). Tracing the peaks/troughs, it is clear that, as the cavity length decreases, the overall waveform of the reflected light shifts to the left. By tracking the peak values under different forces, a linear fitting curve between the reflection wavelength shift and pressure was generated, as shown in Fig. 4(d). The axial force spectrum sensitivity obtained by finite element simulation is −93.3±1.70nm/N.

The core component of the sensor, the four-microcavity FPI force sensor structure, is integrated through two-photon micronano 3D printing. The specific steps are as follows.

First, a drop of photoresist is placed in the center of the glass slide and then placed into a two-photon 3D printer (Photonic Professional GT2, Nanoscribe). The schematic diagram of two-photon 3D printing technique is shown in Fig. 5(a). In the second step, a 25× magnification objective lens was used for focusing the femtosecond laser light on the glass surface. The laser power and scanning speed are optimized to improve the quality of fabricated devices. In the third step, the glass slide with photoresist was developed and rinsed by isopropyl alcohol (IPA). To improve the fabrication performance, the BisSR photoresist mixed (in mass fraction) by 20% BisGMA, 46.7% SR348OP, and 33.3% PEG600DMA, was prepared for two-photon 3D printing. Considering that the size of the sensor structure designed in this study is too large for the Photonic Professional GT2 two-photon printing system, in order to further improve the accuracy and effect of two-photon printing of the sensor structure, BisSRPEG_2 was cut and printed. During the slicing process, it is important to ensure that the key units of the sensor such as micropillars and diaphragms are located in the same printing area during the slicing process. The cut-block printing of the sensor was completed using a laser intensity of 78 and a scanning speed of 10,000. The printing results show that the cut-block printing results are ideal, with high accuracy, and can achieve a high degree of restoration of the designed sensor model. Figure 5(b) shows the actual scanning electron microscope (SEM) image of the printed sensor.

The integration of the printed sensor structure and wires is achieved through a micromanipulation platform. Figure 5(c) shows the integration steps of the designed sensor and guide wire. First, use a microscopic operating platform to push the five fixed components into the draft holes reserved for the printed sensor. Use UV curable glue (LEAFTOP 9310, China) to dispense glue through another microscopic operating platform. The connection is cured; then, the spring is pushed onto the intended base on the printed substrate and UV curable adhesive is applied to cure the connection. Apply medical-grade UV-curable adhesive to the other side of the printed substrate to form a hemispherical cap at the tip of the wire.

Due to assembly errors and manufacturing tolerances, the actual sensitivity of the designed sensor cannot be fully represented by the simulated sensitivity discussed previously. Therefore, this section describes the experimental characterization of the force measurement performance. As shown in Fig. 6, the force measurement system consists of the designed sensor, four-channel spectrometer (HYPERION SI155, LUNA, USA), lifting platform (AKV13A-65Z, Zolix, China), and force measuring scale (KTRUE, China), composed of sensor fixing fixture. The designed sensor is firmly fixed on the lifting platform using a fixed clamp. By adjusting the lifting platform knob, the vertical movement of the sensor can be controlled. The tails of the four optical fibers are connected to the four-channel spectrometer, and the four-channel spectrometer is connected to the computer. When the entire system is turned on, the four reflection spectra can be clearly seen. In theory, the four waveforms should completely overlap. However, due to errors caused by the integration process, the four waveforms are different during actual measurement. However, we are focusing on the waveform offset; thus, it has no impact on the measurement results. For force measurement in the 90° direction, the force balance is placed horizontally. For force measurement in a 45° spatial direction, the sensor tip and the force measuring balance are at an angle of 45°. In this setup, adjusting the lifting platform ensures contact between the designed sensor and force balance. Real-time changes in the waveform corresponding to the sensor force can be observed. This characterization method draws on the measurement method of guidewire tip load [39].

During the force measurement process, the axial force (Fz) changes from 0 to 0.5 N with an interval of 0.05 N; the spatial force (Fz) changes from 0 to 0.35 N with an increment of 0.05 N. All procedures were performed at room temperature. Incremental force is applied by adjusting the height gauge knob, and spectral data corresponding to stable balance readings are recorded after each force adjustment. After subsequent data processing, the characteristic curve is obtained.

The real-time spectrum obtained during loading was FFT filtered for the applied axial force (Fz). All processed spectral data are then accumulated together with the Y axis offset and specific peaks (troughs) are tracked. The results show good linear drift, indicating that the operating range of the integrated sensor exceeds 0.5 N. The measurement range meets the requirements of various interventional procedures. The maximum axial pressure that the sensor can withstand was tested, and the results showed that its limit value was close to 1 N. Figure 7(a) shows the wavelength shift of the four-channel interference cavity when an axial force (Fz) is applied. Due to the symmetrical arrangement of the flexible structure, all four interference cavities show high similarity in sensitivity and linearity of spectral shifts. Figure 7(b) shows the relationship between the spectral displacement and force of the four interference cavities when an axial force (Fz) is applied, obtained by tracking specific wave peaks. Figure 7(c) depicts the wavelength shift of the four-channel interference cavity during application of a 45° spatial force (Fn). As expected, a set of interference cavities located in symmetrical positions exhibits left and right offsets, demonstrating good symmetry. The other group is located on the neutral axis and shows a relatively small range of wavelength shifts. Figure 7(d) shows the relationship between the spectral displacement and force of the four interference cavities when a 45° spatial force (Fn) is applied, obtained by tracking specific wave peaks. An axial force application and release test was also performed, characterizing one of the interference cavities of the selected channel and counting the hysteresis error of the sensor, as shown in Fig. 7(e). By calibrating the test results, the measurement results show that the force sensitivity of the sensor channel reaches approximately 85.16 nm/N.

In addition, using the calibration curve as the standard, two repeated tests were conducted. The repeatability error, linearity error, and measurement limit of the sensor were characterized using the spectral shift of a single cavity as a representative, as shown in Fig. 7(f). As shown, it can be seen that the force measurement characteristics of the sensor show repeatability and high similarity; it also shows a trend that is highly similar to the previously mentioned simulation results. Some differences between measured and expected data may be due to errors and hysteresis in the manual adjustment of the force loading device, resulting in small inconsistencies between the displayed force and the actual force applied to the sensor. Further, waiting for balance readings to stabilize before recording may introduce potential errors. Due to the limitations of the force loading device, only forces in the range of 0 to 0.35 N can be measured, because forces outside this range will cause significant deflection of the sensor tip direction, resulting in experimental failure.

The results obtained from the 0° axial force and 45° spatial force characterization tests were further analyzed, and the wavelength shifts of the interference cavities in symmetrical positions under different force conditions were processed. The relationship between the wavelength shifts of each interference cavity under the action of the axial force Fz is shown in Fig. 8(a), and the relationship between the wavelength shifts of each interference cavity under the action of the radial force Fx is shown in Fig. 8(b). The corresponding linear equation is obtained using the linear fitting function.

According to the equation, combined with the calibration curve parameters under different external forces, the mapping relationship between the applied force and the wavelength shift corresponding to each interference cavity of the designed sensor can be determined as [S1−S3S2−S4∑Si]=[−231.902.8589.642.85−231.9089.6418.2016.47−339.70][FxFyFz].(25)

The force position estimated by the sensor standard working curve and the actual measured force and error statistics are shown in Table 2. The statistical results show that, after the sensor establishes the standard working curve, the force estimated by the standard working curve is close to the actual measured force result, with a certain error, and the error range is given.Table 2.

Sensor Force Measurement Error Statistics

This paper exhibits the physical model and decoupling principles of the designed sensor for three-axis force measurement and validates them through simulation. The experimental results of force characterization are highly similar to the simulation results, indicating that the sensor has excellent force measurement performance and potential. The force characterization results show that the designed sensor’s single channel has a high sensitivity of approximately 85.16 nm/N. Additionally, the HYPERION si155 four-channel spectrometer comes with its own light source, avoiding the need to purchase a separate light source, significantly saving costs. The spectrometer itself has a high-resolution in the pm range, and, through fitting algorithms, the sensor achieves outstanding resolution of 0.2355 mN, as summarized in Table 3, detailing the sensor’s performance.Table 3.

Sensor Performance

The sensor boasts a small size, occupying less than 1mm×1mm post-integration, compared with existing microforce sensors typically ranging from 2–4mm×2–4mm. It employs a novel concept, utilizing the FPI principle and a symmetrically arranged flexible structure to enable three-axis force decoupling. Additionally, the sensor offers fast processing speed at a low cost, with the core structure formed by TPP providing strong adjustability. Integration is simplified, ensuring high stability of the overall structure post-integration. Superior force measurement performance is achieved, with high sensitivity and resolution, as well as good biocompatibility. Moreover, it demonstrates good electromagnetic compatibility compared with sensors based on electrical and electromagnetic principles, and it surpasses FBG-based sensors in sensitivity and working range due to the flexible structure and symmetrical arrangement of the four optical fibers, enhancing sensor stability and reliability under force. In addition, compared with force sensors based on electrical and electromagnetic principles, it has good electromagnetic compatibility, and, compared with force sensors based on FBG, it has higher sensitivity and wider working range. The flexible structure and symmetrical arrangement of the four optical fibers enhance the stability and reliability of the sensor when subjected to force.

Table 4 compares the performance of microforce sensors, especially three-axis force sensors, used in minimally invasive surgeries. In terms of sensor size, the piezoresistive sensors can achieve smaller size, while the sensitivity and sensing range are limited. It should be noted that the proposed sensor shows high sensitivity, which is two orders of magnitude higher than that of previously reported FBG-based force sensors. Additionally, for sensors based on FPI principles, the proposed sensor’s structure and manufacturing method significantly improve the force measurement limit of sensors with similar principles, potentially promoting force sensing across different scales.Table 4.

Comparison of Force Sensors for Minimally Invasive Surgeries

While the sensitivity values obtained from force characterization experiments align well with simulation predictions, effectively validating the proposed approach, there are still minor differences in the measured results of simulation and characterization experiments due to errors in manufacturing, assembly, and the difference between simulated and actual material parameters. The paper acknowledges that the use of TPP in the sensor minimizes manufacturing errors, primarily attributing errors to assembly and measurement. To reduce these errors in the future, the authors suggest refining the assembly process through skilled operations and designing more precise auxiliary fixtures. Further, designing a more accurate force measurement system, such as using electrode-adjustable lifting platforms and recording real-time spectral changes through a computer, could minimize errors in the force measurement process.

This paper presents an FPI-based force sensor capable of measuring three-axis spatial forces. The sensor is suitable for integration at the tip of intervention guidewires, enabling real-time contact pressure measurement during surgery. Additionally, it can be utilized for tissue palpation in certain pathological areas. Further, the sensor holds potential applications as a force feedback module in robot-assisted intervention surgeries. The designed sensor exhibits sensitivity two orders of magnitude higher than that of previously reported FBG-based fiber force sensors and can be integrated into medical guidewires with a diameter as small as 0.035 in., meeting clinical requirements. Future work will involve optimizing existing procedures and platforms, conducting in vitro gel channel experiments and animal trials to further validate and enhance the entire system. Integration with machine learning or other data processing models for batch spectral processing is envisioned, along with the design of a software interface for intelligent display of the sensor’s force measurement capabilities. Exploring potential applications of the sensor in other intervention instruments through appropriate structural adjustments also holds promise for enhancing the safety of intervention surgeries.

Acknowledgment. The authors would like to thank the Key Laboratory of Special Optical Fiber and Optical Access Network of Shanghai University for its support in optical detection, and Mingche Biotechnology (Suzhou) Co., Ltd. for the valuable discussion.