Design of 3D printed pressure-reducing insoles based on changes in parameters of lattice structure

Uneven distribution of pressure on the bottom of the foot or excessive local pressure shall cause discomfort. And when it gets severe, this pressure would even damage the health of the human foot, especially for people like the elderly, diabetic patients and pregnant women. Decompression footwear can effectively reduce pressure on the foot and reduce the risk of injury. However, mass-produced pressure-reducing footwear lacks pertinence due to individual differences in human plantar pressure and foot shape data. This paper presents a design, using gradient lattice structures, for four kinds of 3D printed pressure-reducing insoles. It turns out that full contact insoles with non-uniform distribution of lattice structure did the best in reducing peak pressure of the whole foot, which was 60.42% lower than that of bare foot, 17.24% of flat insole with uniform distribution of lattice structure, 13.68% of mass-produced pressure-reducing footwear. The effect on pressure reduction is significant.


Introduction
As our standards of living improve, people pay more and more attention to foot health.Excessive or uneven distribution of plantar pressure will reduce foot comfort and affect the quality of life, 1 which can lead to ulcers in severe cases and even amputations, 2 especially for special groups like diabetics.Pressure-reducing footwear can effectively reduce plantar pressure. 3But due to individual differences in foot structure, pressure-reducing of mass-produced footwear often has certain limitations, and it is difficult to target to disperse pressure and reduce foot injuries. 4Customized footwear can reduce plantar pressure to a great extent, 5 but it is mainly for people with serious conditions and generally has high cost and long production cycle. 63D printing technology in making pressure-reducing insoles can reduce the production costs while shortening the time.Facing the complicated 3D printing market, how do we choose the appropriate 3D printing materials, methods, and lattice structure, furthermore, develop a 3D printing method for the production of pressure-reducing insoles, so as to adjust and improve the pressure distribution on the soles of special people, reduce the partly pressure overload, protect their foot health as much as possible, and reduce the chance of ulcers and even amputations.It is of great practical significance to realize the rapid design and customization of pressure-reducing insoles.

Program description
Numerous studies have been conducted by medical and sports-related industries to reduce plantar pressure. 7In the case of diabetic foot, for example, it has been shown that the hardness of the sole material affects an important indicator for plantar pressure.Compared with ordinary flat insoles, soft full-contact insoles can effectively reduce peak contact pressure and increase contact area, reducing the incidence of foot ulcers. 8,9here are several main design factors of diabetic insoles, including geometric outline, hardness, and thickness, while geometric outline is the main factor in determining peak contact pressure and hardness is the secondary one. 10Compared to flat insoles, full-contact insoles help to reduce peak contact pressures on the forefoot and hindfoot by 19.8%-56.8%. 11This reduced pressure will be redistributed to the midfoot and the newly increased contact area. 12The use of soft insole materials and increased insole thickness within a certain degree can both help to expand the foot contact area and reduce peak pressures.The combination of multiple design factors can reduce stresses to a greater extent. 13It has been demonstrated that shape and pressure based custom insoles can disperse stress better in the metatarsal region than traditional diabetic orthotic insoles. 143D printing, a low-cost additive manufacturing technology, has emerged as a new approach to customizing pressure-reducing insoles.
8][19] However, there are individual differences in human plantar pressure distribution, and it is more pronounced among special groups, 20 and simple adjustment of insole design contours or bulk adjustment of the local material cannot achieve the pressure reduction effect we expect.Therefore, different material properties are required for different regions of the insole.Functional gradient materials are more conducive to adapting to specific foot contours and foot pressure, 21 resulting in better reduction of plantar pressure, compared to uniformly textured designs.And the development of 3D printing technology has made it possible to design pressurereducing insoles with gradient mechanical properties through lattice structures. 22,23In this paper, a 3D printed pressure-reducing insole design method based on the variation of lattice structure parameters is proposed for the ideas above.
Firstly, a suitable 3D printing method and a proper material & lattice structure are selected; secondly, a lattice sample model is established to explore the relationship between 3D printing lattice structure and mechanical properties to provide scientific basis for designing insoles; thirdly, 3D printed pressure-reducing insoles are designed and produced with gradient mechanical properties; finally, the pressure-reducing effect of 3D printed pressure-reducing insoles is verified as follows (Figure 1).

Sample production
3D printed insoles filled with lattice structures can reduce weight and material usage, while disperse pressure by changing the density.Currently, only a few lattices have been repeatedly studied and validated.One of them is the octahedral cellular structure (OCS).This is a special three-dimensional cellular structure that can be represented by the octahedral volume of eight tilted pillars.It is obvious from the cellular structure that the same load response mechanism will be exhibited in all three main directions.Therefore, only one main direction needs to be studied when exploring its mechanical properties. 24Although there has been a large amount of papers studying its mechanical properties, [25][26][27] energy absorption effects, etc., [28][29][30] its application in insole design is unclear.The octahedral structure is in the spotlight due to its relatively simple deformation mechanism and potential for application in high energy absorbing interlayer structures, which is in line with the properties required for the structure of the insole design in this paper.Therefore, the minimum lattice structure is finally determined as the octahedral structure (Figure 2).The characteristics of the 3D printed structure lattice result in differences in the mechanical properties of different size specification lattices.In the mean time, ordinary uniformly distributed insole structures and materials are often difficult to achieve customized decompression and decompression effects.As a result, 3D printed lattices with homogeneous structures cannot be used directly.And it is necessary to test the mechanical properties of different lattice size specifications.Then the decompression insole shall be designed according to its mechanical property characteristics.
Here, the Grasshopper plugin of Rhino is used to build prototype models.The Sample of Battery connection method is shown in Figure 3.To ensure the successful design of the insole, it is necessary to make each cell edge successfully connected with others.So the cell size in the scheme is defined as 5 3 5 3 5 mm.The variation of the radius of the cell structure size is also included, from 0.3 to 1.1 mm.The unit cell is filled in a square with the structure size of 20 3 20 3 20 mm.After various printing techniques and materials are compared, the polyurethane acrylate (PUA) material is finally determined to be used with Digital Light Processing (DLP) technology (Figure 4).

Test instruments
The impact resistance, fatigue resistance, and vibration damping performance of octahedral structures of different sizes filled into cubes are compared.The instruments used include a servo material multifunctional high and low temperature control testing machine (GOTECH, AI-7000-NGD), a foam plastic repeated compression testing machine (GOTECH, GT-7049-B), and a sports shoes shock absorption testing machine (GOTECH, GT-7042-AF2).

Test results and discussion of samples
After comparing the test results of impact resistance, fatigue resistance, and vibration damping of different samples, it was found that (Figure 5): for flexible objects, the maximum pressure value they can withstand decreases when they are kept in compression, reflecting a kind of unloading ability, which is an expression of impact resistance.After the structure completes the unloading process, the maximum pressure value can only rely on the material's own characteristics.The difference in pressure change after 20 s is the unloading capacity of the structure.The results show that the radius of a single rod in an octahedral structure is directly proportional to its impact resistance, and the larger the radius of the lattice monopole, the better the strength and the ability to withstand greater pressure (Figure 5(a)).According to formula (1), the compression deformation rate of all octahedral structure samples is within 1.5%, and the structural stability and fatigue resistance are excellent (Figure 5(c)).The radius of single rod of octahedral structure is inversely proportional to the damping property (0.3-0.5 mm no valid data detected).The smaller the radius of the lattice monopole, the better the absorption of energy and the more it can play a role in shock absorption and protection (Figure 5(b)).When the decompression insoles are designed, the appropriate single rod radius is selected according to the actual printing, forming conditions, and different pressure areas.The single rod radius with the best damping performance in the pressure concentration area, the best impact resistance in the main support and easy-to-strain area is selected, so that the mechanical strength of the insole can be ensured while achieving the effect of pressure distribution and decompression Among them, a is the compression deformation rate (%), L 0 is the original height of the sample (mm), and L 1 is the height of the sample after 1000 compressions and 0.5 h of standing (mm).

Acquisition of human data
The number of people with diabetes is increasing every year. 31Diabetic foot, one of the major complications of diabetes, is mainly caused by sensory neuropathy and excessive mechanical stress.Reducing mechanical stress on the foot can effectively reduce the incidence of diabetic foot. 32Based on the view above, in this study, our aim is to make pressure-reducing insoles for patients with diabetic foot.The first step is to obtain the subject's foot shape data and plantar pressure data.One subject was selected according to the 1999 World Health Organization (WHO) criteria for the diagnosis of type II diabetes.Currently, the subject has no calluses or ulcers on the foot.Specific information is shown in Table 1.
The subject's feet were scanned with Ifoot-s 3D scanner to extract the subject's foot contour data.Considering the wearing scenario of the insole and the wearing condition is mostly under weight-bearing condition, the foot data of the subject was collected while standing.After scanning, the original SCM file was converted into the STL format common to 3D modeling software, and the foot model was used as the contour base for the subsequent insole design (Figure 6).
To extract the foot pressure data of the subjects, the plantar pressure data of the subjects were collected with an Rs-scan flatbed plantar pressure measurement system.The gradient structure of the insole is designed with reference to the plantar pressure data, so as to optimize the plantar pressure distribution and achieve the purpose of pressure distribution and pressure reduction of the insole.Compared to static plantar pressure data, dynamic walking plantar pressure data better reflect the real wearing condition of plantar pressure distribution (Figure 7, the colors of different zones represent different pressure values).

Determine insole design parameters
The effect of insole design on pressure reduction based on plantar pressure distribution, foot contour by changing the single rod radius of the lattice structure, and changing the outer contour of the insole shall be investigated.Based on the design ideas above, a total of four 3D printed insoles are designed, including: full contact insole with non-uniform distribution of lattice structure (NC); full contact insole with uniform distribution of lattice structure (UC); flat insole with non-uniform distribution of lattice structure (NF); flat insole with uniform distribution of lattice structure (UF).The specific design scheme of each insole is shown in Figure 8 and Table 2.
The subject's plantar pressure distribution map is imported into Rhino as a design reference.Different colors represent different pressure values.The single  rod radius of the lattice in different parts of the insole is adjusted according to the pressure value.The insole is divided into different pressure zones, one single rod radius used in each zone and distributed in a gradient from the high pressure region outward.The insole is divided into four zones according to the amount of pressure: the red area is the key area, which is the part that needs to be focused on; the yellow area is the high pressure area; the green area is the medium pressure area; and the remaining of the insole is the low pressure area.Depending on the region, its corresponding lattice monopole radius is divided into four types (Figure 8).The specific radius of the lattice monopole for each area needs to be considered based on the actual printing and molding conditions and mechanical properties.The Grasshopper is used to build the lattice structure.The Battery is connected as in Figure 9.
Since the size of the sample and the actual insole are different, the success rate of printing is also different.The larger the volume of the same structure, the more likely the blockage will occur inside the print.The clogged lattice structure will produce huge changes in mechanical properties, so the lattice parameters are adjusted as much as possible to avoid clogging in this test.In the actual printing of insoles, severe clogging occurred when the lattice radius was 1.1 mm.The clogging was relieved when the lattice radius was reduced and the clogging disappeared when the lattice radius was 0.75 mm.Considering that the insole needs to have a certain strength to support the weight of the human body and to achieve the role of energy absorption and pressure dispersion locally, the final set of lattice radius of the insole is shown in Table 2.The shape of the octahedral lattice structure is not flat enough.So based on the purpose of improving the comfort of the insole, the surface of the insole needs to be attached to a layer of PU material when the printing is finished.The insole is designed with a 1 mm thick and 5 mm wide border wall on the periphery of the upper surface for easy attachment of subsequent materials.The full-contact insole with non-uniform distribution of lattice structure is modeled as an example in Figure 10.
Different lattice single rod radius is set in different color parts of the insole (as in Figure 8).The metatarsal toe area and the key area of the heel have the smallest lattice single rod radius design, indicated by red.These structures will be deformed under compression to reduce the contact pressure.Green (the difference area between the outer and inner ring) and yellow are the transition areas.On the one hand, the transition between the high-pressure area and the low-pressure area can help the insole transform smoothly in shape.On the other hand, it help target to disperse the pressure in the high-pressure and medium-pressure areas.The rest of the edge of the low-pressure areas (including the inner circle of green lines) lattice single rod radius are the largest, playing an effective support role.The upper surface of the insole is bonded with a veneer   (made of PU) to improve comfort while preventing stress concentration and improving the surface quality of the insole.This study only need to verify whether personalized 3D printed insoles would have a reduction effect on plantar pressure.And studies have shown that there is no significant difference in plantar pressure distribution between the left and right foot of the same person. 32So only the right foot insole is designed and produced for this experiment.
The wear resistance of lattice structure insoles has not been verified compared with traditional solid structure insoles.And it will change with the change of lattice single rod radius.Since there is no corresponding test standard for 3D printed lattice insoles, this test refers to the standard BS EN344 to test the bending resistance of insoles.The non-uniformly distributed flat insoles with the thinnest thickness and the smallest lattice radius are selected.It is most prone to fracture, so the test results are most representative.It is found that after 40,000 times of bending (the standard is 30,000 times), no fracture is found in all parts of the insoles, indicating that the four models of this study has a certain degree of wear resistance.

Methods
In order to verify the pressure reduction effect of 3D printed insoles, it is necessary to test the pressure distribution with the 3D printed insoles.Since the 3D printed insoles are thick and no appropriate shoes are available for this test, a sockliner is used to assist the test.The subject wore a sockliner on the right foot and wrapped the Pedar-x pressure test insole and the 3D printed insole.Due to the small extension of the sockliner, the insole did not slide or fall off when walking.In order to exclude the influence of the binding force of the sockliner on the plantar pressure, the left and right foot were lifted before the test and the pressure was zeroed using the Pedar-x software.During the test, the subject's left foot was wearing the shoe with a sole thickness of about 2 cm.The thickness of each area of the four printed insoles was between 1 and 2 cm, and the thickness of the left and right was basically the same to ensure normal walking.At the same time, one mass-produced pressure-reducing insole (X: The material is mainly PU, with a thickness of 6 mm at the front and 8 mm at the rear) was selected with the same shoe to compare with four custom-made insoles, a total of five insoles.The order was randomized during the test.Subjects were told about the test and filled out the test informed consent form before the test, and all tests were performed on a flat surface.A 5-min walking adaptation was performed before the test to familiarize with the insoles and the experimental site.Subjects were dynamically tested at a speed of 1.2 m/s.Data collection was started when the subject's condition reached stability, with each collection lasting 30 s.After making sure that valid  experimental data are collected, continue with the next set, until three sets of valid data were collected.Test the pressure on the soles of the feet of subjects wearing five types of insoles and barefoot respectively.To ensure the comparability of the barefoot test data, the socks were not taken off during the barefoot test, and the test process was as shown in Figure 11.
The pressure distribution between the foot and the insole is measured using the Pedar-x insole pressure measurement system (the new German Pedar system), which is thin enough to be placed between the foot and the insole to accurately measure the pressure at each site, with a sampling frequency set at 100 Hz.The sole of the foot is divided into 10 zones for comparison purposes: T1 (Toe 1), T2-T5 (Toe 2-5), M1 (Metatarsus 1), M2 (Metatarsus 2), M3 (Metatarsus 3), M4 (Metatarsus 4), M5 (Metatarsus 5), MF (Medial Foot), HM (Heel Medial), and HL (Heel Lateral).

Experimental results
As is shown in Figure 12, compared with barefoot, the peak pressure (PP) in the high pressure areas of M2, M3, M4, M5, HM, and HL decreased with the insoles.And the peak pressure areas of T1, T2-5, and MF, where the peak pressure was smaller in barefoot condition, increased with the insoles.And more uniform distribution of peak pressure is detected across the plantar area of the foot.Five insoles are softer and more prone to deformation compared to the ground.When wearing, due to the weight of the foot sunken, the results show that other parts of the force less contact area with the insole increased, bearing more pressure.The distribution of peak pressure changes on the bottom of the foot.Compare five types of insoles: M3, M5, and HM areas have the best pressure reduction effect when wearing NC insoles; The M2 area has the best pressure reduction effect when wearing UF insoles; The M4, HL areas have pretty good pressure reduction effect when wearing NC, UC insoles.When wearing X insoles at the same time, T1 increases the most; T1, T2-5 increase the most when wearing NF insoles; MF increases the most when wearing UF insoles.Compared to barefoot, the difference in peak pressure reduction of the whole foot of the five insoles is ranked as: NC .UC .UF .NF .X.Among the five insoles, the peak pressure of the whole foot was most significantly reduced by 60.42% when wearing NC insoles compared to barefoot.
Pressure-time integral represents the area under the pressure-time curve in the region.It can be analyzed to understand the cumulative effect of ground reaction forces on the soles of the feet.Thus, the impact of the shoes on the human body can be determined. 33As it can be seen from Figure 13, the PTI of M2, M3, M4, M5, HM, and HL in the barefoot state are larger.Excessive mechanical stress combined with the accumulation of time can lead to calluses and even ulcers.With the five insoles, the PTI of M2, M3, M4, M5, HM, and HL all decreases, and the PTI of T1, T2-5, and MF increases.It can be seen that the insole has a dispersing   and lowering effect, similar to the results for peak pressure.Compared to barefoot, the whole-foot PTI reduction difference of the five insoles is ranked as follows: NC .UC .X .NF .UF.Among the five insoles, the PTI of the whole foot was most significantly reduced by 58.11% when wearing NC insoles compared to barefoot.
To observe the difference in plantar pressure between NC insoles and other insoles, according to the following formula (2), obtain Figure 14: Among them, b is the degree of change (%), P is the data for other insoles, and P NC is the data for NC insoles.According to this formula, a positive value indicates a decrease in pressure in the area where the NC insole is worn, and a negative value indicates an increase in pressure in the area where the NC insole is worn.From Figure 14, it can be seen that: the NC insole has the best pressure reduction and pressure distribution effect compared with other insoles, and its effect is mainly achieved by distributing the higher pressure in the regions of M2-M5, HM, and HL to the originally less pressurized regions of T1-T5 and MF.The PTI also shows similar results.Compared to the bare foot, M2, M3, M4, M5, HM, and HL were reduced by 61.91%, 66.41%, 48.91%, 57.13%, 63.65%, and 57.79% respectively, when wearing the NC insoles.Compared with the mass-produced insoles, the peak pressures in different parts of the insoles were reduced by up to 41.78% when using NC insoles, except for MF and T1-T5 regions.The custom insoles showed better pressure reduction and more uniform distribution of plantar pressure intensity compared to massproduced insoles, which is also in line with the results of previous studies. 5Compared with UF insoles, the peak pressure in all regions was reduced up to 41.87% when using NC insoles, except for T1, M1, and M2 regions where the peak pressure was originally smaller.It shows that the NC insoles with customized design based on foot type and plantar pressure have better pressure reduction effect, and it is necessary to design the insoles for different pressure areas.
Overall, the whole-foot peak pressure was reduced by 60.42% compared to barefoot when wearing NC  insoles, 17.24% compared to UF insoles, 13.68% compared to mass-produced insoles.The whole foot PTI was reduced by 57.72% compared to bare foot, 22.52% compared to UF insoles, and 25.68% compared to the mass-produced insoles.Meanwhile, the NC insole had the most obvious effect of pressure reduction on the high pressure area of the subject's foot, up to 66.41%, which shows that the NC insole made by the new method proposed in this paper has a good effect of pressure reduction and pressure distribution.
The insole base thickness was set at 10 mm in this study due to structural unit size limitations.This would affect direct matching with commercially available shoes, but a thicker insole could replace the midsole.Follow-up studies should develop mass-producible footwear products without midsoles.

Conclusion
The abnormal increase in peak plantar pressure in diabetic patients may lead to local tissue ulceration, which may cause many serious consequences.The distribution of foot pressure in different individuals requires different insole designs to reduce local plantar pressure.Compared with traditional custom insoles, which require the development of molds and cost a lot of time and money, 3D printed insoles can shorten the production time and reduce the cost while effectively distributing the plantar pressure, 4,34 which can help the further application and promotion of custom insoles.In this study, a new method for making 3D printed pressurereducing insoles is proposed, which aim to produce the most suitable insoles based on the existing lattice structure and the foot size and plantar pressure distribution of the wearer.The validation results prove the effectiveness and reliability of the method.There is a huge market potential for diabetic patients and other people with similar needs.This method also has implications for the use of new materials and lattice structures for the production of pressure-reducing insoles.

Declaration of conflicting interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Figure 5 .
Figure 5. Test results of different samples: (a) impact resistance of different samples, (b) vibration damping of different samples, and (c) fatigue resistance of different samples.

Figure 6 .
Figure 6.3D model of the foot.

Figure 7 .
Figure 7. Plantar pressure profile of the subject.

Figure 12 .
Figure 12.Comparison of peak pressure under different conditions.

Figure 13 .
Figure 13.Comparison of pressure time integrals under different conditions.

Figure 14 .
Figure 14.Results of NC insole compared to other states: (a) percentage decrease in peak pressure and (b) percentage decrease in PTI.

Table 1 .
Basic information of the subject.

Table 2 .
Variation of single rod radius of insole lattice.