CN114376729B - Bone traction needle force sensing system based on FBG optical fiber - Google Patents
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- 210000000988 bone and bone Anatomy 0.000 title claims abstract description 85
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- 210000004197 pelvis Anatomy 0.000 description 3
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- A61B34/00—Computer-aided surgery; Manipulators or robots specially adapted for use in surgery
- A61B34/30—Surgical robots
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- A61B17/56—Surgical instruments or methods for treatment of bones or joints; Devices specially adapted therefor
- A61B17/58—Surgical instruments or methods for treatment of bones or joints; Devices specially adapted therefor for osteosynthesis, e.g. bone plates, screws, setting implements or the like
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Abstract
The invention discloses a bone traction needle force sensing system based on FBG optical fibers, which comprises optical fibers and a bone traction needle, wherein: the optical fibers comprise FBG optical fibers 1 to 4; the FBG optical fibers 1-3 are arranged on the outer surface of the bone traction needle along the length direction of the bone traction needle; the FBG optical fiber 4 is arranged in the hollow shaft of the bone traction needle along the length direction of the bone traction needle and coincides with the central shaft of the bone traction needle so as to sense the axial force applied to the bone traction needle; three equidistant grooves forming an included angle of 120 degrees are formed in the outer surface of the bone traction needle in the radial direction, and FBG optical fibers 1-3 are arranged in the grooves and used for sensing radial force born by the bone traction needle. According to the invention, the interaction force perception model between the surgical instrument and the bone and soft tissue is established by constructing the mapping relation between the deformation of the surgical instrument and the restoring force, so that unnecessary damage to a patient caused by overlarge restoring force in the restoring operation process is avoided.
Description
Technical Field
The invention belongs to the technical field of medical instruments, relates to a bone traction needle force sensing system, and in particular relates to a bone traction needle surgical instrument with deformation detection capability based on Fiber Bragg Gratings (FBGs).
Background
Currently, there is an increasing number of high-violence injuries, mainly pelvic fractures. Because the pelvis anatomical structure is complex, the position is deep, and a plurality of important blood vessels, nerves and other organs are distributed around, secondary injury and operation complications are very easy to generate in the resetting operation process, and the death and disability rate of unstable pelvis fracture are up to 10-50%. With the development of minimally invasive technology, the technology of closed reduction of pelvic fracture and minimally invasive screw represented by robots can avoid the damage and complications during or after the operation caused by incision reduction, and provides a new technical means for solving the problems of complex and high-difficulty operation. However, the main current challenges are that the complex mechanical environment around the pelvis fracture causes mismatch of states between external instrument operation and internal bone block movement in the fracture closed reduction process, so that clinical problems of overlarge reduction force, poor stability and the like are caused.
In the traditional reduction operation, a bone traction needle is implanted into a dislocated bone block through a minimally invasive technology, and an operation robot controls a mechanical arm to draw the bone needle so as to complete the fracture reduction operation. In surgical robots, six-dimensional force sensors are used to measure external forces applied to an object. The six-dimensional force sensor is fixed at the tail end of the surgical robot, and the external force born by the bone traction needle is represented by the reading of the six-dimensional force sensor in the process of resetting the bone traction needle pulled by the mechanical arm.
The external force applied by the bone needle is measured by the six-dimensional force sensor, and although the measured reading is relatively accurate, two main disadvantages exist. Firstly, the six-dimensional force sensor is far away from bone tissues, and external force born by the bone tissues cannot be accurately represented: the fixed position of the six-dimensional force sensor is arranged at the tail end of the surgical robot, the tail end of the bone needle is connected with the tail end of the surgical robot, and the tip of the bone needle is fixedly connected with bone tissue, so that the position of the six-dimensional force sensor is far away from the bone tissue, the reading of the six-dimensional force sensor cannot be used as the representation of the external force applied to the bone tissue, and an accurate mapping relation cannot be established. Secondly, the six-dimensional force sensor at the tail end of the surgical robot cannot respond to the acting force relation between each bone needle and bone tissue: in the operation process, a plurality of spicules are usually required to sense the external force born by bone tissues at the same time, but the six-dimensional force sensor can only sense the external force born by one spicule or the resultant force born by a plurality of spicules, and the stress measurement of the spicules and the stress mapping relation with the bone tissues cannot be established.
Disclosure of Invention
Based on the problems, the invention provides a bone traction needle force sensing system based on FBG optical fibers, which establishes an interactive force sensing model between an instrument and bone and soft tissues by constructing a mapping relation between the deformation of the surgical instrument and the restoring force, so as to avoid unnecessary damage to a patient caused by overlarge restoring force in the restoring operation process.
The invention aims at realizing the following technical scheme:
a bone traction needle force sensing system based on FBG optical fibers, comprising optical fibers and bone traction needles, wherein:
the optical fibers comprise three optical fibers, namely an FBG optical fiber 1 to an FBG optical fiber 3;
the FBG optical fibers 1-3 are arranged on the outer surface of the bone traction needle along the length direction of the bone traction needle;
three equidistant grooves forming an included angle of 120 degrees are formed in the outer surface of the bone traction needle in the radial direction, and FBG optical fibers 1-3 are arranged in the grooves and used for sensing radial force born by the bone traction needle.
Further, the optical fiber further comprises an FBG optical fiber 4, and the FBG optical fiber 4 is arranged in the hollow shaft of the bone traction needle along the length direction of the bone traction needle and coincides with the central shaft of the bone traction needle so as to sense the axial force applied to the bone traction needle.
An FBG force sensing system two-dimensional force decoupling model established by using the bone traction needle force sensing system, wherein the model is as follows:
Δs t ＝k t F t
wherein Δs i For sensor readings, Δλ i For displacement of FBG fiber i in bragg wavelength, k εi For the strain coefficient, ε i For the local strain of FBG fiber i in relation to lateral forces, i=1, 2,3, k ΔT As a constant coefficient related to temperature, deltalambda mean Is the average value of the wavelength variation of the FBG optical fibers 1 to 3, deltas t For wavelength reading of the sensor Δs t ＝[Δs 1 Δs 2 Δs 3 ] T ，k t Is a 2 x 3 matrix of coefficients representing the reading of deltas from the sensor wavelength t To transverse force F t Linear mapping of F t ＝[F x F y ] T ，F x And F y The radial force is the radial force of the FBG fibers 1 to 3.
The three-dimensional force decoupling model of the FBG force sensing system established by the bone traction needle force sensing system is as follows:
O＝N·F；
wherein O= [ O ] 1 ,O 2 ,O 3 ,O 4 ] T N is the sensitivity matrix between the wavelength variation and the external force, f= [ F x ,F y ,F z ] T Is exposed to the FBG sensorForce;
o is calculated by the following formula:
O i ＝Δλ i -ΔS；
wherein O is i Equivalent wavelengths (i=1, 2,3, 4) of the FBG fibers 1 to 4 after temperature decoupling, Δλ 1 、Δλ 2 、Δλ 3 、Δλ 4 The central wavelength offset of the FBG optical fibers 1 to 4, the delta S is the average value of the wavelength offset under the action of the radial force of the FBG optical fibers 1 to 3,
delta T is the temperature variation, ρ e Is the strain coefficient alpha Λ And alpha T Coefficient of thermal expansion and coefficient of thermo-optic, F z Is an axial force;
f is calculated by the following formula:
ε F ＝K·F；
wherein ε F ＝[ε B1 ,ε B2 ,ε B3 ,ε C ] T The strain of the FBG fibers 1 to 4,
ε C ＝F z /(K 3 ·L 1 )，
the deformation of the FBG optical fibers 1 to 3 under the action of external radial force is respectively shown,
the deformation of the FBG optical fibers 1 to 3 under the action of external axial force is respectively L 1 For the total length, K, of the force sensor arrangement 3 For a total axial stiffness of zone 2, K is the strain transition matrix;
n is calculated by the following formula:
wherein B is 1 ＝(d f /2)·(d c /K 1 )；B 2 ＝-B 4 ＝(d f ·cos(π/6)/2)·(d c /K 1 ·L 1 )；B 3 ＝B 5 ＝-(d f ·sin(π/6)/2)·(d c /K 1 ·L 1 )；B 6 ＝(K 2 -K 3 )/(K 2 ·K 3 ·L 1 )，d f Is the circumferential diameter of the optical fiber, d c To apply the distance from the point of action of the external force to the grating region, K 1 Total bending stiffness of zone 1, K 2 For a total axial stiffness of zone 1, K 3 The total axial rigidity of the region 2 is that of the bone traction needle except the threaded part, and the region 1 is that of the whole region inside the bone traction needle.
Compared with the prior art, the invention has the following advantages:
1. the FBG fiber-based force sensor designed by the invention has the advantages that the fiber is arranged on the surface of the bone traction needle, the grating area is closer to bone tissues than the six-dimensional force sensor, the stress of the bone tissues can be further measured, and the accurate mapping relation from the bone tissues to the reading of the FBG force sensor can be established through the analysis of the FBG fiber stress model.
2. The force sensor based on the FBG optical fiber, which is designed by the invention, has a small structure, the FBG force sensor is connected with each spicule, the force mapping relation between each spicule in the spicules and the bone tissue can be measured by the sensor, and further the force measurement of the spicules and the force mapping relation between the spicules and the bone tissue are established, so that the operation robot can conveniently control the spicules to reset and pull through the parallel mechanism, and the relative force balance of the spicules is maintained.
3. The invention skillfully combines the fiber Bragg grating technology with the bone traction needle, and the precedent of applying the fiber Bragg grating in the bone needle operation is not found in the found data.
4. The invention establishes a bone traction needle three-dimensional force decoupling model based on FBG optical fibers, and establishes a mapping relation between external force applied to the sensor and optical fiber offset.
5. The force sensor based on the FBG optical fiber is not limited to a bone traction needle in application, and can be used as other surgical medical instruments.
Drawings
FIG. 1 is a schematic diagram of a bone traction needle force sensing system based on FBG fibers;
FIG. 2 is a cross-sectional view of an optical fiber arrangement;
fig. 3 is a schematic diagram of sensor force sensing under radial and axial forces, (a) radial force, (b) axial force.
Detailed Description
The following description of the present invention is provided with reference to the accompanying drawings, but is not limited to the following description, and any modifications or equivalent substitutions of the present invention should be included in the scope of the present invention without departing from the spirit and scope of the present invention.
Example 1:
the bone traction needle force sensing system based on the FBG optical fiber designed in the embodiment is shown in fig. 1. Firstly, the number of optical fibers is required to be determined, three optical fibers are theoretically required to sense the three-dimensional force condition of the bone needle in the operation environment, but the fiber Bragg gratings are also susceptible to temperature influence besides being influenced by strain, so four optical fibers of the FBG optical fibers 1-4 are designed and arranged to sense the three-dimensional force of the bone needle; secondly, the arrangement form of the bone needle needs to be determined, the three-dimensional force born by the bone needle is divided into axial force and radial force, so that four optical fibers are divided into two parts to be arranged, one optical fiber (FBG optical fiber 4) is arranged on the central shaft of the bone needle, the optical fiber is coincided with the axial force direction and is only sensitive to the axial force so as to sense the axial force born by the bone needle, the three remaining optical fibers (FBG optical fibers 1-FBG optical fibers 3) are arranged on the outer surface of the bone needle, and three equidistant grooves which form 120-degree included angles with each other are formed in the radial direction of the bone traction needle and are used for arranging the designed FBG sensors so as to sense the radial force born by the bone needle. Fig. 2 is a cross-sectional view of an optical fiber arrangement.
The FBG force sensing system designed in this embodiment measures force based on the fiber bragg grating principle, and in the force sensing process, the FBG fiber sensor is simplified into a spring model, and the schematic diagram is shown in fig. 3.
In fig. 3, the deformation of the fiber bragg grating when the sensor is subjected to radial and axial forces is shown in fig. (a) and (b), respectively. In the figure, the area of the spicule except the threaded part is defined as 1 area, the grating area for sensing strain is arranged in 1 area, the FBG optical fibers 1-3 are arranged on the outer surface of the spicule, the surface of the spicule comprises a threaded area, the threaded area enters the human body in the operation process, and in order to ensure the disinfection safety in the operation process, the FBG optical fibers 1-3 are arranged in the area of the outer surface 1 of the spicule. Because the strain of the other regions except the region 1 does not affect the FBG fibers 1 to 3 due to the special structure of the fiber bragg grating, the deformation is calculated by using only the region 1, and when an external force acts on the front end of the sensor, the FBG fibers 1 to 3 are deformed by being pulled or pressed. The FBG optical fiber 4 is positioned in the hollow shaft of the bone traction needle, and the length of the FBG optical fiber is not changed due to stress. The FBG optical fibers 1 to 3 are in radial force F x And F y Under the action, the deformation generated by the grating is as follows:
wherein,,
the deformation of the FBG optical fibers 1 to 3 under the action of external radial force is respectively d f Is the circumferential diameter of the optical fiber, d c To apply the distance from the point of action of the external force to the grating region, K 1 Is the total bending stiffness of zone 1.
The deformation condition of the fiber Bragg grating under the action of the axial force is shown as a graph (b), in the graph, the deformation condition of the FBG fibers 1 to 3 under the action of the axial force is only influenced by the bending rigidity of the 1 region, and the deformation of the FBG fibers 1 to 3 under the action of the axial force is as follows:
wherein,,
deformation of the FBG optical fibers 1 to 3 under the action of external axial force is respectively shown as K 2 Is the total axial stiffness of zone 1.
Defining the whole area inside the spicule as 2 areas, fixing the FBG optical fiber 4 on the central hollow shaft line in the 2 areas, arranging the FBG optical fiber 4 inside the spicule hollow shaft, and the FBG optical fiber 4 is different from the threaded part of the outer surface to be avoided in the 1 areas, wherein the 2 areas penetrate through the spicule and are deformed by axial force to be:
Δx c ＝F z /K 3 (5)
wherein Deltax is c For the deformation of the FBG optical fiber 4 under the action of axial force, K 3 Is the total axial stiffness of zone 2.
According to the formula (5), the external force F acting on the present invention is decomposed into radial force F x 、F y And axial force F z When the FBG fibers 1 to 4 are subjected to the strain of:
ε C ＝F z /(K 3 ·L 1 ) (9)；
wherein L is 1 Which is the total length of the force sensor device.
According to formulas (6) - (9), the relationship between the external force and the stress to which the FBG fibers 1 to 4 are subjected is:
ε F ＝K·F (10)；
wherein ε F ＝[ε B1 ,ε B2 ,ε B3 ,ε C ] T The strain of the FBG fibers 1 to 4 is f= [ F ] x ,F y ,F z ] T Is the external force received by the FBG sensor, and K is the strain conversion matrix.
Fiber bragg gratings are very sensitive to temperature and strain, and are obtainable by the principle of fiber bragg gratings:
wherein Deltalambda b Is the center offset of the fiber Bragg grating, lambda b Is the center wavelength of the fiber Bragg grating, epsilon is the strain born by the fiber Bragg grating, delta T is the temperature variation, and rho e Is the strain coefficient alpha Λ And alpha T The coefficient of thermal expansion and the coefficient of thermo-optic, respectively.
In this embodiment, the same center wavelength λ is selected for the four optical fibers, and the center wavelength shift amounts of the FBG optical fibers 1 to 4 are:
wherein Deltalambda 1 、Δλ 2 、Δλ 3 、Δλ 4 The center wavelength shift amounts of the FBG fibers 1 to 1 are respectively set.
In order to eliminate the influence of temperature on the fiber Bragg grating in the embodiment, a relatively common self-differential compensation method is adopted to perform temperature compensation, and the average value of wavelength offset under the action of radial forces of the FBG fibers 1 to 3 is subtracted:
O i ＝Δλ i -ΔS (13)；
wherein O is i For equivalent wavelengths (i=1, 2,3, 4) of the FBG fibers 1 to 4 after temperature decoupling, Δs is an average value of wavelength shift amounts under the radial force of the FBG fibers 1 to 3,
the method comprises the following steps of establishing a mapping relation between wavelength change of the fiber bragg grating and external force after temperature decoupling:
O＝N·F (14)；
wherein O= [ O ] 1 ,O 2 ,O 3 ,O 4 ] T N is the sensitivity matrix between the wavelength variation and the external force, N is calculated by the following formula:
wherein B is 1 ＝(d f /2)·(d c /K 1 )；B 2 ＝-B 4 ＝(d f ·cos(π/6)/2)·(d c /K 1 ·L 1 )；B 3 ＝B 5 ＝-(d f ·sin(π/6)/2)·(d c /K 1 ·L 1 )；B 6 ＝(K 2 -K 3 )/(K 2 ·K 3 ·L 1 )。
The mapping relation between the wavelength displacement of the fiber bragg grating and the external force is established through formulas (14) and (15), namely the three-dimensional force decoupling model of the FBG force sensing system established in the embodiment, and the design of the FBG fiber sensor force sensing system is completed.
Example 2:
this embodiment differs from embodiment 1 in that the two-dimensional force measuring method does not arrange the central FBG fiber 4, and the specific method is as follows:
strain is linearly related to moment and is therefore proportional to the lateral force exerted on the bone tip:
wherein: epsilon m The strain of the FBG optical fiber is M is bending moment caused by transverse force, r is the radial distance from the axis of the spicule on the cross section of the spicule to the FBG optical fiber, I is moment of inertia and F t For external forces applied at the spicule tip, d is the axial distance of the spicule tip to the FBG fiber.
The displacement of the Bragg wavelength of the fiber bragg grating sensor is linearly related to the local strain and the temperature change:
Δλ＝k ε ε+k ΔT ΔT (17)；
wherein Deltalambda is the central variation of the Bragg grating, epsilon is the local strain, deltaT is the temperature variation, k ε 、k ΔT Constant coefficients associated with strain and temperature, respectively.
The common mode of the three fiber grating sensors is strain caused by axial force and temperature variation. The common mode is eliminated by subtracting the average of the three FBG sensor bragg wavelength shifts. The remaining differential mode is called sensor reading deltas i ：
Wherein Deltalambda i For displacement of FBG fiber i in bragg wavelength, k εi For the strain coefficient, ε i For the local strain of FBG fiber i in relation to lateral forces, i=1, 2,3.
By subtracting the average value of each wavelength shift, common terms such as noise, axial strain, and temperature components can be removed. From the expression we can derive the sensor reading Δs i And corresponding radial force F x 、F y There is a linear relationship between:
the two-dimensional force decoupling model of the FBG force sensing system built by the invention is built up.
Claims (1)
1. The three-dimensional force decoupling model of the FBG force sensing system established by using the bone traction needle force sensing system is characterized in that the bone traction needle force sensing system comprises an optical fiber and a bone traction needle, wherein:
the optical fibers comprise three optical fibers, namely an FBG optical fiber 1 to an FBG optical fiber 3;
the FBG optical fibers 1-3 are arranged on the outer surface of the bone traction needle along the length direction of the bone traction needle;
three equidistant grooves forming an included angle of 120 degrees are formed in the outer surface of the bone traction needle in the radial direction, and FBG optical fibers 1-3 are arranged in the grooves and used for sensing radial force applied to the bone traction needle;
the optical fiber further comprises an FBG optical fiber 4, wherein the FBG optical fiber 4 is arranged in the hollow shaft of the bone traction needle along the length direction of the bone traction needle and coincides with the central shaft of the bone traction needle so as to sense the axial force applied to the bone traction needle;
the FBG force sensing system three-dimensional force decoupling model is as follows:
O＝N·F；
wherein O= [ O ] 1 ,O 2 ,O 3 ,O 4 ] T N is the sensitivity matrix between the wavelength variation and the external force, f= [ F x ,F y ,F z ] T Is the external force applied by the FBG sensor, F x 、F y For radial force, F z For axial force, T represents the transpose;
the O is calculated by the following formula:
O i ＝Δλ i -ΔS；
wherein O is i Is equivalent wavelength delta lambda of the FBG optical fibers 1 to 4 after temperature decoupling i Is delta lambda 1 、Δλ 2 、Δλ 3 、Δλ 4 ，Δλ 1 、Δλ 2 、Δλ 3 、Δλ 4 The center wavelength shift amounts of the FBG fibers 1 to 4 are shown as lambdaThe center wavelength, deltaS, is the average value of the wavelength offset under the action of the radial force of the FBG optical fibers 1 to 3,
delta T is the temperature variation, ρ e Is the strain coefficient alpha Λ And alpha T The thermal expansion coefficient and the thermo-optic coefficient are respectively;
the F is calculated by the following formula:
ε F ＝K·F；
wherein ε F ＝[ε B1 ,ε B2 ,ε B3 ,ε C ] T The strain of the FBG fibers 1 to 4,
ε C ＝F z /(K 3 ·L 1 )，
the deformation of the FBG optical fibers 1 to 3 under the action of external radial force is respectively shown,
the deformation of the FBG optical fibers 1 to 3 under the action of external axial force is respectively L 1 For the total length, K, of the force sensor arrangement 3 For a total axial stiffness of zone 2, K is the strain transition matrix;
the N is calculated by the following formula:
wherein B is 1 ＝(d f /2)·(d c /K 1 )；B 2 ＝-B 4 ＝(d f ·cos(π/6)/2)·(d c /K 1 ·L 1 )；B 3 ＝B 5 ＝-(d f ·sin(π/6)/2)·(d c /K 1 ·L 1 )；B 6 ＝(K 2 -K 3 )/(K 2 ·K 3 ·L 1 )，d f Is the circumferential diameter of the optical fiber, d c To apply an external force to the distance from the grating region, L 1 For the total length, K, of the force sensor arrangement 1 Total bending stiffness of zone 1, K 2 For a total axial stiffness of zone 1, K 3 The total axial rigidity of the region 2 is that of the bone traction needle except the threaded part, and the region 1 is that of the whole region inside the bone traction needle.
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