**4. Experiments**

There are several tasks, such as data preparation in training and evaluation of the proposed calibration system. The KITTI dataset provides images captured with a stereo camera and point clouds acquired using a LiDAR. The dataset consists of 21 sequences (00 to 20) from different scenarios. The Oxford dataset provides point clouds acquired using two LiDARs. In addition, both datasets provide initial calibration parameters and visual odometry information.

We used the KITTI dataset for LiDAR-stereo camera calibration. We referred to the method proposed by Lv et al. [1] in using the 00 sequence (4541 frames) for testing and using the rest (39,011 frames) of the sequences for training. We used the Oxford dataset for LiDAR-LiDAR calibration. Of the many sequences in the Oxford dataset, we used the 2019-01-10-12-32-52 sequence for training and the 2019-01-17-12-32-52 sequence for evaluation. The two LiDARs that were used to build the Oxford dataset were not synchronized. Therefore, we used visual odometry information to synchronize the frames. After the synchronization, the unsynchronized frames were deleted, and our Oxford dataset consisted of 43,130 frames for training and 35,989 frames for evaluation.

We did not apply the same hyper-parameter values to all five networks (Net1 to Net5) because of the large difference in the range of allowable deviations for rotation and translation in Rg1 and Rg5. Because Net5 is trained with Rg5, which has the smallest deviation range, and is applied last in determining the calibration matrix, we trained Net5 using different hyper-parameter values from other networks. Such hyper-parameters included S, *Vr*, *Vt*, G, λ1, λ2, and *B*, which are the length of a side of a voxel, the number of voxels with data among voxels in a voxel space of the reference sensor, the number of voxels with data among voxels in a voxel space of the target sensor, the number of output nodes of the FC2 and FC3 in the AM, the weight of the loss function *Lrot*, the weight of the loss function *Ltrs*, and the batch size, respectively.

Through the experiments with the Oxford dataset, we observed that data screening is required to enhance the calibration accuracy. The dataset was built with two LiDARs mounted at the left and right corners in front of the roof of a platform vehicle. Figure 2 shows a point cloud for one frame in the Oxford dataset. This point cloud contains points generated by scanning the surface of the platform vehicle by LiDARs. We confirmed that the calibrations performed on point clouds containing these points degrade the calibration accuracy. Therefore, to perform calibration after excluding these points, we set a point removal area to [Horizon: −5–5 m, Vertical: −2–1 m, Depth: −5–5 m] for the target sensor and [Horizon: −1.5–1.5 m, Vertical: −2–1 m, Depth: −2.5–1.5 m] for the reference sensor. Experimental results with respect to this region cropping are provided in Section 4.3.1.

We trained the network for a total of 60 epochs. We initially set the learning rate to 0.0005 and halved it when the epochs reached 30, and we halved it again when the epochs reached 40. The batch size *B* was determined to be within the limits allowed by the memory of the equipment used. We used one NVIDIA GeForce RTX 2080Ti graphic card for all our

experiments. Adam [41] was used for model optimization, and hyper-parameters *β*1 = 0.9 and *β*2 = 0.999 were used.

**Figure 2.** Point cloud constituting one frame in the Oxford dataset. The green dots represent points obtained by the right LiDAR, and the red dots represent the points obtained by the left LiDAR.

#### *4.1. Evaluation Using the KITTI Dataset*

Figure 3 shows a visual representation of the results for performing calibration on the KITTI dataset using the proposed five networks. In this experiment, we transform a point cloud using the calibration matrix inferred from the proposed network and using the ground-truth parameters given in the dataset. We want to show how consistent these two transformation results are. Figure 3a,b show the transformation of a point cloud by randomly sampled deviations from Rg1 and the calibrated parameters given in the KITTI dataset, respectively. The left side of Figure 3c shows the transformation of the point cloud by *RT*1 predicted by the trained Net1. This result looks suitable, but as shown to the right of Figure 3c, it can be seen that the points measured on a thin column were projected to positions that deviated from the column. The effect of iterative refinement appears here. Calibration does not end at Net1 but continues to Net5. Figure 3d shows the transformation of the point cloud by *RTonline* obtained after performing calibration up to Net5. By comparing the result of Figure 3d with the result shown in Figure 3c, we can see that the calibration accuracy is improved: suitable alignment even with the thin column.

Table 1 presents the average performance of calibrations performed without temporal filtering on 4541 frames for testing on the KITTI dataset. From the results shown in Table 1, we can see the effect of iterative refinement. From Net1 to Net5, the improvements are progressive. Our method achieves an average rotation error of [Roll: 0.024◦, Pitch: 0.018◦, Yaw: 0.060◦] and an average translation error of [X: 0.472 cm, Y: 0.272 cm, Z: 0.448 cm].

**Table 1.** Quantitative results of calibration performed on the KITTI dataset without temporal filtering. See footnotes 1,2 for hyper-parameter settings.

1 S = 5, (*Vr*, *Vt*) = (96, 160), G = 1024, (*λ*1, *λ*2) = (1, 2), *B* = 8. 2 S = 2.5, (*Vr*, *Vt*) = (384, 416), G = 128, (*λ*1, *λ*2) = (0.5, 5), *B* = 4.

**Figure 3.** Results of applying the proposed method to a test frame of the KITTI dataset. (**a**) Transformation by randomly sampled deviations. (**b**) Transformation by given calibrated parameters. (**c**) Transformation by *RT*1 inferred from Net1. (**d**) Transformation by *RTonline* obtained from iterative refinement by five networks.

Figure 4 shows two examples of error distribution for individual components by means of boxplots. From these experiments, we confirmed that temporal filtering provides suitable calibration results regardless of the amount of arbitrary deviation. The dots shown in Figure 4a,b are both obtained by transforming the same point cloud of the target sensor by randomly sampled deviations from Rg1, but the sampled deviations are different. As can be seen from the boxplots in Figure 4e–h, the distribution of calibration errors was similar despite the large difference in sampled deviations.

Table 2 shows the calibration results for our method and for the existing CNN-based online calibration methods. From these results, it can be seen that our method achieves the best performance. In addition, when these results are compared with the results shown in Table 1, it can be concluded that our method achieves significant performance improvement through temporal filtering. CalibNet [2] did not specify a frame bundle.

**Table 2.** Comparison of calibration performance between our method and other CNN-based methods.

**Figure 4.** Calibration results and error distribution when temporal filtering was applied. (**a**) Transformation by randomly sampled deviation from Rg1. (**b**) Transformation by randomly sampled deviation from Rg1. (**c**) Calibration results from random deviations shown in (**a**). (**d**) Calibration results from random deviations shown in (**b**). (**e**) Rotation error for the results shown in (**c**). (**f**) Rotation error for the results shown in (**d**). (**g**) Translation error for the results shown in (**c**). (**h**) Translation error for the results shown in (**d**).

Figure 5 graphically shows the changes in the losses calculated by Equations (10) and (11) for training the proposed networks on the KITTI dataset. In this figure, the green graph shows the results of training with randomly sampled deviations from Rg1, and the pink graph shows the results of training with randomly sampled deviations from Rg5. The horizontal and vertical axes of these graphs represent epochs and loss, respectively. From these graphs, we can observe that the loss reduction decreases from approximately the 30th epoch. This was consistently observed, no matter what deviation range the network was trained on or what hyper-parameters were used. There were similar trends in loss reduction for rotation and translation. Given this situation, we halved the initial learning rate after the 30th epoch of training. Training was performed at a reduced learning rate for 10 epochs

after the 30th epoch. After the 40th epoch, we halved the learning rate again. Training continued until the 60th epoch, and the result that produced the smallest training error among the results obtained from the 45th to the 60th epoch was selected as the training result. When Net1 was trained, the hyper-parameters were set as S = 5, (*Vr*, *Vt*) = (96, 160), G = 1024, (*λ*1, *λ*2) = (1, 2), and *B* = 8. When Net5 was trained, the hyper-parameters were set as S = 2.5, (*Vr*, *Vt*) = (384, 416), G = 128, (*λ*1, *λ*2) = (0.5, 5), and *B* = 4. In Figure 5, the training results before the 10th epoch are not shown because the loss was too large.

**Figure 5.** Changes in loss calculated during the training of Net1 and Net5 on the KITTI dataset. (**a**) *Lrot* calculated using Equation (10). (**b**) *Ltrs* calculated using Equation (11).

#### *4.2. Evaluation Using the Oxford Dataset*

Figures 6 and 7 show the results of performing calibration on the Oxford dataset using the proposed five networks. In these figures, the green dots represent the points obtained by the right LiDAR, which is considered to be the target sensor, and the red dots represent the points obtained by the left LiDAR. Figure 6a,b show the results of the transformation of a point cloud from the target sensor by randomly sampled deviations from Rg1 and calibrated parameters given in the Oxford dataset, respectively. Figure 6c shows the result of the transformation of the point cloud by *RT*1 inferred from the trained Net1. Figure 6d shows the result of the transformation of the point cloud by *RTonline* obtained after performing calibration up to Net5. Similar to the results of the calibration performed using the KITTI dataset, the results of Net1 look suitable, but they are not suitable when compared with the results shown in Figure 6d. The photo on the right side of Figure 6c shows that the green and red dots indicated by an arrow are misaligned. In contrast, the photo on the right side of Figure 6d shows that the green and red dots indicated by an arrow are well aligned. We show through this comparison that calibration accuracy can be improved by the iterative refinement of five networks even without temporal filtering.

**Figure 6.** Results of applying the proposed method to a test frame of the Oxford dataset. (**a**) Transformation by randomly sampled deviations. (**b**) Transformation by given calibrated parameters. (**c**) Transformation by *RT*1 inferred from Net1. (**d**) Transformation by *RTonline* obtained from iterative refinement by five networks.

**Figure 7.** Calibration results and error distribution when temporal filtering was applied to the Oxford dataset. (**a**) Transformation by randomly sampled deviations from Rg1. (**b**) Transformation by randomly sampled deviations from Rg1. (**c**) Calibration results from random deviations shown in (**a**). (**d**) Calibration results from random deviations shown in (**b**). (**e**) Rotation error for the results shown in (**c**). (**f**) Rotation error for the results shown in (**d**). (**g**) Translation error for the results shown in (**c**). (**h**) Translation error for the results shown in (**d**).

Table 3 presents the average performance of calibrations performed without temporal filtering on 35,989 frames for testing in the Oxford dataset. Our method achieves an average rotation error of [Roll: 0.056◦, Pitch: 0.029◦, Yaw: 0.082◦] and an average translation error of [X: 0.520 cm, Y: 0.628 cm, Z: 0.350 cm]. In this experiment, we applied the same hyper-parameters to all five networks. They are S = 5, (*Vr*, *Vt*) = (224, 288), G = 1024, (*λ*1, *λ*2) = (1, 2), and B = 8.

**Table 3.** Quantitative results of calibration performed on the Oxford dataset without temporal filtering.

Figure 7 shows two examples of the error distribution of individual components by means of boxplots, as shown in Figure 4. From these experiments, we can see that temporal filtering provides suitable calibration results regardless of the amount of arbitrary deviation, even for LiDAR-LiDAR calibration. The green dots shown in Figure 7a,b are both obtained by transforming the same point cloud of the target sensor with randomly sampled deviations from Rg1, but the sampled deviations are different. As shown in Figure 7e–g, the distribution of calibration errors is similar despite the large difference in sampled deviations. In these experiments, the size of the frame bundle used in the temporal filtering was 100.

Table 4 shows the calibration performance of the proposed method with temporal filtering. Our method achieves a rotation error of less than 0.1◦ and a translation error of less than 1 cm. By comparing Tables 3 and 4, it can be seen that temporal filtering achieves a significant improvement in performance.

**Table 4.** Quantitative results of calibration on Oxford dataset with temporal filtering.

Figure 8 graphically shows the changes in the losses calculated by Equations (10) and (11) in training the proposed networks with the Oxford dataset. Compared with the results shown in Figure 5, we observed that the results from this experiment were very similar to the experimental results achieved with the KITTI dataset. Therefore, we decided to apply the same training strategy to the KITTI and Oxford datasets. However, the settings of the hyper-parameter values that were applied to the network were different. When Net1 was trained, the hyper-parameters were set as S = 5, ( *Vr*, *Vt*) = (224, 288), G = 1024, (*λ*1, *λ*2) = (1, 2), and *B* = 8. When Net5 was trained, the hyper-parameters were set as S = 5, (*Vr*, *Vt*) = (224, 288), G = 1024, ( *λ*1, *λ*2) = (0.5, 5), and *B* = 4.

**Figure 8.** *Cont*.

**Figure 8.** Changes in calculated losses during Net1 and Net5 training on the Oxford dataset. (**a**) Rotation loss *Lrot* calculated using Equation (10). (**b**) Translation loss *Ltrs* calculated using Equation (11).

#### *4.3. Ablation Studies*

#### 4.3.1. Performance According to the Cropped Area of the Oxford Dataset

At the beginning of Section 4, we mentioned the need to eliminate some points in the Oxford dataset that degraded calibration performance. To support this observation, we presented in Table 5 the results of experiments with and without the removal of those points. However, although there is a difference in the calibration performance according to the size of the removed area, it is difficult to theoretically determine the size of the area to be cropped. Table 5 shows the results of the experiments by setting the area to be cut in two ways. Through these experiments, we found that the calibration performed after removing points that caused the performance degradation generally produced better results than the calibration performed without removing those points. These experiments were performed with the trained Net5, and the hyper-parameters were as follows. S = 5, V = (224, 288), G = 1024, *λ* = (1, 2), and B = 8.

**Table 5.** Comparison of calibration performance according to the cropped area on the Oxford dataset.

4.3.2. Performance According to the Length of a Voxel Side, S

We conducted experiments to check how the calibration performance changes according to S. Tables 6 and 7 show the results of these experiments. Table 6 shows the results for the KITTI dataset, and Table 7 shows the results for the Oxford dataset. We performed an evaluation according to S with a combination of Rg1 and Net1 and a combination of Rg5 and Net5. These experiments showed that the calibration performance improved as S became smaller. However, as S became smaller, the computational cost increased, and in some cases, the performance deteriorated. We tried to experiment with fixed values of hyper-parameters other than S, but naturally, as S decreased, the hyper-parameters *Vr* and *Vt* increased rapidly. This was a burden on the memory, and thus it was difficult to keep the batch size B at the same value. Therefore, when S was 2.5, B was 4 in the experiment performed on the KITTI dataset, and B was 2 in the experiment performed on the Oxford dataset. However, for S greater than 2.5, B was fixed at 8. In addition, there were cases where the performance deteriorated when S was very small, such as 2.5, which was considered to be the result of a small receptive field in the FEN. Even in the experiments

performed on the Oxford dataset, when S was 2.5 in Net1, the training loss diverged near the 5th epoch, so the experiment could no longer be performed. For training on the KITTI dataset, S was set to 2.5 in Net5, and S was set to 5 in Net1 to Net4. However, for training on the Oxford dataset, S was set to 5 for both Net1 and Net5.

**Table 6.** Comparison of calibration performance according to S on the KITTI dataset.

**Table 7.** Comparison of calibration performance according to S on the Oxford dataset.

4.3.3. Performance According to the Bundle Size of Frames

We conducted experiments to observe how the calibration performance changes according to the bundle size of the frame for temporal filtering. Tables 8 and 9 show the results of these experiments. Table 8 shows the results for the KITTI dataset, and Table 9 shows the results for the Oxford dataset. We performed the experiments as presented in Section 3.4.3. Because 100 runs had to be performed, the position of the starting frame for each run was predetermined. For each run, we took the median of the values of each of the six parameters associated with rotation and translation inferred from the frames in the bundle, and we calculated the absolute difference between this median and the deviation randomly sampled from Rg1. The error of each parameter shown in Tables 8 and 9 was obtained by adding up the error of the corresponding parameters calculated for each run and dividing the sum by the number of runs. Through these experiments, we found that temporal filtering using many frames improves the overall calibration performance. However, if we look carefully at the results presented in the two tables, the effect is not shown for all parameters. Considering this observation and the processing time, the bundle size of the frame was set to 100.

**Table 8.** Comparison of calibration performance according to the bundle size of frames for temporal filtering on the KITTI dataset.

**Table 9.** Comparison of calibration performance according to the bundle size of frame for temporal filtering on the Oxford dataset.


**6. Asymptotics of Solutions in the Case** *b >* **0 and** *d* **= 0**

Firstly, we consider initial conditions from *S*+. Then, on the first step *t* ∈ [0, *T*], Equation (2) has the form

$$
\ddot{u} + \mu = 0.\tag{24}
$$

Therefore, the solution has the form

$$
\mu(t) = p\_R e^{-t}.\tag{25}
$$

Since the solution to (25) belongs to the interval *u* ∈ (0, *pR*) in the interval *t* ∈ (0, *T*], then in the segment *t* ∈ [*T*, 2*T*], it depends on the values of function *f* . It has the form

$$
\mu(t) = p\_R e^{-t} + \lambda \int\_T^t e^{s-t} f(p\_R e^{T-s}) ds. \tag{26}
$$

In this segment, the asymptotics of the solution to (2) crucially depend on the values of the integral in Formula (26). Below, we assume that this integral preserves its sign on the segment *t* ∈ (*T*, 2*T*] (if the integral changes its sign, then we cannot construct the asymptotics of the solution at the segment *t* ∈ [2*T*, 3*T*] for an arbitrary unknown function *f*). Consider the first case:

$$\int\_{T}^{t} e^{s-t} f(p\_R e^{T-s}) ds > 0 \text{ for all } t \in (T, 2T]. \tag{27}$$

Then, expression (26) is greater than *pR* on the segment *t* ∈ [*T* + *δ*1, 2*T*] (here, *δ*1 ≥ 0 is some asymptotically small by *λ* value; it has order *O*(*λ*−1) at *λ* → +∞). In the segment *t* ∈ [2*T*, 2*T* + *δ*1], the leading term of the asymptotics of the solution to Equation (2) coincides with the leading term of the asymptotics of the solution to Equation (24) with the initial conditions

$$
\mu(2T) = p\_R e^{-2T} + \lambda \int\_T^T e^{s-2T} f(p\_R e^{T-s}) ds\_\prime
$$

and in the segment *t* ∈ [2*T* + *δ*1, 3*T*], Equation (2) has the form of (24). This is why in the whole segment *t* ∈ [2*T*, 3*T*], the solution to (2) has the form of

$$u(t) = \lambda \left( \int\_{T}^{2T} e^{s - 2T} f(p\_R e^{T - s}) ds + o(1) \right) e^{-(t - 2T)}.\tag{28}$$

Note that Expression (28) is greater than *pR* in the segment with length *O*(ln *λ*) at *λ* → +∞ (and this is why Equation (2) has the form of (24) in this segment), and this expression decreases and tends to zero at *t* → +∞. Therefore, there exists a time moment *t*∗ = 2*T* + (1 + *o*(1))ln *λ* > 3*T* such that *u*(*t*∗) = *pR* and *u*(*t*∗ + *s*) > *pR* on the interval *s* ∈ [−*T*, 0). Thus, we come to the initial situation (the function *u*(*t*∗ + *s*) belongs to the set *S*+), and if we take this function as the initial conditions to our equation, then we obtain a positive relaxation cycle of Equation (2) with the amplitude *O*(*λ*) and period *t*∗ = 2*T* + (1 + *o*(1))ln *λ*.

We obtain the following result.

**Theorem 2.** *Let b* > 0 *and d* = 0*, and* (27) *holds. Then, for all sufficiently large λ* > 0*, Equation* (2) *has a positive relaxation cycle with the asymptotics*

$$\begin{aligned} u(t) &= p\_R e^{-(t - nt\_\*)} , & t \in [nt\_\*, nt\_\* + T] \\ u(t) &= p\_R e^{-(t - nt\_\*)} + \lambda \int\_{T + nt\_\*}^t e^{s - t} f(p\_R e^{nt\_\* + T - s}) ds , & t \in [nt\_\* + T, nt\_\* + 2T] \\ u(t) &= \lambda \left( \int\_{nt\_\* + T}^{nt\_\* + 2T} e^{s - nt\_\* - 2T} f(p\_R e^{nt\_\* + T - s}) ds + o(1) \right) e^{-(t - nt\_\* - 2T)} , & t \in [nt\_\* + 2T, (n + 1)t\_\*] \end{aligned} \tag{29}$$

*(where n* = 0, 1, 2, ... *represents number of periods of cycle) and the period t*∗ = 2*T* + (1 + *o*(1))ln *λ at λ* → +∞*.*

Consider the second case:

$$\int\_{T}^{t} e^{s-t} f(p\_{\mathbb{R}} e^{T-s}) ds < 0 \text{ for all } t \in (T, 2T]. \tag{30}$$

Then, expression (26) is less than *pL* in the segment *t* ∈ [*T* + *δ*2, 2*T*] (here, *δ*2 > 0 denotes an asymptotically small by *λ* value such that *u*(*T* + *δ*2) = *pL*), and this is why Equation (2) in the segment *t* ∈ [2*T* + *δ*2, 3*T*] has the form of (6). Thus, in the segment *t* ∈ [2*T*, 3*T*], the solution has the form

$$u(t) = \lambda \left( \int\_{T}^{2T} e^{s-2T} f(p\_R e^{T-s}) ds - b + o(1) \right) e^{-(t-2T)} + \lambda b. \tag{31}$$

Note that expression (31) is an increasing function and that there exists a time moment *t*1 > 2*T* + *δ*2 such that *u*(*t*1) = 0. It is easy to see that

$$e^{-(t\_1 - 2T)} = \frac{b}{b - \int\_T^{2T} e^{s - 2T} f(p\_R e^{T - s}) ds}. \tag{32}$$

On the segment *t* ∈ [2*T* + *δ*2, *t*1 + *T* + *δ*3] equation has the form of (6), and therefore, Formula (31) holds for the solution in this segment (here, *δ*3 < 0 is an asymptotically small by *λ* value that denotes a time moment such that *u*(*t*1 + *δ*3) = *pL*).

It follows from (32) that

$$
\lambda \mu (t\_1 + T + \delta\_3) = \lambda b (1 - e^{-T} + o(1)). \tag{33}
$$

Since the value (33) is positive and has order *O*(*λ*) at *λ* → +∞, then Equation (2) has the form of (24) in the time interval *t* ∈ [*t*1 + *δ*4 + *T*, *t*∗) (here, *δ*4 > 0 denotes an asymptotically small by *λ* value such that *u*(*t*1 + *δ*4) = *pR*, and *t*∗ denotes a first time moment such that *t*∗ > *t*1 + *T* + *δ*4 and *u*(*t*∗) = *pR*). Therefore, the solution has the form

$$u(t) = \lambda b(1 - e^{-T} + o(1))e^{-(t - (t\_1 + T))}.\tag{34}$$

Note that *t*∗ = *t*1 + *T* + (1 + *o*(1))ln *λ*. This is why *u*(*t*∗ + *s*) > *pR* for all *s* ∈ [−*T*, 0). Thus, *u*(*t*∗ + *s*) belongs to the set *S*+, and therefore, if we take this function as the initial condition, we get a sign-changing relaxation cycle with the amplitude of the order *O*(*λ*) and period *O*(ln *λ*) at *λ* → +∞.

If we consider initial conditions from the set *S*−, then on the first step *t* ∈ [0, *T*], the equation has the form of (6) and the solution has the form of (7). Since *b* > 0, there exists an asymptotically small by *λ* value *δ* > 0 such that *u*(*δ*) = *pR* and *u*(*t*) > *pR* for all *t* ∈ [*δ*, *T*]. Then, for all *t* > *T* + *δ*, until then, the *u*(*t*) = *pR* equation has the form of (24) and the solution has the form

$$
\mu(t) = \lambda b(1 - e^{-T} + o(1))e^{-(t-T)}.\tag{35}
$$

We denote as *tR* a time moment such that *tR* > *T* and *u*(*tR*) = *pR*. This value exists because Expression (35) decreases and tends to zero at *t* → +∞. Note that *tR* = *O*(ln *λ*) at *λ* → +∞. Therefore, function *u*(*tR* + *s*) (*s* ∈ [−*T*, 0]) belongs to the set *S*+, and we return to a problem considered earlier in this section.

From the results of this section we obtain the following statement.

**Theorem 3.** *Let b* > 0*, d* = 0*, and condition* (30) *holds. Then, for all sufficiently large λ* > 0*, Equation* (2) *has a sign-changing relaxation cycle with the asymptotics*

$$\begin{aligned} u(t) &= p\_R e^{-(t - nt\_\*)}, & t \in [nt\_\*, nt\_\* + T], \\ u(t) &= p\_R e^{-(t - nt\_\*)} + \lambda \int\_0^t e^{s - t} f(p\_R e^{nt\_\* + T - s}) ds, & t \in [nt\_\* + T, nt\_\* + 2T], \\ u(t) &= \lambda \left( \int\_{nt\_\* + T}^{nt\_\* + 2T} e^{s - nt\_\* - 2T} f(p\_R e^{nt\_\* + T - s}) ds - b + o(1) \right) e^{-(t - nt\_\* - 2T)} + \lambda b, \\ u(t) &= \lambda b (1 - e^{-T} + o(1)) e^{-(t - (nt\_\* + t\_1 + T))}, & t \in [nt\_\* + 2T, nt\_\* + t\_1 + T], \\ u(t) &= \lambda b (1 - e^{-T} + o(1)) e^{-(t - (nt\_\* + t\_1 + T))}, & t \in [nt\_\* + t\_1 + T, (n + 1)t\_1]. \end{aligned}$$

*(where n* = 0, 1, 2, ... *represents the number of periods of a cycle) and period t*∗ = *t*1 + *T* + (1 + *o*(1))ln *λ at λ* → +∞*.*

The cycles of Equation (2) in the case that *b* > 0 and *d* = 0 are shown in Figure 4.

**Figure 4.** Relaxation cycles of Equation (2) in the case that *b* > 0 and *d* = 0; function *f*(*u*) satisfies the condition (**a**) (27) (**b**) (30). Values of parameters: *λ* = 104, *T* = 3, *pL* = −1, *pR* = 2, *b* = 2, and *d* = 0.


**1. Introduction**

Soils are essential to human survival, and they provide a wide diversity of ecosystem services. Among them, soils are at the base of food production, carbon storage and cycles to atmosphere, water availability, turning biomass into valuable nutrients and degrading toxic elements, and supporting biodiversity [1]. Soil surveys are a relevant source of soil information and environmental data for many uses in agriculture and, otherwise, are fundamental for evaluating land capability and preventing degradation [2]. Ramalho Filho and Pereira [3] highlight the importance of assessing regional conditions and soil properties to recommend adequate landuse management.

have been interpreted to accentuate carbonate radicals, ferrous iron, and hydroxyl

*Pedometric Tools Applied to Zoning Management of Areas in Brazilian Semiarid Region*

The identification of homogeneous zones of management consists in grouping areas whose environmental characteristics, as relief and soil, are similar. The design of homogeneous zones must be done according to the soil management, considering as well the risk of degradation, and it contributes to the sustainable land-use planning. Sánchez and Silva [26] pointed out that management areas present similar response when applied similar agronomic practices and they are subject to the same

The cluster analysis deals with segmentation of a set of *N* objects into clusters (groups) in a fashion that the same type of datasets falls in a cluster that is different from those with dissimilar datasets [27]. The results of cluster analysis reveal internal data structure and improve understanding of data. There are many cluster algorithms that are available for data partitioning into. This analysis was used to delineate management zone methods [28], and the authors prefer to apply fuzzy cluster algorithms, and they are commonly used to define management zones for precision agriculture. To develop management zones [29], the cluster analysis was conducted by Management Zone Analyst 1.0.1 (Agricultural Research Services, University of Missouri, Columbia), with a combination of variables (elevation-Electrical

Conductivity-EC, ECah-%Na; elevation-ECah-%Na, elevation-pH 1:1-%Na).

The study was conducted in an area located between 9°530

Juazeiro in Bahia State, northeast region of Brazil (**Figure 1**).

The hypothesis of this study is that the use of soil legacy data allied with modern tools that are able to analyze large datasets can assist the definition of soil potential and limitations to agricultural practices and thus assist the land-use planning and zoning. The work was developed from a legacy dataset of soil surveys made by the *Companhia de Desenvolvimento do Vale do São Francisco* (CODEVASF) [30] in the

The specific goals of this study are (i) to identify soil key properties for definition of different management zones based on area databased and literature; (ii) to harmonize the dataset according predefined properties; (iii) to produce soil key property maps through digital soil mapping; and (iv) to create a map zoning the area according the potential to agricultural uses. This approach was used to establish the main trends from the profile collection by means of soil-depth functions and to select soil key properties adequate for the area (flatland landscape and semiarid climate), in this way, separating the areas according to their agriculture

30″W (with 34,437.82 hectares), in the municipality of

The biome in the region studied was the caatinga [31], an ecoregion characterized by xeromorphic vegetation with broadleaf thorny shrubs and trees that shed their leaves seasonally, cactus plants, and sparse arid-adapted grasses [32]. The climate is characterized as semiarid with dry winter and rainy summer, and the coldest month mean temperature remains above 18°C (BSwh' in the Köppen classification). The average annual rainfall is 400 mm, with the rainy season extending from November to April (highest precipitation in March); and average annual temperature is around 26°C. The xerothermic indexes are between 200 and 150,

0″ and 9°360

30″ S and

radicals, respectively, in exposed soil and geologic materials [25].

risks and limitations of agricultural use.

*DOI: http://dx.doi.org/10.5772/intechopen.88526*

Brazilian semiarid region.

**2. Materials and methods**

**2.1 Study area and dataset**

30″ and 40°230

comprising of 7 to 8 dry months.

potentials.

40°340

**41**

However, in Brazil, even though this is well-known, the soil class information is not commonly taken into account in planning or land-use zoning. One of the problems is the small scale of available maps from systematic soil surveys (1:250,000–1:1,000,000) in the country; this small scale is not suitable for recommendations regarding soil management at the farm level [4]. This limits the implementation of land-use zoning and soil sustainable management practices and policies.

The northeast region of Brazil presents complex and heterogeneous natural features in relation to rainfall, soil, and vegetation. It represents a huge challenge for the use and management of soil and water in sustainable agricultural systems. The soil degradation observed in some areas of this region is due to irregular rainfall, soil fertility conditions, and population pressures in a typically fragile environment [5].

Despite of the environmental variability, the northeast region of Brazil has a unique biome with a particular vegetation type (named "caatinga"). The majority of soils present shallow superficial horizons and profiles and very low organic carbon contents [6–8]. The rainfall deficit together with an inappropriate soil management for agricultural use can lead to desertification processes and to increase soil salinity in many areas, further degrading the land. Also common is the presence of rocks on the soil mass and/or surface layers and soils with high clay activity, both implying strong limitations for tillage. Thus, knowing the distribution of soil classes and properties is a requirement for land-use zoning.

The manipulation and analysis of a large soil profile collection, in the existing datasets, can be difficult due to the wide variability of horizon depths and thickness, as well as the variability among and between soil classes and orders. Addressing this issue, studies about the variability of soil properties along with depth were developed by [9–15]. Beaudette et al. [16] introduced the algorithm for quantitative pedology (AQP) package, which gathers tools to produce standard profile sketches highlighting differences in soil properties between horizons. It allows to standardize profile sketches, according to Munsell color chart, and dataset harmonization by applying the slice-wise algorithm, among other useful tools to express variations inside a given soil profile collection.

Quantitative studies have been developed in soil science through numerical modeling relationships between environmental variables and soil, which are applied to a geographic dataset to create a preliminary or predictive map [17, 18]. All these techniques are known as pedometrics [17], which represents an interface between statics and soil science, supporting predictive analysis related with soil classes and attributes [19, 20]. Based in pedometric concepts, the digital soil mapping (DSM) allows to study the relationships between soil and forming factors represented by spectral bands from remote sensing data, surface numerical models, and thematic maps [17]. Remote sensing data deserves an important place in digital soil mapping, particularly in flat landscapes, where morphometric covariates have lesser influence in soil formation [21].

Landsat spectral bands, particularly in the short-wave infrared range (SWIR), are commonly used to represent the environmental covariates of parent material and/or soil. Different mineral assemblages will have different spectral reflectances, which may be separable by analyzing bands 1–5 and 7 [22, 23]. The normalized difference vegetation index (NDVI) values range between 1 and +1. High positive values usually indicate the occurrence of dense green vegetation, pointing to an appropriate supply of water and nutrients. Low values express limited photosynthetic activity, and negative ones correspond to sparse lacking ground coverage [24]. The soil enhancement ratios of Landsat spectral band ratios 3:2, 3:7, and 5:7

#### *Pedometric Tools Applied to Zoning Management of Areas in Brazilian Semiarid Region DOI: http://dx.doi.org/10.5772/intechopen.88526*

have been interpreted to accentuate carbonate radicals, ferrous iron, and hydroxyl radicals, respectively, in exposed soil and geologic materials [25].

The identification of homogeneous zones of management consists in grouping areas whose environmental characteristics, as relief and soil, are similar. The design of homogeneous zones must be done according to the soil management, considering as well the risk of degradation, and it contributes to the sustainable land-use planning. Sánchez and Silva [26] pointed out that management areas present similar response when applied similar agronomic practices and they are subject to the same risks and limitations of agricultural use.

The cluster analysis deals with segmentation of a set of *N* objects into clusters (groups) in a fashion that the same type of datasets falls in a cluster that is different from those with dissimilar datasets [27]. The results of cluster analysis reveal internal data structure and improve understanding of data. There are many cluster algorithms that are available for data partitioning into. This analysis was used to delineate management zone methods [28], and the authors prefer to apply fuzzy cluster algorithms, and they are commonly used to define management zones for precision agriculture. To develop management zones [29], the cluster analysis was conducted by Management Zone Analyst 1.0.1 (Agricultural Research Services, University of Missouri, Columbia), with a combination of variables (elevation-Electrical Conductivity-EC, ECah-%Na; elevation-ECah-%Na, elevation-pH 1:1-%Na).

The hypothesis of this study is that the use of soil legacy data allied with modern tools that are able to analyze large datasets can assist the definition of soil potential and limitations to agricultural practices and thus assist the land-use planning and zoning. The work was developed from a legacy dataset of soil surveys made by the *Companhia de Desenvolvimento do Vale do São Francisco* (CODEVASF) [30] in the Brazilian semiarid region.

The specific goals of this study are (i) to identify soil key properties for definition of different management zones based on area databased and literature; (ii) to harmonize the dataset according predefined properties; (iii) to produce soil key property maps through digital soil mapping; and (iv) to create a map zoning the area according the potential to agricultural uses. This approach was used to establish the main trends from the profile collection by means of soil-depth functions and to select soil key properties adequate for the area (flatland landscape and semiarid climate), in this way, separating the areas according to their agriculture potentials.

## **2. Materials and methods**

#### **2.1 Study area and dataset**

The study was conducted in an area located between 9°530 0″ and 9°360 30″ S and 40°340 30″ and 40°230 30″W (with 34,437.82 hectares), in the municipality of Juazeiro in Bahia State, northeast region of Brazil (**Figure 1**).

The biome in the region studied was the caatinga [31], an ecoregion characterized by xeromorphic vegetation with broadleaf thorny shrubs and trees that shed their leaves seasonally, cactus plants, and sparse arid-adapted grasses [32]. The climate is characterized as semiarid with dry winter and rainy summer, and the coldest month mean temperature remains above 18°C (BSwh' in the Köppen classification). The average annual rainfall is 400 mm, with the rainy season extending from November to April (highest precipitation in March); and average annual temperature is around 26°C. The xerothermic indexes are between 200 and 150, comprising of 7 to 8 dry months.

of assessing regional conditions and soil properties to recommend adequate land-

(1:250,000–1:1,000,000) in the country; this small scale is not suitable for recommendations regarding soil management at the farm level [4]. This limits the implementation of land-use zoning and soil sustainable management practices and

The northeast region of Brazil presents complex and heterogeneous natural features in relation to rainfall, soil, and vegetation. It represents a huge challenge for the use and management of soil and water in sustainable agricultural systems. The soil degradation observed in some areas of this region is due to irregular rainfall, soil fertility conditions, and population pressures in a typically fragile environment [5]. Despite of the environmental variability, the northeast region of Brazil has a unique biome with a particular vegetation type (named "caatinga"). The majority of soils present shallow superficial horizons and profiles and very low organic carbon contents [6–8]. The rainfall deficit together with an inappropriate soil management for agricultural use can lead to desertification processes and to increase soil salinity in many areas, further degrading the land. Also common is the presence of rocks on the soil mass and/or surface layers and soils with high clay activity, both implying strong limitations for tillage. Thus, knowing the distribution of soil classes and

The manipulation and analysis of a large soil profile collection, in the existing datasets, can be difficult due to the wide variability of horizon depths and thickness, as well as the variability among and between soil classes and orders. Addressing this issue, studies about the variability of soil properties along with depth were developed by [9–15]. Beaudette et al. [16] introduced the algorithm for quantitative pedology (AQP) package, which gathers tools to produce standard profile sketches highlighting differences in soil properties between horizons. It allows to standardize profile sketches, according to Munsell color chart, and dataset harmonization by applying the slice-wise algorithm, among other useful tools to express variations

Quantitative studies have been developed in soil science through numerical modeling relationships between environmental variables and soil, which are applied to a geographic dataset to create a preliminary or predictive map [17, 18]. All these techniques are known as pedometrics [17], which represents an interface between statics and soil science, supporting predictive analysis related with soil classes and attributes [19, 20]. Based in pedometric concepts, the digital soil mapping (DSM) allows to study the relationships between soil and forming factors represented by spectral bands from remote sensing data, surface numerical models, and thematic maps [17]. Remote sensing data deserves an important place in digital soil mapping, particularly in flat landscapes, where morphometric covariates have lesser influence

Landsat spectral bands, particularly in the short-wave infrared range (SWIR), are commonly used to represent the environmental covariates of parent material and/or soil. Different mineral assemblages will have different spectral reflectances, which may be separable by analyzing bands 1–5 and 7 [22, 23]. The normalized difference vegetation index (NDVI) values range between 1 and +1. High positive values usually indicate the occurrence of dense green vegetation, pointing to an appropriate supply of water and nutrients. Low values express limited photosynthetic activity, and negative ones correspond to sparse lacking ground coverage [24]. The soil enhancement ratios of Landsat spectral band ratios 3:2, 3:7, and 5:7

properties is a requirement for land-use zoning.

inside a given soil profile collection.

in soil formation [21].

**40**

not commonly taken into account in planning or land-use zoning. One of the problems is the small scale of available maps from systematic soil surveys

*Multifunctionality and Impacts of Organic and Conventional Agriculture*

However, in Brazil, even though this is well-known, the soil class information is

use management.

policies.

#### *Multifunctionality and Impacts of Organic and Conventional Agriculture*

As covariates, Landsat 5 TM spectral bands were used in this study (**Table 1**), from September 1989, available in http://www.dgi.inpe.br/CDSR/. The NDVI values range between 1 and + 1. In the study area, most of the NDVI values were

*Pedometric Tools Applied to Zoning Management of Areas in Brazilian Semiarid Region*

Quantitative soil properties, such as clay and sand content, can be estimated along the depth of soil profile through slice-wise algorithm [16] implemented in R software through algorithm for quantitative pedology (AQP) package [46]. The functions calculate an estimative of the main trend of values, represented by median and the variation interval by quartiles (25th and 75th of data distribution). The values shown in a column corresponds to percentage of soil profiles contribut-

Initially, Pearson's linear correlation analysis was used to measure the linear association between variables, to determine among the soil properties defined by AQP, which correlated with environmental covariates (**Table 1**). This analysis was implemented in R [46], through the function cor.test, according to [42, 44, 47]. In Pearson's correlation the p-value defines whether or not two variables are statistically correlated, and for this study, it was defined that values lower than 0.02

The modeling procedure to execute the random forest (RF) prediction was performed in R software, through randomForest (RF). RF is a nonparametric technique developed by Breiman [48] as an extension of classification and regression tree (CART) systems, to improve the performance of the predictors. To implement the RF models, three parameters are necessary: number of trees in the forest (ntree); minimum amount of data in each terminal node (nodesize); and number of covariates used in each tree (mtry) [49]. The ntree value was set to system default (500), although more stable results can be achieved with a larger number [50]. The

**(m)**

Band 1 30 0.450–0.515 [23, 39–42]

NDVI (Band 4 - Band 3)/(Band 4 + Band 3) 30 — [11, 23, 41–44] Band 3/Band 2 30 —

Band 2 30 0.525–0.605 Band 3 30 0.630–0.690 Band 4 30 0.755–0.900 Band 5 30 1.550–1.750 Band 7 30 2.090–2.350

Band 3/Band 7 30 — Band 5/Band 7 30 —

GSI (Band 3 - Band 1)/(Band 3 + Band

*Covariates used in spatial prediction of soil properties.*

2 + Band 1)

*\*Landsat 5 satellite*

**Table 1.**

**43**

**Spectral range (μm)\***

30 — [45]

**References**

below 0.1, indicating little vegetation cover in the study area [39].

**2.3 Modeling procedures**

ing with the function at each depth.

*DOI: http://dx.doi.org/10.5772/intechopen.88526*

indicate that the correlation is significant.

**Covariates Spatial resolution**

At the study site, a portion of the original vegetation has been removed, and signs of land degradation such as bare soils are common. The landscape is mainly compounded by flat surfaces, with maximum slopes of 8%, and plateaus are common in the region. Geology comprises of limestone rocks from the caatinga formation, gneiss-granite rocks of the Caraiba-Paramirim complex, and recent colluvium/ alluvium sediments [33].

The soils types in the northeast region of Brazil show large variation, according to parent material and relief, from shallow and with high content of basic cations (Ca, Mg, K, and Na) to deep and leached profiles [34]. Dominant soil classes according to the World Reference Base for Soil Resources [35] are Vertisols, Cambisols, and Planosols, with smaller extension of Regosols, Acrisols, and Luvisols.

#### **2.2 Soil input data and covariates**

The soil properties used in this study were sand, clay, and cation exchange capacity (CEC), determined according to [36]. The selection of soil properties was based on two main conditions: (i) presenting variability according to depth and ii) having importance to agricultural management (e.g., clay or sodium (Na) content).

From the original dataset, with 523 profiles, the ones with complete morphological description and analytical data were selected, performed by *Companhia de Desenvolvimento do Vale do São Francisco* (CODEVASF) in 1989 [29]. So, the input dataset comprised of the topsoil (0–20 cm) and subsoil (20–60 cm) layers for 290 soil profiles from a soil survey (legacy data). The sampling was performed according to the requirements of national soil survey service, correspondent to the detailed soil survey level [37, 38].

### *Pedometric Tools Applied to Zoning Management of Areas in Brazilian Semiarid Region DOI: http://dx.doi.org/10.5772/intechopen.88526*

As covariates, Landsat 5 TM spectral bands were used in this study (**Table 1**), from September 1989, available in http://www.dgi.inpe.br/CDSR/. The NDVI values range between 1 and + 1. In the study area, most of the NDVI values were below 0.1, indicating little vegetation cover in the study area [39].


*Article* **Fabrication of Three-Dimensionally Deformable Metal Structures Using Precision Electroforming**

**Seitaro Kumamoto 1,2 , Souichiro Fukuyama 1, Seiya Nagano 1, Keiichiro Yasuda 2, Yusuke Kitamura 3, Masaaki Iwatsuki 4 , Hideo Baba 4, Toshihiro Ihara 3 , Yoshitaka Nakanishi 3,5 and Yuta Nakashima 3,5,6,7,\***

**Abstract:** It is difficult to fabricate three-dimensional structures using semiconductor-process technology, because it is based on two-dimensional layered structure fabrication and the etching of thin films. In this study, we fabricated metal structures that can be dynamically deformed from two-dimensional to three-dimensional shapes by combining patterning using photolithography with electroforming technology. First, a resist structure was formed on a Cu substrate. Then, using a Ni sulfamate electroforming bath, a Ni structure was formed by electroforming the fabricated resist structure. Finally, the resist structure was removed to release the Ni structure fabricated on the substrate, and electroforming was used to Au-plate the entire surface. Scanning-electron microscopy revealed that the structure presented a high aspect ratio (thickness/resist width = 3.5), and metal structures could be fabricated without defects across the entire surface, including a high aspect ratio. The metallic structures had an average film thickness of 12.9 μm with σ = 0.49 μm, hardness of 600 HV, and slit width of 7.9 μm with σ = 0.25 μm. This microfabrication enables the fabrication of metal structures that deform dynamically in response to hydrodynamic forces in liquid and can be applied to fields such as environmental science, agriculture, and medicine.

**Keywords:** precision processing; electroforming; MEMS; metal structures; deformation

#### **1. Introduction**

In fields such as electronic-equipment manufacturing, biotechnology, and medicine, miniaturization and large-scale integration of systems are advancing, and process technology is being used to upgrade the functions of materials, substrates, and microdevices [1–6]. This development includes the demand for various structures with complex shapes, such as three-dimensional structures for realizing effective microregional chemical reactions, mixing, and analyses in various fields, including biological microelectromechanical systems (bioMEMSs) and micro total analysis systems (μTASs) [7–11]. Studies on the fabrication of simple 2.5-dimensional structures with metals have been conducted, by devising methods for laminating and tapering to achieve these structures. However, these metal structures are

**Citation:** Kumamoto, S.; Fukuyama, S.; Nagano, S.; Yasuda, K.; Kitamura, Y.; Iwatsuki, M.; Baba, H.; Ihara, T.; Nakanishi, Y.; Nakashima, Y. Fabrication of Three-Dimensionally Deformable Metal Structures Using Precision Electroforming. *Micromachines* **2022**, *13*, 1046. https://doi.org/10.3390/ mi13071046

Academic Editor: Nikolaos Tapoglou

Received: 25 May 2022 Accepted: 27 June 2022 Published: 30 June 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

static. Dynamic devices include structures in which polymers such as polydimethylsiloxane deform upon the application of pressure [12] and movable structures such as propellers that employ photopolymerization reactions [13]. However, although resin materials deform dynamically, it is impossible to perform various chemical modifications on structural surfaces. Single-crystal silicon can be combined with multiple materials to form a three-dimensional structure, but it is brittle. Although three-dimensionally deformable materials include comb actuators used in silicon material, chemical modification of the surfaces cannot be performed. In contrast, precision processing, such as cutting and grinding, may be used to produce free three-dimensional shapes for metal materials. However, such processing can cause variations by as much as 10 μm [14–16], which is unsuitable when the required precision is on the order of microns. One option for processing that can be realized with high precision and a high aspect ratio is deep reactive ion etching (DRIE) of silicon [17–20], used in anisotropic processing. DRIE is widely employed for producing dynamic random-access memories (DRAMs) and other devices. However, the cost of fabrication is a problem, as expensive equipment and time are required to achieve the necessary degree of vacuum. In comparison, high aspect ratios can be fabricated easily, as the combined photolithographic patterning and electroforming technique does not require a high vacuum or expensive equipment. However, the use of electroforming technology requires a seed-layer-forming process, which poses problems for productivity. The Lithographie, Galvanoformung, and Abformung (LIGA) process [21,22] is utilized when microelectromechanical system (MEMS)-level microfabrication techniques are required. However, X-ray equipment is expensive, posing problems for productivity and simplicity [23]. Precision electroforming technology, which combines photolithography and electroforming technology, has the advantages of better dimensional accuracy and higher productivity, compared with machining approaches such as cutting and grinding, and enables high-speed replication of the parent mold [24]. However, most extant studies on robust structures for miniaturization and precision improvement are concerned with fabricated structures [25–28], whereas those on structures with three-dimensional deformability are lacking. The microstructure accuracy has been reported to be limited to a 10% variation in a 50 μm design [29]. If a method with a higher aspect ratio and accuracy could be developed, microfabrication technology could be improved, and precision components could be produced. There are some examples of using precision electroforming technology to fabricate electric-shaver blades, but the structures are robust, require a hand-pushing force, and do not exhibit chemical modification. If a structure that deforms from a two-dimensional shape into a three-dimensional shape due to the hydrodynamic force could be produced via precision electroforming, the scope of the microdevice application (adaptation) would be expanded in a useful manner. μTAS has the advantage of reducing the amount of liquid required and shortening the analysis time by using a small amount of liquid. In microfluidic systems, the flow rate is approximately 1 μL/min−1 mL/min [30–32]. The device must be agitated because it is difficult to mix the liquid when the width and depth of the flow channel decrease, the Reynolds number decreases, and the flow becomes laminar. For example, it would be advantageous to create a structure that dynamically agitates the inside of a microchannel to enable effective mixing. Furthermore, if it can dynamically deform into a three-dimensional structure or agitate, it can be applied to cases in which the liquid is fed in fixed quantities or filtered according to the flow rate. Therefore, in this study, we focused on the use of precision electroforming technology to investigate a method of fabricating an original metal structure capable of three-dimensional elastic deformation in response to a hydrodynamic force. Although flat-shaped structures can be fabricated using semiconductor processes, this method can produce structures that deform three-dimensionally by a hydrodynamic force. Furthermore, we evaluated its physical properties and basic operations.

#### **2. Experimental Method**

#### *2.1. Design of a Three-Dimensional Elastically Deformable Metal Structure*

Figure 1 presents the designs of the eight types of fabricated metallic structures. Types A and E consist of multiple slits arranged in comb-like shapes. The total length of the slits is approximately 6 mm, and the slit widths in Types A and E are 10 μm and 20 μm, respectively. In these structures, the root portion of the comb teeth is deformed at its origin by hydrodynamic forces, and plate-like structures mutually intersect. Types B and C are structures in which multiple slits are arranged in an arc shape, the slit width is 10 μm, and the pitches are 250 μm and 500 μm, respectively. Types F and G are similar structures wherein multiple slits are arranged in an arc shape, the slit width is 20 μm, and the pitches are 250 μm and 500 μm, respectively. In structures with these arc-shaped slits, the slit portions are deflected by the fluid force received and deform into shapes similar to that of an insect net. Metallic structures that deform into three-dimensional shapes of Types A–C and E–G have elastic structures and are designed to return to their original shapes when the hydrodynamic force is unloaded, even when deformed in response to hydrodynamic forces. Types D and H are structures with fine pores on flat plates, having diameters of 10 μm and 20 μm and pitches of 20 μm and 40 μm, respectively. These structures were fabricated to demonstrate that the three-dimensional deformation of a metal structure requires machining and design ingenuity.

**Figure 1.** Overview of metal structure designs. The metal structures were designed with diameters of 15 mm and slit widths of 10 μm and 20 μm. Types A and E are comb-shaped, and Types B, C, F, and G are structures with multiple slits arranged in an arc shape. Types A–C and E–G have elastic structures and are designed to deform into three-dimensional shapes due to hydrodynamic force. The reason for utilizing different slit widths of 10 μm and 20 μm was to confirm that the thin film could be fabricated as the designed structure. The structures with fine pores on flat plates in Types D and H were fabricated to demonstrate the designs that needed to be devised.

#### *2.2. Methods for Evaluating Physical Properties of Metal Structures*

The stiffness of the fabricated material must be adjusted to fabricate a three-dimensionally deformable metal structure. It is important to consider the stiffness of the Ni structure for device design and performance, as it changes the shape maintenance and deformation capacities of the Ni structure. In addition, the film thickness, hardness, and slit width must be homogeneous. In Ni electroforming, the current is concentrated at the edge and outer peripheral portion of the substrate, owing to the current distribution problem, resulting in a thicker film [33]. Therefore, the film-thickness variation within the substrate plane was evaluated with four different distances, d = 24, 48, 60, and 84 mm, between the cathode and anode. The film thickness was measured at 89 locations within the substrate surface using a fluorescent X-ray film-thickness meter (SFT-9400, SII Nanotechnology Co., Ltd., Chiba, Japan). Furthermore, to evaluate the stiffness of the metal structures, the hardness of four

types of metal structures was measured by adjusting the material with a film thickness of 40 μm. For the hardness measurements, a microhardness tester (HM-221, Mitutoyo Corporation, Kawasaki, Japan) was used to obtain measurements at nine points under a load of 0.49 N and a loading time of 10 s for determining the mean value. Furthermore, for the dimensions of the slit width of the fabricated metallic structure, a digital microscope (VHX-6000, KEYENCE Co., Ltd., Osaka, Japan) was used to measure the 12 in-plane locations for evaluating the variations.

#### *2.3. Metal Structure Fabrication Method*

Figure 2 shows the electroforming apparatus used to fabricate the metal structures. A Cu plate for a 4-inch silicon wafer (Yamamoto Plating Tester Co., Ltd., Tokyo, Japan) was employed as the cathode, and a Ni anode plate containing sulfur (Yamamoto Plating Tester Co., Ltd.) was utilized as the anode. A YPP-15,031 (Yamamoto Plating Tester Co., Ltd.) was used as the rectifier for the electroforming. Table 1 lists the basic configuration of the electroforming bath used in this study; the concentration of nickel sulfamate tetrahydrate in the bath (nickel sulfamate 900, JX Metal Shoji Co., Ltd., Tokyo, Japan) was 600 g/dm3. The boric acid in the bath (Nacalai Tesque Inc., Kyoto, Japan) was prepared at a concentration of 30 g/dm3. The pH of the electroforming bath was 4.0 ± 0.1, and the temperature of the electroforming bath was 40 ± 2 ◦C. The temperature was controlled by a temperature-control unit. The anode and cathode areas were 165 cm2 and 136 cm2, respectively. Ni dissolves on the anode side and Ni is deposited on the substrate on the cathode side. Moreover, Ni metal is deposited, and a Ni electroformed structure is formed. The chemical equations for the anode and cathode sides are shown in Equations (1)–(4) and (5)–(6), respectively.

$$\text{Ni} \rightarrow \text{Ni}^{2+} + 2\text{e}^- \tag{1}$$

$$\text{Ni} + \text{H}\_2\text{O} \rightarrow \text{NiO} + 2\text{H}^+ + 2\text{e}^- \tag{2}$$

$$\text{3Ni} + 4\text{H}\_2\text{O} \rightarrow \text{Ni}\_3\text{O}\_4 + 8\text{H}^+ + 8\text{e}^- \tag{3}$$

$$2\,\mathrm{H}\_{2}\mathrm{O} \rightarrow \mathrm{O}\_{2} + 4\mathrm{H}^{+} + 4\mathrm{e}^{-} \tag{4}$$

$$\text{Ni}^{2+} + 2\text{e}^- \rightarrow \text{Ni} \tag{5}$$

$$\text{2H}^+ + \text{2e}^- \rightarrow \text{H}\_2\tag{6}$$

**Figure 2.** (**a**) is Experimental setup for electroforming. A Cu plate was used for the cathode, and a Ni anode plate containing sulfur was used for the anode, while d is the distance between the cathode and anode. (**b**) is Plating jig and the auxiliary cathode was installed at the periphery of the facility to ensure uniform film thickness.

**Table 1.** Bath composition for Ni electroforming.

#### **3. Results and Discussion**

#### *3.1. Evaluation of Fabricated Substrate in-Plane Film Thickness*

To evaluate the in-plane film thickness variation of the substrate produced by Ni electroforming, we measured the film thickness by setting a target film thickness of 10 μm and processing it for 10 min. Subsequently, the inter-electrode distance was set to the four aforementioned distances, d = 24, 48, 60, and 84 mm. Figure 3 shows the relationship between the inter-electrode distance and the electron-coating thickness. The longer the inter-electrode distance, the thinner is the film produced by Ni electroforming, and the average film thickness is the smallest at 6.7 μm with d = 84 mm. The variations are at their smallest with d = 48 mm, with an average film thickness of 12.9 μm and a standard deviation σ of 0.49 μm. Figure 4 shows the film-thickness distribution at each interelectrode distance. Negligible differences are observed in substrate in-plane film thickness, and the film-thickness variation is the smallest when d = 48 mm. With electroforming, the current is concentrated in the outer peripheral portion of the substrate when the distance between electrodes is large, and the current concentration in the central portion is high when the inter-electrode distance is small [34]. This suggests that d = 48 mm is suitable for achieving uniform film thickness. For d = 24, 48, and 60 mm, film thickness was more than 10 μm because only a small amount of electroforming was deposited on the auxiliary cathode installed at the periphery of the facility to ensure uniform film thickness, and the inside of the substrate became thick. Furthermore, because the electroforming is proportional to the electroforming time [35,36], if the throwing power is good, the desired film thickness may be expected. Based on these results, to suppress film-thickness variation in the various metal structures arranged on the substrate, we applied d = 48 mm in the subsequent evaluation. This is because the resulting coating thickness at the outermost peripheral portion being thin shows the interpolated numerical values of the unplated area and adjacent portion at the electroforming contact point, so can be ignored.

**Figure 3.** Evaluation of variations in Ni-coating thickness. The inter-electrode distance during Ni electroforming was set to four values, and the film thickness was measured by performing processing

for 10 min at a target film thickness of 10 μm. The average film thickness of 12.9 μm and σ = 0.49 μm minimized the variation at an interelectrode distance of 48 mm. As the coating thickness is proportional to the electroforming time, if the variation is small, the desired film thickness can be obtained via time adjustment.

**Figure 4.** Substrate in-plane-coating thickness distribution. The average film thickness is 12.3 μm and σ = 0.72 μm, with a 60 mm inter-electrode distance, and at 48 mm, the variation is minimized, with an average film thickness of 12.9 μm and σ = 0.49 μm. There is almost no difference in the substrate in-plane film thickness with a 48 mm inter-electrode distance, and the variation is the smallest in this case.

#### *3.2. Evaluation of Stiffness of Metal Structures*

Figure 5 shows the hardness measurement results for the four types of samples, to evaluate the stiffness of the Ni structure. Sample (a) is a Ni coating obtained from the basic bath in Table 1, (b) is a coating adjusted with a high-hardness additive, (c) is a Ni–P alloy coating, and (d) is a sample of Ni–P coating heat-treated at 350 ◦C for 1 h. Compared to the Ni films in samples (a) and (b), the Ni–P alloy films in samples (c) and (d) are harder, especially in the sample (d), which was heat-treated and had a high Vickers hardness of 950 HV. This high hardness is thought to be due to crystallization [37,38] of the Ni–P alloy by heat treatment. However, we found that the samples (c) and (d) were much more difficult to deform than the other samples [39], and the coating cracked from simple bending, making them unsuitable as three-dimensional elastically deformable structures (Supplementary Materials Figure S1). Further, while sample (a) was easily deformed at approximately 300 HV, good stiffness with 600 HV hardness and elastic deformation were achieved when the plated coating was adjusted with a high curing additive in the sample (b); hence, we used this sample in subsequent evaluations. The Young's modulus of the sample (b) was 200 GPa. Figure 6 shows a schematic of the deformation expected when a metallic structure is subjected to hydrodynamic forces. When a solution is poured into a metal structure at a constant rate, hydrodynamic forces cause the metal structure to deform elastically into a certain shape. When the hydrodynamic force increases, the deformation of the metal structure increases and returns to normal when the hydrodynamic force is removed.

**Figure 5.** Ni-coating-hardness measurement results. Sample (**a**) is a Ni coating obtained from a basic bath, (**b**) is a coating adjusted by adding 5 mL/L [40] of sulfurous additive to the basic bath, (**c**) is a coating adjusted by adding 20 g/L of phosphorus acid to the basic bath, and (**d**) is a coating of the sample (**c**) heat-treated at 350 ◦C for 1 h. Sample (**b**) has a hardness of 600 HV and achieves stiffness allowing elastic deformation.

**Figure 6.** Schematic of deformation of metal structures due to hydrodynamic forces. (**a**) Initial state of the metal structure. (**b**) When the hydrodynamic forces are small, the deformation of the metal structure is small. (**c**,**d**) The greater the hydrodynamic forces is, the greater the deformation of the metal structure.

#### *3.3. Fabrication of Three-Dimensionally Deformable Structures by Precision Electroforming*

Ni structures are intended to be applied to filters. It is possible to perform various chemical modifications on the surface of the Ni structure by adding Au plating, which can add functions to the structural surface. Typical examples include the modification of self-assembled monolayers (SAMs), frequently used in analytical chemistry and biochemistry, and antibody modifications for antigen-antibody interactions. Figure 7 shows the fabrication process of a metal structure with a fine pattern. In the photolithography process, a 30 μm positive liquid resist (AZ P4903, Merck Performance Materials Co., Ltd., Tokyo, Japan) was applied to a Cu substrate by a spin coater (MS-A150, Mikasa Co., Ltd.) (Figure 7a) and was exposed to light at 1.75 J/cm2 using a mask aligner (MA-20, Mikasa Co., Ltd.) (Figure 7b). A resist structure to serve as a mold was developed using an AZ 400 K Developer (Merck Performance Materials Co., Ltd.) (Figure 7c). To release the Ni structure from the Cu substrate, chromate treatment (2 g/dm3, 2 min, 30 ◦C) with potassium dichromate solution was applied on the Cu substrate before Ni electroforming. Next, using an electroforming bath, we fixed a Ni plate containing sulfur to the anode and a fabricated resist structure to the cathode to form a Ni structure by electroforming (Figure 7d). The resist structure was released using stripping solution (AZ Remover 700, Merck Performance Materials Co., Ltd.). By removing the resist structure, we obtained a metal structure of the desired shape by releasing the Ni structure from the Cu substrate with tweezers (Figure 7e). Figure 8 shows the improvements in contact exposure in photolithography. As the liquid resist used has a high viscosity of 1550 mm2/s, the resist was approximately 60 μm thick in the outer peripheral portion of the substrate post resist coating. The resist was physically removed using a 5 mm wide and 1 mm thick stainless-steel stick within 3 mm of the substrate edge, and the resist thickness was uniform at 30 μm. The removal of the excessively thick resist eliminated the gap between the mask and substrate, and the variation of the slit width decreased. Figure 9 shows photographs of the Ni structure fabricated by this process. We found eight types of structures, Types A–H, could be fabricated without defects, even in the slit portion or overall surface. Figure 10 shows the dimensional measurement results for the slit width of the Ni structure. By optimizing the photolithography conditions, the variation of the slit width improved from σ = 3.74 to σ = 0.25 μm. The slit width of Types A–D was 7.9 μm on average, with a design value of 10 μm, and the slit width of Types E–H was 18.3 μm on average, with a design value of 20 μm. In addition, the variation for all eight types was σ = 0.25–0.37 μm, and the fabrication was found to be precise. Although the slit width was approximately 2 μm smaller than the target value, it was expected that the desired slit width could be obtained by adjusting the design value. When fabricating a microstructure, the fact that the slit width becomes smaller than the target value is an advantage that may be adopted for various applications. The metal structure was fixed in the device shown in Figure 11, and hydrodynamic force was applied to demonstrate that the structure can deform from a two- to three-dimensional shape. Pressure was applied to the metal structure in a 9 mm diameter area around the center. Figure 12 presents a photograph of when a hydrodynamic force is applied to structures with a Type A comb shape and a Type B arc shape with multiple slits. The deformation amount of the Ni structures fabricated by this process changes according to the magnitude of the hydrodynamic force, and the structures return to their original shapes when the applied force is removed. Furthermore, if there is continuous flow at a constant rate, it is possible to maintain a constant deformation and the shape of the fluid. Incidentally, Types D and H, which have micropores formed in-plane, are self-supporting structures similar to the other structures. However, they do not deform into three-dimensional shapes under hydrodynamic forces.

**Figure 7.** Schematic of the precision electroforming process. (**a**) A photoresist is applied on a Cu substrate. (**b**) Curing of photoresist by ultraviolet irradiation. (**c**) Mold creation by developing the photoresist. (**d**) Fabrication of Ni metal structures on Cu substrates by Ni electroforming. (**e**) Removal of the Ni structure to obtain a metal structure of the desired shape.

**Figure 8.** Improvement of the photolithography process. (**a**) After resist coating, the resist at the edge of the substrate is thick at approximately 60 μm. (**b**) Resist at the edges is physically removed after improvement. The thickness of the resist is uniform at 30 μm. There is no gap between the mask and substrate in the contact exposure.

**Figure 9.** Photographs of the fabricated Ni structures. Eight types of Ni structures were fabricated precisely. Metal structures that deform three-dimensionally of Types (**A**–**C**) and (**E**–**G**) return to the original state even when deformed by hydrodynamic force. Metal structures of Types (**D**) and (**H**) are formed using the same processes and materials as metal structures that deform three-dimensionally and do not deform into three-dimensional shapes. All types appear warped under the light from the digital microscope, but the Ni structures are not warped after electroforming.

**Figure 10.** Metal-structure slit-width dimensions before and after improvement of the photolithography process. The dimensional variation decreases from σ = 3.74 to σ = 0.25 μm as a result of optimizing the photolithography conditions. The desired slit width is expected if the design value is adjusted.

**Figure 11.** Overview of the device for the experiment. (**a**) The metal structure was fixed inside the device, and the hydrodynamic force was applied. The metal structure was fixed to an acrylic tube with an inner diameter of 9 mm. (**b**) Pressure was applied to the metal structure in a 9-mm-diameter area around the center.

**Figure 12.** Photographs of three-dimensionally deformable metal structures. Type A is combshaped, and Type B is a metal structure with multiple arc-shaped slits. The deformation quantity l changes with the magnitude of the hydrodynamic force. When the hydrodynamic force is unloaded, the structure returns to its original state. The deformation of the Type A structure at a flow rate of 300 mL/h was approximately 110 μm, and that at a flow rate of 2400 mL/h was approximately 820 μm. The deformation of the Type B structure at a flow rate of 300 mL/h was approximately 40 μm, and that at a flow rate of 2400 mL/h was approximately 90 μm. The deformations of both

structures increased linearly with increasing flow rate. In addition, a comparison of the simulated and measured deformation of the two metal structures under a flow rate of 300 mL/h revealed that Type A showed deformation of approximately 120 μm (simulation value), and the measurement result was 110 μm, while Type B showed deformation of approximately 40 μm (simulation value), and the measurement result was 40 μm. Under low flow-rate conditions, the simulated and measured results showed good agreement (Supplementary Materials Figure S2). There was no plastic deformation, even under conditions with a flow rate of 2400 mL/h. As there were no realistic conditions for exceeding 2400 mL/h, it was not possible to verify until plastic deformation occurred. In this study, as a limitation to elastic deformation, results were shown for conditions with a flow rate of 300–2400 mL/h.

Figure 13 shows a cross-sectional scanning-electron microscopy (SEM) image of a Type B metal structure fabricated using 10 μm and 2 μm as the target film thicknesses for Ni electroforming and Au plating, respectively. Type B is obtained with Au coating from the basic baths in Table 2. The digital microscopy and cross-sectional SEM images show that there are no pinholes or cracks on the surface of the metal structure, demonstrating the absence of structural defects. The Ni electroforming thickness is 10.1 μm, the Au-plating thickness is 2 μm, and the film thickness can be formed as designed. In addition, a structure with a high aspect ratio (film thickness/slit width = 3.9) could be fabricated with good precision using this process. Incidentally, the yield of the fabricated structure is 90%. The three-dimensionally deformable microstructure fabricated using the process developed in this study can be applied to bioMEMSs, analysis chips, and μTASs from the perspective of size. Therefore, these structures may be expected to be applied in the biomedical field.

**Figure 13.** Cross-sectional photograph of a Type B three-dimensionally deformable metal structure (slit width: 10 μm) fabricated with a Ni electroforming thickness of 10 μm and Au-plating thickness of 2 μm. The tapered shape is due to the effect of diffraction of light during exposure.

**Table 2.** Bath composition for Au plating.

#### **4. Conclusions**

The objectives of this study were to fabricate a metal structure that can be elastically deformed into a three-dimensional shape in response to hydrodynamic forces and to propose a fine pattern fabrication approach using precision electroforming. Physical properties, such as the film thickness, hardness, and slit width, were evaluated to fabricate the fine metal structures using this technique. Based on the results, we achieved σ = 0.49 μm with an average film thickness of 12.9 μm and σ = 0.25 μm with a hardness of 600 HV and slit width of 7.9 μm. The conditions for fabricating precision metal structures were also evaluated. When the intended metal structure was fabricated using the derived conditions, we successfully fabricated metal structures capable of dynamically deforming into threedimensional shapes according to the hydrodynamic force. In this study, structures with hardness ranging 300–950 HV and flow velocities of 300–2400 mL/h were investigated, but they were within the elastic deformation range and did not deform plastically. As the type of metal and physical properties of metal structures fabricated using this technique can be varied, these structures can be applied to various fields and applications such as bioMEMSs and μTASs in the future.

**Supplementary Materials:** The following supporting information can be downloaded at: https: //www.mdpi.com/article/10.3390/mi13071046/s1. Figure S1: Simplified flexural evaluation of four types of Ni film samples (a)–(d). The Ni films in (a) and (b) were found to deform elastically and return to their original shapes without damage. The samples with Ni-P alloys in (c) and (d) cracked and broke while bending. In addition, they did not return to their original shapes. Figure S2: Simulation analysis results for the deformation of the Type A and B metal structures. The conditions used in this analysis are summarized in Table S1. The measured deformation and simulation results were compared. Under a flow rate of 300 mL/h, Type A showed a deformation (simulation value) of approximately 120 μm, and the measurement result was 110 μm, whereas Type B showed a deformation (simulation value) of approximately 40 μm, and the measurement result was 40 μm. Under a flow rate of 2400 mL/h, Type A showed a deformation (simulation value) of approximately 1080 μm, and the measurement result was 820 μm, whereas Type B showed a deformation (simulation value) of approximately 280 μm, and the measurement result was 90 μm. Thus, the simulation and measurement results agree well under the condition of a low flow rate. Table S1: Deformation analysis conditions.

**Author Contributions:** Conceptualization, Y.N. (Yuta Nakashima); methodology, Y.K., M.I., H.B., T.I., Y.N. (Yoshitaka Nakanishi) and Y.N. (Yuta Nakashima); validation, S.K. and K.Y.; formal analysis, S.K.; investigation, S.K., S.F., S.N. and Y.N. (Yuta Nakashima); resources, S.K., K.Y., Y.K., M.I., H.B., T.I., Y.N. (Yoshitaka Nakanishi) and Y.N. (Yuta Nakashima); writing—original draft preparation, S.K. and Y.N. (Yuta Nakashima); writing—review and editing, Y.N. (Yuta Nakashima); project administration, Y.N. (Yuta Nakashima); supervision, Y.N. (Yuta Nakashima); project administration, Y.N. (Yuta Nakashima); funding acquisition, Y.N. (Yuta Nakashima). All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was partly supported by a fund from the Japan Society for the Promotion of Science (JSPS) KAKENHI, via the Grant-in-Aid for Young Scientists (A) 16H06078 and the Ministry of Economy, Trade and Industry (METI) under projects to support the advancement of strategic core technologies, 17939048. The funding sources were not involved in the study design, concept, data collection, analysis, interpretation, manuscript preparation, or submission.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** All the data generated or analyzed during this study are included in this published article.

**Conflicts of Interest:** The authors declare that they have no conflict of interest.

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**5. Conclusion**

To analyze the effect of the reduction of anthropogenic sources on PM and O3 concentrations, it is also necessary to analyze the effect of winds and other meteorological variables. Furthermore, long-range transport of pollutants and natural sources of pollutants such as wildfires or dry soils caused by drought need to be taken into account to assess the effect of policy interventions aimed at reducing anthropogenic sources of air pollutants in Greater Mexico City. According to the results of this study, during the 2020 dry season in Mexico City, there was a statistically significant reduction of PM2.5 and PM10 concentrations, but there was an increase in ozone.


**1. Introduction**

LPHR is "an electronic, lifelong resource of health information needed by individuals to make health decisions" [1] and to "improve the quality and efficiency of their own health care" [2, 3]. Building electronic health record (EHR) was required by "the Health Insurance Portability and Accountability Act of 1996 (HIPAA)" [4]. The first "HIPAA Privacy Rule was released" [4] to "improve privacy standards and to restrict the disclosure of Protected Health Information (PHI) and personal identifiers to unauthorized individuals" [4]. In 2009, "the Health Information Technology for Economic and Clinical Health Act (the HITECH Act) was enacted" [5] to remediate a loophole in HIPAA Privacy Rule and promote personal health record (PHR). Untethered (cross-organizational) [6] PHR has been a preferred choice of building LPHR [6]. LPHR is attractive to patients because patients can have holistic view of their health information that are scattered in multiple information systems at various facilities. Federal agencies and local governments have been promoting PHR adoption in the past two decades with numerous "laws and regulations, incentives, and penalties" [3, 7, 8]. However, "the LPHR adoption rate has been low" [3, 8] in the United States. A.A. Abd-alrazaq et al. found out that "patients' privacy and security concerns is a major negative factor impacting LPHR adoption" [3, 7]. Patients like to fully control privacy and security of their own LPHR [3, 7]. "However, little is known how to model and construct a scalable and interoperable LPHR with patient-controlled security and privacy that both patients and providers trust" [3]. Solving this problem is "considered important to increase LPHR adoption rate and improve the efficiency as well as the quality of care" [3].

To protect the security and privacy of LPHR, encryption is an intuitive and good choice of solution [9–16]. Encryption can prevent external security attack, however, it cannot defend against insider threat [3, 17]. We argued that insider threat can be remediated via a secure access control model that is implemented correctly at user or session or process level [3, 18, 19]. Combining access control model with encryption is a better resolution. Traditional access control model, in which users are well known, has been used to couple with attribute-based encryption (ABE) as an approach. However, in PHR systems, users can be known or unknown. To overcome this problem, we proposed next generation access control which offers "open access surroundings" where "users can be centrally known or unknown" [3]. We chose the "National Institute of Standards and Technology (NIST)" "Next Generation Access Control (NGAC)" [20], a type of "attribute-based access control (ABAC)" model [3, 21]. Nevertheless, NGAC suffers a race condition in distributed system. This led to our proposal of a "novel Blockchain-enabled Next Generation Access Control (BeNGAC) model" [3] using permissioned blockchain that can ease the race condition. We explained the merits of the new model with additional benefits brought by blockchain technology. We offered the freedom of choice of encryption methods to PHR generators. With BeNGAC as the core of the LPHR access control mechanism, we designed the BET-LPHR that both patients and providers can trust. We discussed two application limitations of the design: a) when the secret private key is lost; b) when the patient cannot directly authorize the access. Possible solutions are offered to solve the limitations. We also compared our approach with prior works.


**Section 5**

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**5. Acknowledgment**

**6. References**