**Dietary Plant Origin Bio-Active Compounds, Intestinal Functionality and Microbiome**

Printed Edition of the Special Issue Published in *Nutrients* Elad Tako Edited by

www.mdpi.com/journal/nutrients


**1. Introduction**

Micromirrors as scanning devices are reported intensively in literature with different electromechanical transducer principles. They are mostly classified into the electrostatic, electrothermal, electromagnetic, and piezoelectric micromirrors [1–5]. The piezoelectric transducer principle offers the advantages of high deflections at moderate excitation voltages and high dynamic ranges. Furthermore, a high degree of miniaturization and the monolithic integration of actuators and sensor elements is possible. In addition to the commonly used transducer material, lead zirconate titanate (PZT), piezoelectric AlN, and AlScN thin films can alternatively be used as piezoelectric transducers for actuation. Since 2018, several AlN and AlScN-based micromirrors have been presented. Shao et al. [6] presented the first AlN-based micromirror. The microsystem with a 0.2 × 0.2 mm2 mirror plate area and L-shaped bending actuators reached a resonant scan angle of 4◦ at 5 V and 63.3 kHz. Since then, further publications on AlN-based micromirrors have followed. Since June 2019, our preliminary work [7,8] includes resonantly operated 1D micromirrors with a 600 nm AlN film, a mirror plate length of 0.8 mm, and a chip size of 2 × 3 mm2 . Large scan angles of up to 137.9◦ at 20 V and 3.4 kHz were reached in air. In October 2020, two 2D micromirror designs with a footprint of 2 × 2 mm2 and mirror plate diameter of 0.7 mm were developed to realize Lissajous and spiral scan trajectories [9]. For the Lissajous scanning design, a scan angle of 92.4◦ at 12,060 Hz and 123.9◦ at 13,145 Hz was reached at 50 V for the x- and y-axis, respectively. The spiral scanning design reached

**Citation:** Stoeckel, C.; Meinel, K.; Melzer, M.; Žukauskaite, A.; ˙ Zimmermann, S.; Forke, R.; Hiller, K.; Kuhn, H. Static High Voltage Actuation of Piezoelectric AlN and AlScN Based Scanning Micromirrors. *Micromachines* **2022**, *13*, 625. https:// doi.org/10.3390/mi13040625

Academic Editor: Huikai Xie

Received: 8 March 2022 Accepted: 7 April 2022 Published: 15 April 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/).

a scan angle of 91.2◦ at 13,834 Hz and 50 V. In 2021, a 2D circular-scanning AlN-based mircomirror with a large aperture of 7 mm for laser material processing was published by Senger et al. [10]. In air, a scan angle of 5◦ is reached at 40 V and 1265 Hz. Due to the application, no large deflection angles were specified. In order to achieve higher deflections with larger mirror apertures, vacuum packaging is often used in literature. A wobbling mode AlN-scanner for automotive applications was published in October 2019 by Pensala et al. [11]. The microsystem with an aperture of 4 mm and 6.75 × 6.75 × 2 mm3 chip size reached a scan angle of 30◦ at 1 V and 1.6 kHz by the implementation of a vacuum package. In 2020, Senger et al. [12] also presented a vacuum-packaged AlN-based micromirror with a 5.5 mm aperture. A Lissajous scan pattern with 50◦ × 20◦ scan angle was realized.

The previously mentioned micromirrors are exclusively driven in resonance to achieve sufficiently large tilt angles. Resonance frequency deviations, caused by variations of the ambient conditions like mechanical vibration and temperature change or heating due to light losses during laser irradiation, lead to a change of the tilt angle and, finally, result in errors in image formation and reconstruction [4,13]. Therefore, a static or quasi-static working mode has many advantages in regards of the electronics and drivers. In March 2019, Gu-Stoppel et al. presented an AlScN-based quasi-static micromirror with mirror plate diameter of 0.8 mm [14]. The mirror plate is mounted onto a pillar, which is deflected by four actuators hidden beneath. A high static scan angle of 50◦ at 150 VDC was achieved by this novel construction. The challenge with this concept is a complex manufacturing process, which includes different wafer bonding processes for the micromirror assembly.

In this work, the static deflection and high voltage performance of the Design 1 MOEMS in [8] is investigated. Additionally, a technology is developed using a 2 µm Al0.68Sc0.32N with high thickness as transducer material for a direct comparison of the performance of the MOEMS with higher piezoelectric coefficient. Furthermore, the design is optimized for a chip size with twice the length and width of MOEMS (Design 2) to identify the performance gain for different chip footprints and further increase the deflection. By reducing the silicon spring width in relation to previous designs, the stiffness is decreased, targeting a high deflection per voltage.

### **2. Design**

In Figure 1 the schematics of the fabricated Al(Sc)N micromirrors with 2 × 3 mm2 and 4 × 6 mm2 footprint are shown. In Table 1 the mirrors parameter are shown. The mirror plate is connected with two actuators by four L-shaped springs. The design and FEA of the 2 × 3 mm2 MOEMS is shown by Meinel et al. [8]. The MOEMS design and FEA process for optimization of the leverage effect is described by Meinel et al. [7] previously. In this publication, the static deflections of the MOEMS are calculated analytically. The parameters for the analytical calculation are given in Table 1. The actuators are described in a quarter symmetrical model of the MOEMS (Figure 2). The piezoelectric unimorphs are divided into two separate actuators in parallel. The actuator has the length *l* and the width *w*. Both actuators have a free displacement ξ0 and a blocking force *F*0.

$$\xi\_0 = -3 \cdot \frac{d\_{31} \cdot l^2}{t\_p^2} \cdot \frac{AB \cdot (B+1)}{D} \cdot V \tag{1}$$

$$F\_0 = -\frac{3}{4} \cdot t\_p \cdot E\_p \cdot d\_{31} \cdot \frac{AB \cdot (B+1)}{AB+1} \cdot \left(\frac{w\_1}{l\_1} + \frac{w\_2}{l\_2}\right) \cdot n \cdot V \tag{2}$$

$$A = \frac{E\_S}{E\_p};\ B = \frac{t\_S}{t\_p};\ D = A^2 \cdot \mathcal{B}^4 + 2A \cdot \left(2\mathcal{B} + 3\mathcal{B}^2 + 2\mathcal{B}^3\right) + 1\tag{3}$$

The free displacement is defined by the deflection of the longest actuator in the system. The blocking force is a sum of all four actuators *n* of the system. The actuator force in relation to the displacement at the leverage arm ξ*p* can be described as *Fp* ξ*p* :

$$F\_p\left(\xi\_p\right) = -\frac{F\_0}{\mathfrak{f}\_0} \cdot \xi\_p + F\_0 \tag{4}$$

The microsystem has a resonance frequency as a result of the systems stiffness *C* and mass *m*. The mass is approximated as the mirror plate mass only. The stiffness is calculated by the resonance frequency *f* of the system. The force in relation to the stiffness and the deflection at the center of the mass ξ*m* can be described as *Fc*(ξ*m*).

$$F\_{\mathfrak{C}}(\xi\_{\mathfrak{m}}) = \mathbb{C} \cdot \xi\_{\mathfrak{m}} = 4\pi^2 \cdot f^2 \cdot m \cdot \xi\_{\mathfrak{m}} \tag{5}$$

**Table 1.** Comparison of the parameter of the micromirror designs and transducer materials.

1 Symbolism according to Figures 1 and 2.

The relation between ξ*m* and ξ*p* is defined by the leverage arm distance to the center *bp* and the distance to the area center *bm*:

$$
\mathfrak{E}\_m = \frac{b\_m}{b\_p} \cdot \mathfrak{E}\_p \tag{6}
$$

The momentum of the actuators and the systems stiffness are in an equilibrium:

$$\mathbf{M}\_p = \mathbf{M}\_m \tag{7}$$

$$F\_p \cdot b\_p = F\_c \cdot b\_m \tag{8}$$

$$\left(-\frac{F\_0}{\mathfrak{F}\_0} \cdot \mathfrak{E}\_p + F\_0\right) \cdot b\_p = \left.\mathbb{C} \cdot \frac{b\_m}{b\_p} \cdot \mathfrak{E}\_p \cdot b\_m\right.\tag{9}$$

**Figure 1.** Schematic of the presented micromirror designs.

**Figure 2.** Quarter symmetrical model of the MOEMS: (**a**) Design 1; and (**b**) Design 2.

The deflection at the leverage arm position in relation to the leverage arm distance to the center of the MOEMS can be calculated with this equilibrium of the momentum:

$$\mathfrak{E}\_p(b\_p) = \frac{F\_0}{\frac{F\_0}{\xi\_0} - \frac{b\_m^2}{b\_p^2} \cdot \mathbb{C}} \tag{10}$$

The deflection at the edge of the mirror plate *ξe* in relation to the lever arm position *bp* is given by Equation (11).

$$\xi\_{\varepsilon}(b\_{p}) = \frac{F\_{0}}{\frac{F\_{0}}{\xi\_{0}} + \frac{b\_{m}^{2}}{b\_{p}^{2}} \cdot \mathcal{C}} \cdot \frac{b\_{m}}{b\_{p}} \cdot \frac{\frac{\varepsilon}{2}}{b\_{m}} = \frac{F\_{0}}{\frac{F\_{0}}{\xi\_{0}} + \frac{b\_{m}^{2}}{b\_{p}^{2}} \cdot \mathcal{C}} \cdot \frac{e}{\mathcal{D}b\_{p}}\,. \tag{11}$$

= ிబ ಷబ

మ

∙ ଶ

(10)

(11)

It should be noticed, that a LDV-based measurement of the deflection will not be done at the exact edge of the mirror plate, due to irregular reflections of the light. The measurement of the mirrors deflection in this paper is done in a distance to the mirror edge of approximately 50 µm. Additionally, the analytic equations do not include losses of the elastic energy, or mechanical stress and strain in the torsion springs. measurement of the mirrors deflection in this paper is done in a distance to the mirror edge of approximately 50 µm. Additionally, the analytic equations do not include losses of the elastic energy, or mechanical stress and strain in the torsion springs. In Figure 3 the mirror plate deflection is shown in relation to the lever arm distance to the center. An optimum lever arm length can be identified, depending on the systems

ሺሻ = ிబ ಷబ బ ି ್ మ ್ మ ∙

The deflection at the edge of the mirror plate in relation to the lever arm position

*Micromachines* **2022**, *13*, x 6 of 15

൫൯ = ிబ ಷబ

మ

∙ ∙ మ

is given by Equation (11).

In Figure 3 the mirror plate deflection is shown in relation to the lever arm distance to the center. An optimum lever arm length can be identified, depending on the systems mass and stiffness as well as the blocking force and free deflection of the actuators. The parameter of silicon height, piezoelectric charge coefficient, and resonance frequency are estimated within a 10% limit of variation. For Design 1 with AlN as transducer and a 40 µm lever arm distance the calculated deflection is in the range of 65 nm/V to 116 nm/V. Using Al0.68Sc0.32N and Design 1 increases the deflection up to 143 nm/V to 241 nm/V. Design 2 has a lever arm distance to the center of 80 µm. For this design and Al0.68Sc0.32N a deflection of 563 nm/V to 959 nm/V is calculated. mass and stiffness as well as the blocking force and free deflection of the actuators. The parameter of silicon height, piezoelectric charge coefficient, and resonance frequency are estimated within a 10% limit of variation. For Design 1 with AlN as transducer and a 40 µm lever arm distance the calculated deflection is in the range of 65 nm/V to 116 nm/V. Using Al0.68Sc0.32N and Design 1 increases the deflection up to 143 nm/V to 241 nm/V. Design 2 has a lever arm distance to the center of 80 µm. For this design and Al0.68Sc0.32N a deflection of 563 nm/V to 959 nm/V is calculated.

**Figure 3.** The static mirror plate deflection (mechanical tilt angle) per voltage in relation to the lever arm distance to the center is given for different designs and transducer materials. The parameter substrate height, piezoelectric charge coefficient, and resonance frequency are estimated with a 10% limit of variation. Therefore, an upper and lower limit of the approximated variation to the mechanical tilt angle is given. **Figure 3.** The static mirror plate deflection (mechanical tilt angle) per voltage in relation to the lever arm distance to the center is given for different designs and transducer materials. The parameter substrate height, piezoelectric charge coefficient, and resonance frequency are estimated with a 10% limit of variation. Therefore, an upper and lower limit of the approximated variation to the mechanical tilt angle is given.

#### . **3. Fabrication**

The wafers with AlN and Al0.68Sc0.32N piezoelectric layers are processed with an identical process flow and process parameters, except for the deposition and etching of the piezoelectric material. Figure 4 illustrates the device fabrication process flow. The microsystem fabrication is based on 150 mm SOI technology with 575 µm thick handle wafer and 20 µm device-silicon thickness. First, a 1 µm thermal oxide is grown by oxidation. LPCVD silicon nitride with a layer thickness of 100 nm is used as an isolation layer due to its selectivity against HF wet etching processes. The piezoelectric layer stack starts with a seed layer of 100 nm platinum. For a better adhesion with the substrate, a 20 nm titanium film is used. The Pt is deposited in <111> orientation to minimize the elastic energy to a <0002> Al(Sc)N crystal. A 600 nm AlN or 2000 nm Al0.68Sc0.32N, respectively, and a 100 nm PECVD SiO2 layer are deposited as piezoelectric material. Table 1 summarizes the PVD deposition conditions for the AlN and Al0.68Sc0.32N layer. DC magnetron process with an Al target (double ring magnetron target 120 mm and 123–236 mm, purity 5N5) in 100% nitrogen atmosphere is used for AlN. In the case of Al0.68Sc0.32N, co-sputtering

from 5N5 Al and 4N pure Sc targets in pulsed DC mode in 100% nitrogen atmosphere is used at combined power of 1000 W. AlScN growth optimization, as well as structural and compositional analysis are discussed elsewhere [15,16].

**Figure 4.** Fabrication process flow: (**a**) Initial layer stack; (**b**) AlN wet etching; (**c**) Pt structuring; (**d**) Dry etching of silicon nitride and wet etching of silicon oxide, aluminum deposition; (**e**) backside structuring by DRIE; and (**f**) dry etching of device silicon.

The adhesion of photoresists during the AlN wet etch process is not sufficient. Therefore, a 100 nm SiO2 is the hard mask material for the patterning process. AlN and Al0.68Sc0.32N wet etching is done with 85% phosphoric acid solution (H3PO4) at 80 ◦C (Figure 4b). The etch rate of AlN is 1.4 nm/s. The Al0.68Sc0.32N has a etch rate of 6.7 nm/s. Test wafer with Al0.86Sc0.14N have etch rates of 4.2 nm/s. This indicates a correlation of higher etch rates and higher Scandium ratios in the piezoelectric transducer.

The platinum and titanium are structured via tungsten hard mask by a dry etch process (Figure 4c) which is monitored with an optical emission spectrometer. By analyzing the species in the plasma, an etch stop can be defined as soon as the Ti/Pt is etched and the dry etching of the silicon nitride starts. In Figure 4d, the silicon nitride is patterned by RIE and the silicon oxide is wet etched. This enables an aluminum deposition on a smooth silicon surface. The 800 nm aluminum layer serves as reflective layer on the mirror plate and as upper electrode for excitation of the piezoelectric actuators. After wet etching of the aluminum layer, the handle wafer silicon is structured by DRIE using the buried SiO2 of the initial SOI wafer as etch stop (Figure 4e).

By variation of the exposure parameters in the lithography as well as the DRIE parameters, a side wall shift of the silicon springs can be done to reduce the systems stiffness. This process can be done by using different resists, exposure times, or another DRIE process recipe. For the wafer with AlN this side wall shift is about 0.85 µm at each sidewall. This results in a change of the spring with from a = 5 µm to a0 = 3.3 µm. For the wafer with Al0.68Sc0.32N a side wall shift of 1.35 µm is used. The lower stiffness should result in higher deflection per voltage and further increase the MOEMS performance compared to systems with high resonance frequency.


In this chapter, taking the planar 4-DOF manipulator as an example, numerical calculation is carried out to verify the effectiveness of the proposed control scheme. First, we will check the control performance without joint torque optimization by making *H*T *J* T *F*d in (6.23a) be 0. Secondly, a dynamic simulation example of joint torque optimization is introduced to illustrate the superiority of the control strategy. Finally, the adaptability and optimization performance of this method are verified by simulation experiments under different initial conditions.

#### *6.5.1 Simulation Setup*

As shown in Fig. 6.2, a contact surface in the workspace can be described as *y* = 0, the end-effector can move freely along the horizontal axis, and the desired contact force *F*d is aligned with the vertical direction. The stiffness coefficient *k f* is

#### 6.5 Illustrative Examples 117

set to be 1000N/mm. Control positive control gains are set as α = 10, β = 10, *k* = 8, ε = 0.005, respectively. Physical constraints of joint angles, velocities and torque are defined as θmin = [−2, −2, −2, −2] T rad, θmax = [2, 2, 2, 2] T rad, θ˙min = [−2, −2, −2, −2] T rad/s, θ˙max = [2, 2, 2, 2] T rad/s, τ min = [−10, −10, −10, −10] T Nm, τ max = [10, 10, 10, 10] T Nm, respectively.

#### *6.5.2 Position-Force Control Without Optimization*

In this part, the robot is controlled to offer a constant contact force on the surface while tracking a given trajectory. It is remarkable that joint torque optimization is not investigated yet. The initial joint angles are selected as θ0 = [1.57, −1.26, −0.52, −0.52] T rad. The desired trajectory is defined as *x*d = [0.25 + 0.1*cos*(0.5*t*), 0] T, and the contact force is defined as *F*d = [0, −1] T N. Numerical results are shown in Fig. 6.3. When simulation begins (*t* < 0.5*s*), the position error is big, and there is no contact between the robot and surface. Correspondingly, both contact force and result torque are zero. Under the RNN based controller (6.23), joint velocities reach the maximum value, the end-effector approaches to the surface rapidly from the initial position, and the tracking error converges to zero quickly, the corresponding joint configurations are shown in Fig. 6.3a. As the robot approaches the contact surface, the robot slows down quickly, and the contact force rises from zero, the then converges to the desired value smoothly. In the stable state (*t* > 2 s), both contact force *F* and end-effector track the desired command, the tracking errors are zero, which means the robot tracks

**Fig. 6.3** Numerical results when tracking a time varying force command along a trajectory without optimization. **a** Profiles of the end-effector (black dashed line) and the corresponding joint configurations. **b** Profiles of position error. **c** Profiles of contact force. **d** Profiles of joint angles. **e** Profiles of joint velocities. **f** Profiles of joint torque

both desired trajectory and force successfully. Correspondingly, joint angles change periodically, which enables the robot to achieve dynamic tracking. This will also lead to a periodic change in result torque in joint space, as shown in Fig. 6.3f. During the whole process, boundary of joint angles, velocities and torque are all ensured.

#### *6.5.3 Position-Force Control with Optimization*

In this part, joint torque optimization is introduced to make full use of redundancy resolution. The proposed position-force control scheme is firstly validated in a fixed point case, and then extended to dynamic cases.

#### *(1) Position-Force Control on A Fixed Point*

In this simulation, the robot is wished to offer a constant contact force *F*d = [0, −10] T at a fixed point *x*d = [0.3, 0] T. The initial values of joint angles are also θ0 = [1.57, −1.26, −0.52, −0.52] Trad. Numerical results are shown in Fig. 6.4. At the beginning of simulation, the robot moves at its maximum speed (2 rad/s), making the regulation error converge quickly. Then it slows down as the regulation error is small. At *t* = 0.5 *s*, robot touches the surface, which leads to the emergence of contact force. Using the proposed controller, both control error of motion and force converge to zero smoothly. Correspondingly, the Euclidean norm of joint torque also converges to a constant value (3.7 N2/m2). From Fig. 6.4e, f, joint angles and velocities do not exceed their limits, showing that the proposed scheme could handle inequality constraints effectively. To further demonstrate the validity of the optimization scheme, comparative simulations without optimization are also carried out. The obtained Euclidean norm of joint torque without optimization is shown as the red dashed line (4.3 *N*2/*m*2 in stable state). After introducing joint torque optimization strategy, 16% off of torque consumption is achieved.

#### *(2) Position-Force Control Along A Straight Line*

Then we check the optimization scheme in dynamic control. Both the desired path *x*d and desired force *F*d are time varying. The expected signals are defined as *x*d = [0.25 + 0.1*cos*(0.5*t*), 0] T, *F*d = [0, 20 − 2*cos*(0.5*t*)] T N, respectively. The initial values of joint angles are the same as the previous case. Numerical results are shown in Fig. 6.5. We also define a index to scale the torque consumption as *J*τ = *T* 0 ||τ (*t*)||2 2d*t*.

When simulation begins, high joint speed ensures the fast convergence of tracking error, which is very similar to the previous simulation. After *t* = 2*s*, high precision trajectory tracking is realized by the control strategy, as well as the contact force. Comparative simulation without joint torque optimization is carried out. Figure 6.5d shows the comparison of Euclidean norms of joint torque with and without optimization. Correspondingly, *J*τ decreases 16.2% from 142 to 119, showing the validity of the proposed scheme. It is notable that all physical constraints are guaranteed. Dynamic change of joint configurations is shown in Fig. 6.5a.

#### *(3) Position-Force Control Along An Arc Surface*

In this part, the end-effector is controlled to track a quarter-circular surface, which is centered at [0.3, 0.3] Tm with radius 0.2 m, and is provided a constant force of 10 N in the vertical direction. The initial values of joint angles are selected as θ0 = [1.5708, −0.9851, −1.1714, 0] Trad. Numerical results are shown in Fig. 6.6. The trajectory of end-effector is shown in Fig. 6.6a, while in Fig. 6.6b, optimization is not introduced. The proposed controller enables the robot to achieve precision control of both position and force, and at the same time, by adjusting its joint angles, the

**Fig. 6.4** Numerical results when the robot is controlled to offer constant force at a fixed point. **a** Profiles of the end-effector (black dashed line) and the corresponding joint configurations. **b** Profiles of position error. **c** Profiles of contact force. **d** Comparison of Euclidean norm of joint torque with and without optimization. **e** Profiles of joint angles. **f** Profiles of joint velocities

joint torque consumption is reduced, i.e., *J*τ decreases 17.6% from 88.1 to 72.6. It is remarkable that the physical constraints are also guaranteed.

#### *(4) Adaptability to Different Initial Settings*

To further illustrate the joint optimization scheme, another fixed-point control is presented. Desired signals are set as *x*d = [0.3, 0] T and *F*d = [0, −10] T. The initial

**Fig. 6.5** Numerical results when tracking a time varying force command along a straight line with optimization. **a** Profiles of the end-effector (black curve) and the corresponding joint configurations. **b** Profiles of position error. **c** Profiles of contact force. **d** Comparison of Euclidean norm of joint torque with and without optimization. **e** Profiles of joint anges. **f** Profiles of joint velocities

values of joint angles is selected as θ0 = [1.8850, −1.8850, −1.2566, 0] T rad, consequently, the corresponding position of the end-effector is exactly the same as *x*d. As shown in Fig. 6.7a, the robot adjusts its posture and stops in final state, while keeping its end-effector on the fixed point. This phenomenon is similar to the null-space movement based on pseudo-inverse methods. However, different with pseudo-inverse

**Fig. 6.6** Numerical results when tracking a time varying force command along an arc surface with optimization. **a** Time history of the end-effector (black curve) and the corresponding joint configurations with optimization. **b** Time history of the end-effector (black curve) and the corresponding joint configurations without optimization. **c** Profiles of contact force. **d** Profiles of position error. **e** Comparison of Euclidean norm of joint torque with and without optimization. **f** Profiles of joint angles

based method, the RNN based motion-force controller is capable of handling physical inequalities, at the same time, joint torque optimization is achieved from 4.3 to 3.7. Further more, there in no need to calculate pseudo-inverse of Jacobian matrix, which will save computing cost effectively.

**Fig. 6.7** Numerical results when the initial position of end-effector locates on the desired fixed point. **a** Profiles of joint configurations. **b** Profiles of Euclidean norm of joint torque with and without optimization. **c** Profiles of joint angles. **d** Profiles of joint velocities

Finally, a group of verifications for fixed point position-force control with different initial joint angles are carried out, the desired signals are the same as the previous simulation. As shown in Fig. 6.8, although the initial joint angles are different, at steady state, the robot reaches the same joint angle, which shows the adaptability of the RNN based control strategy.

#### **6.6 Question and Answer**

#### **Q1:** "*What's the complexity of the proposed RNN?*"

**Answer:** The network is organized in a one-layer architecture, which consists of 2*m* + 3*n* neurons, namely ω ∈ R*n*, λ1 ∈ R2*m* and λ2 ∈ R2*n*. Despite the difference between the proposed neural network with traditional recurrent neural networks, from both the mathematical description Eq. (23) and the architecture, one characteristic of the established neural network can be found that the neural network uses its historical information to calculate the output at current moment, which is also a typical feature of recurrent neural networks.

**Fig. 6.8** Time history of robot- s joint configurations in fixed point control from different initial joint angle θ0. **a** θ0 = [0.9, −0.75, −1.5, −1.6] T rad. **b** θ0 = [1.8, −0.3, −1.6, 0.6] T rad. **c** θ0 = [1.9, −1.5, −1.6, −0.6] T rad. **d** θ0 = [0.5, −0.5, −1.6, −0.6] T rad. **e** θ0 = [0.7, −0.3, −2, 0.2] T rad. **f** θ0 = [0.3, −1.5, −1.6, −0.6] T rad

**Q2:** "*As described in Section II, the matrices* Σ*f and* Σ¯ *f are crucial in the controller design, however, the authors didnt show the details. How to obtain those matrices in actual applications requires detailed description.*"

**Answer:** Σ*f* and Σ¯ *f* are used to realize the decoupling of the contact force and tracking error of the end-effector.When the contact surface is known, the combination of Σ*f* , Σ¯ *f* and *St* enables the normalized description of the control tasks.

**Q3:** "Limited stiffness of the manipulator elements can lead to state variables oscillations. Have you observed such work of the object?"

**Answer:** The limited stiffness of the manipulator elements can lead to state variables oscillations. In this chapter, the QP type formulation is obtained based on static modeling method, and inertial force is not taken into account. The condition of the modeling method is that the process is quasi-static. In other words, the relative motion of the end-effector and the workpiece is very slow. In the experiment tests, we also found that some oscillation would occur if some parameters are appropriately tuned. In this case, a damping coefficient can be introduced to handle the oscillations.

**Q4:** "*In real manipulator significant issue is related to control of electric drives. In mentioned structures, internal control loop, related to torque control, introduces some delays for external speed controllers. Have you considered such problem?*"

**Answer:** In this chapter, we mainly focus on projection RNN based controller design in kinematic level, and the control command is selected as joint velocity signals. Therefore, we assume that the robot controller can provide an ideal response to the joint velocity command. Although the delay is unavoidable for real systems, when the control frequency is set as 100 Hz, experimental results could show the effectiveness of the proposed controller. From Eq. (23), it can be observed that the force control is realized by adjusting the joint velocities base on the RNN, which is consistent with the idea of admittance control. In our experiment, the velocity control in the inner loop is done by the robot controller, and we assume that it provide an ideal response to the joint velocity command. It is remarkable that the uncertainties in the dynamic level such as friction and disturbances do affect the performance of position-force control in the outer loop, but these uncertainties can be suppressed by the closed-loop control mechanism of the controller itself.

**Q5:** "*Could you explain real impact of projection operator PR on work of the control system?*"

**Answer:** The projection operator *P*Ω plays an important role in guaranteeing the bounded-ness of the output of neural network i.e., the boundedness of ω can be ensured introducing *P*Ω . As described in Eq. (17), based on escape velocity method, both the boundedness of joint angles and velocities are guaranteed.

**Q6:** "*RNN uses delays during data processing, so the calculation step size seems to be important for overall work. Have you considered such issue?*"

**Answer:** We did consider this problem. The faster the RNN calculates, the better performance can be achieved. But at the same time, it would also lead to a increase of computational burden, which may make the system unstable. In our experiment, the control period is set to be 10 ms.

#### **6.7 Summary**

This chapter focuses on motion-force control problem for redundant manipulators, while physical constraints and torque optimization are taken into consideration. Firstly, tracking error and contact force are modeled in orthogonal spaces respectively, and then the control problem is turned into a QP problem, which is further rewritten in velocity level by rewriting objective function and constraints. To handle multiple physical constraints, an RNN based scheme is designed to solve the redundancy resolution online. Numerical experiment results show the validity of the proposed control scheme. Before ending this chapter, it is noteworthy that this is the first chapter to deal with motion-force control of redundant manipulators in the framework of RNNs and redundant manipulators with force sensitivity, e.g., grinding robots, can be readily controlled with the proposed RNN model but cannot with existing RNN models in this field.

#### **References**

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.


*3.6.1 The classification of diabetic retinopathy (DR) and DME*

The classification of diabetic retinopathy (DR) and DME have evolved over the years. About five decades ago, experts in ophthalmology gathered in Airlie House for a symposium to review the state of knowledge of DR; an outcome from that meeting was developing a standardized classification of DR [68–70]. Afterward, this classification was modified for use by the Diabetic Retinopathy Study (DRS) [69, 70]. The modified Airlie House classification of diabetic retinopathy used in the DRS was further developed for the Early Treatment Diabetic Retinopathy Study (ETDRS). This randomized, prospective study evaluated the efficacy of laser treatment for macular edema [68]. It became the gold standard for many years. The ETDRS introduced the term clinically significant macular edema (CSME). CSME was defined using slit-lamp biomicroscopy, when it met any of the three criteria viz. "(1) thickening of the retina at or within 500 μm of the center of the macula; or (2) hard exudate at or within 500 μm of the center of the macula associated with thickening of the adjacent retina; or (3) a zone of retinal thickening one disc area or larger, any part of which is within one disc diameter of the center of the macula" [71]. After that, fluorescein angiography was used to guide laser treatment [72]. The ETDRS found that macular laser photocoagulation effectively reduced moderate visual loss by at least 50% in laser-treated eyes with CSME compared to untreated eyes [68, 70]. In 2003, an international classification called the Diabetic macular edema disease Severity Scale with greater simplicity was proposed [29, 73]. The DME disease severity scale put forward that DME is 'apparently present' when some apparent retinal thickening or hard exudates exist in the posterior pole; DME is proposed to be 'absent' otherwise [29, 70]. When DME is present, it is classified

into mild, moderate, or severe if the retinal thickening or hard exudate is distant from the center of the macula, approaching the center of the macula but not involving the center and involving the center of the macula, respectively [29, 70]. Ten years after ETDRS, Optical Coherence Tomography (OCT) became the new imaging modality that enabled ophthalmologists to utilize the qualitative and quantitative measurement of central subfield macular thickness (CSMT) and visual acuity to diagnose and determine the response of DME to treatment [29, 72]. OCT is invaluable due to its reliability and reproducibility; its importance in evaluating and monitoring DME cannot be over-emphasized [41, 74].

A classification based only on slit-lamp biomicroscopic evidence of retinal thickening is grossly insufficient to precisely describe DME and determine the appropriate therapeutic modalities for the various morphologies [72, 75].

#### *3.6.2 DME classification based on OCT*

DME classification based on OCT is described using various morphology (1) diffuse edema type (sponge-like diffuse retinal thickening), (2) cystoid macular edema (CME) type (thickening of the fovea with intraretinal cystoid change), (3) serous retinal detachment (SRD) type (thickening of the fovea with subretinal fluid) and (4) vitreomacular interface abnormalities as seen in incomplete or complete posterior vitreous detachment and epiretinal membrane (ERM) formation or vitreomacular traction or both [74–76].

Other parameters deployed by the OCT in DME diagnosis include retinal thickness, volume (quantitative data), and inner and outer layers of the retina [72, 74].

#### **3.7 Clinical presentation (symptoms and signs)**

Patients with DME may be asymptomatic if the macula center is not involved. However, some eyes having center involving DME (CI-DME) have been seen to have no visual disturbance, presumably because of the recent involvement of the center [32]. Depending on the degree of fovea involvement and the chronicity of the edema, patients may present with an array of visual symptoms [32]. These include gradual progressive diminution and distortion of central vision over some time (usually moderate, unlike the severe loss after vitreous hemorrhage or retinal detachment involving the macula in proliferative diabetic retinopathy), metamorphopsia, and loss of color vision. They may also experience poor night vision and 'washing-out of vision in bright sunlight with poor dark–light adaptation [32, 77, 78].

On dilated biomicroscopic examination, retinal thickening may be observed in commonly identified patterns. Focal edema often occurs in association with a cluster of microaneurysms, sometimes surrounded by an incomplete ring of hard exudates. Diffuse DME may be very difficult to identify clinically if the retina is uniformly thickened due to the lack of reference landmarks. Clues include the height of the retinal blood vessels over the pigment epithelium, cystoids spaces, or even loss of the foveal depression. Other features that are sometimes seen with macular edema include variable loss of retinal transparency, a significant number of microaneurysms, intraretinal hemorrhages, and dispersed areas of hard exudates [32].

#### **3.8 Evaluation of DME**

#### *3.8.1 The control of systemic metabolic abnormalities*

The control of systemic metabolic abnormalities observed in diabetes mellitus has a significant effect on the development and progression of

*Current Management of Diabetic Macular Edema DOI: http://dx.doi.org/10.5772/intechopen.100157*

diabetic microvascular complications, including DME [79]. The United Kingdom Prospective Diabetes Study (UKPDS) and the Diabetes Control and Complications Trial (DCCT) did demonstrate that optimal metabolic control could reduce the incidence and progression of DR [50, 80]. To achieve good management of a patient with DME, a multidisciplinary approach involving different medical subspecialists such as ophthalmology, endocrinology, nephrology, neurology, cardiology, orthopedics is key [29]. Systemic workup involving blood investigations helps monitor the systemic status of these patients. These investigations including fasting blood glucose (FBG), glycosylated hemoglobin levels (HbA1C), serum electrolyte, urea, creatinine, and fasting lipid profile. Other investigations that may be required would be based on systemic complaints, examination findings, and other suspected comorbidities [29]. The recommended values for HbA1c, blood pressure, and LDL cholesterol are < 6.5–7%, <130/<85 mmHg, and < 100 mg/dl, respectively [81]. However, many patients fail to achieve or maintain these levels of metabolic control. In patients who significantly reduce HbA1c, there is an associated increased risk of severe hypoglycemia [33, 50, 80]. Managing physicians must recognize correctable risk factors of DR and DME, such as hyperglycemia, hypertension, and/or hyperlipidemia, to ensure appropriate monitoring and referral for eye care.

## *3.8.2 Ophthalmic evaluation*

I. Over the last two decades, a wide range of imaging modalities, including fundus photography, fluorescein angiography (FA), optical coherence tomography (OCT), and OCT-Angiography (OCT-A), have been utilized not only for the diagnosis and classification of disease but also to monitor disease progression and treatment [82]. **Figures 1**–**5** illustrate the significance of these imaging technologies in DR and DME. DME is diagnosed clinically with the slit-lamp biomicroscopy or indirect ophthalmoscopy with features such as visible microaneurysms, hard exudates, cysts, and retinal thickening. However, stereoscopic fundus photography and fluorescein angiography have greater sensitivity in detecting DME than ophthalmoscopy because of superior optics of the former, the enhanced contrast of fluorescein angiography, ability to make confirmation of vascular leakage, and the ability of the observer to evaluate magnified images without the interference of patients moving or blinking [83].

#### **Figure 1.**

*OCT image of both eyes of a patient who suffers from DME in the left eye. The right eye shows typical retinal microstructure, while the left eye shows thickening in the foveomacula area from intraretinal cystic spaces due to diabetic macular edema. Notice that the posterior vitreous membrane is "partly" attached to the retina in both eyes.*

#### **Figure 2.**

*(a) Right eye fundus photograph, with the star shaped appearance of hard exudation, the nasal portion of which involves the fovea. There are dot hemorrhages and microaneurysms involving the temporal macula and superiorly within the superotemporal arcade. Notice the arteriovenous nipping (broken yellow arrows) suggestive of co-existing hypertensive retinopathy. There are opacities within the vitreous. (b) Left eye fundus photograph, a ring of fibrovascular tissue extends from the retina into the pre retinal space and vitreous cavity. Hard exudates, hemorrhages, and microaneurysms are present within the temporal macula beneath the fibrovascular tissue. Contraction of fibrovascular proliferative tissue creates a tractional effect on the inferotemporal arcade (broken yellow arrows).*

#### **Figure 3.**

*OCT images of both eyes as in Figure 2a and b. There is intraretinal cluster of hard exudates and intraretinal cystoid spaces, worse in the right eye (correlating with the fundus photographs). Epiretinal membrane is present in both eyes (broken yellow arrows).*

Stereoscopic fundus photographs provide an opportunity to evaluate and document long-term changes in the retina [32, 82]. The ETDRS study used the 7 standard fields (7SF) 30° photographs of the retina (three horizontally across the macula and four around the optic nerve). This combination gave nearly 75° of visualization [29]. Mydriatic or nonmydriatic fundus imaging with ≥300 mono- or stereo photography is used with or without OCT [84]. Ultra-wide-field imaging is currently used for the screening and detection of DR, as is ultra-wide-field angiography [83].

Fundus fluorescein angiography (FFA) visualizes the retinal vasculature. It identifies lesions of diabetic retinopathy, patchy areas of hypo fluorescence representing ischemia as demonstrated by capillary dropout, areas of impaired BRB function, and microaneurysms manifest as areas of hyper fluorescence demonstrated by leakage of dye and visualize expansion of the foveal avascular zone (FAZ) [59, 82].

#### **Figure 4.**

*Left eye fundus photograph showing extensive fibrovascular tissue proliferation across the macula and optic disc. There is a faint view of retinal hemorrhages in the temporal macula.*

#### **Figure 5.**

*The OCT image of the left eye fundus photograph in Figure 4. Tangential (yellow star) and vertical (yellow dotted arrow) tractional elements in the preretinal space extend into the vitreous. This thick taut hyaloid creates foveomacular traction-induced macular edema (evident as the large cystoid spaces within the macula).*

Previously FFA helped predict prognosis and response to treatment in DME [59]. A case of diffuse DME was defined by fluorescein leakage involving most of the macula. This form of DME is more challenging to treat than focal DME involving

leakage from identified lesions [85]. FFA also revealed the degree of capillary non-perfusion and macular ischemia, shown by an enlarged foveal avascular zone [59]. With the development of ultra-widefield imaging, FFA can now be performed with visualization of up to 200° of the retina. Extensive ischemia in the retinal periphery has been associated with recalcitrant disease, and the ultra-widefield FFA may help identify DME that is likely to be treatment-resistant [59]. It reveals areas of peripheral ischemia and non-perfusion, which can be promptly treated with pan-retinal laser photocoagulation. The significant advantage of FFA is that it was the only imaging modality commonly used in DR that provides information on vascular flow and vessel permeability over time by visualizing leakage and pooling [82]. The disadvantage of FFA is that it is an invasive procedure that involves the administration of intravenous dye. It should be performed carefully, especially in patients with severe DR and associated systemic vascular complications such as severe renal disease and clinical or subclinical cardiovascular disease [29, 82, 86, 87]. The most common adverse reactions are nausea and vomiting, but more severe side effects include localized reactions, urticaria, seizures, and, very rarely, anaphylaxis [29, 82]. Before performing FFA, the ophthalmologist must carefully consider whether the information provided is necessary to make therapeutic decisions and whether the same or equivalent information can be provided by OCT which is noninvasive [83].

II. Since its first introduction, OCT has become the most frequently used diagnostic tool in ophthalmology for the past two decades and has revolutionized clinical imaging for diagnosis and disease management in most retinal diseases, including DME [78, 82]. The diagnostic utility of the OCT can be seen in the case illustrated by **Figures 6** and **7**. The fast, non-invasive, high-resolution imaging available with OCT of the posterior segment allows for close study of the retinal anatomy and assessing retinal thickness profile and morphology in DME [82, 83]. A significant advantage of OCT is that it can be easily repeated several times, within the same day, with a high degree of reproducibility. Therefore, it can be used to monitor the effect of therapy, e.g., intravitreal anti-VEGF given the same day or shortly after, to detect or objectively quantify response to therapy [82, 83]. This value of the OCT to monitor treatment is illustrated with **Figures 8** and **9**.

#### **Figure 6.**

*(a and b) The left eye fundus photograph shows dot hemorrhages, microaneurysms, and few hard exudates, over the macula (a) and extending to the temporal retina (b). This is a clinical diagnosis of non-proliferative diabetic retinopathy and DME.*

#### **Figure 7.**

*OCT of fundus image in Figure 6 showing intraretinal cystoid spaces and a few hard exudates clustering around the cystoid (broken yellow arrows). Hyper reflective digitations are extending into the outer nuclear layer (broken red line).*

#### **Figure 8.**

*This is the OCT image of the same eye as in Figure 7 after intravitreal injection of Bevacizumab. Notice the reduction in intraretinal cystoid space size. The foveomacular retina is no longer thickened, as in Figure 7.*

There are three types of OCT: time-domain (TD), spectral-domain (SD), and swept-source (SS) [82]. Spectral-domain OCT is the most commonly used, allowing three-dimensional raster scans of up to a few hundred B-scans, also creating highresolution images. It supersedes time-domain (TD)-OCT, the first generation that allowed imaging of 6 radial cuts only [78, 83]. The most recent third-generation OCT technology uses a swept-source (SS) light source that allows high-speed imaging and provides three-dimensional raster images of high microstructural resolution, also referred to as optical histology [78]. OCT is highly sensitive and more accurate in

**Figure 9.**

*This serial OCT shows longitudinal follow-up of a case of recurrent macular edema, which resolves after initial treatment with intravitreal Ranibizumab. However, recurrence of edema (broken yellow arrow) occurs after an attempt at extending the injection interval from monthly to two monthly, then three monthly (treat and extend protocol). The resolution of edema (broken red arrow) occurs again after repeating intravitreal injection of Ranibizumab. The macula remains dry at subsequent visits.*

diagnosing DME when compared to fundus stereo photography and biomicroscopy [78], see **Figures 1, 3** and **5**. It is currently the gold standard for the diagnosis and monitoring of DME.

It is used to determine whether DME is center-sparing or center -involving, an essential criterion in determining treatment [78]. A limitation noted is that image segmentation could be a problem in eyes with marked DME and dome-shaped macula [88].

OCT not only identifies the presence or absence of disease activity such as the intra-retinal fluid (IRF) and the sub-retinal fluid (SRF) as seen in DME, it localizes them in the retina. It allows for quantification to assess the disease's response to anti-VEGF therapy [89], as demonstrated in **Figure 9**. It has been demonstrated that OCT using microstructural changes seen in IRF and SRF at baseline can prognosticate response to intravitreal treatments [90].

III. Certain features of retinal morphology seen on the SD-OCT, such as central subfoveal thickness (CST), vitreoretinal interface abnormalities, and the epiretinal membrane (ERM), can be used as surrogate markers and act as predictive factors for visual acuity (VA) outcomes in the treatment of DME [91–93]. CST was initially used as a predictor of visual outcome after treatment due to the ease of identifying and obtaining this parameter, but this had limitations [92]. Consequently, other aspects of OCT have been investigated to determine their usefulness as possible biomarkers and correlations for VA and treatment outcomes. These include an external limiting membrane (ELM) and ellipsoid zone (EZ) disruption, and disorganization of retinal inner layers (DRIL) [91, 92]. Sun et al. described an OCT feature termed disorganization of the inner retinal layers (DRIL) [94]. It was observed that an improvement in DRIL following treatment for DME was predictive of better VA outcomes. There was an association with VA after the resolution of centre-involving DME [95, 96]. An association between DRIL, the disruption of the outer retina, and increasing DR severity have been observed [91].

IV. The role of OCT-A is evolving as a tool in the evaluation of DME. OCT-A is an imaging technique that uses motion contrast and faster scan speeds, including spectral-domain (SD) and swept-source (SS), to obtain three-dimensional cubes, which then undergo automated segmentation into layers [82], as seen in **Figure 10**. In DME, as with FFA, OCTA can visualize the increase in the size of the fovea avascular zone (FAZ) and perifoveal intercapillary area [97], seen in **Figure 11**. It can also *Current Management of Diabetic Macular Edema DOI: http://dx.doi.org/10.5772/intechopen.100157*

#### **Figure 10.**

*A normal OCT-Angiography (OCT-A) scan of the right eye, showing the four segmented layers, including superficial and deep plexi, outer retina and the choriocapillaris layers. Also shown are the cross sectional OCT scans, highlighting the borders and planes of tissue segmentation.*

#### **Figure 11.**

*OCT-A, showing a well perfused macular and what looks like shunt vessels within the foveal avascular zone. The en face OCT images show radiating hard exudates centered on the fovea. The cross sectional OCT shows large intra retinal cystic space in the fovea, and there is aggregation of hard exudates observed within the retina (outer nuclear layer) microstructure.*

study the retinal vascular plexuses in layers, determine microvascular parameters, and correlate them with functional and morphological data [98].

The advantages of OCT-A are: It provides "3-D" imaging information of the macula and visualizes peripapillary capillaries [99]. It is dye-free, thereby suitable for patients with adverse reactions to the dyes and poor intravenous access or renal failure [100]. It is reproducible with a faster acquisition time [99, 101]. An advantage of OCT-A over conventional FA is that the absence of dye leakage using OCT-A enables visualization of the distinct margins and sizes of neovascularization since there is no leaking of dye to obscure the neovascularization complex's margins seen in the later frames of the FFA [33]. The disadvantages of OCT-A include its inability to visualize leakage of dye in the retina, a common feature of inflammatory vascular pathology, and a sign of blood-retinal barrier breakdown [100]. Limitation to detecting peripheral retinal ischemia as it can scan mostly the posterior pole [100]. Studies suggest that in the future management of DME, OCT-A could be used to prognosticate the evolution of visual acuity with the help of biomarkers such as low vascular density (VD) and enlargement of the foveal avascular zone (FAZ) [102– 104]. OCT-A could also be used to aid in the monitoring of the response of DME to anti-VEGF treatment such as Ranibizumab since poor responders show significant damage to the DCP, but not SCP [105, 106].

Initially, the major limitation of OCTA was the small field of view, with the greatest resolution achieved at smaller scanning sizes such as the commonly used 3 × 3 mm scan [33, 82]. Wider field OCTA scans are already available such as the 9 × 9 mm and 12 × 12 mm. Experimental wide-field OCTA using faster scanning OCTA is being researched and could be available in the future [102, 103, 107].

Other drawbacks noted are that OCTA is subject to projection artifacts. Vasculature from outer layers is projected onto the deep plexuses and choriocapillaris, affecting the accurate interpretation of vascular pathology in the deeper layers. It is also prone to movement artifact; patient movement presents as horizontal white lines, and artifact blinking appears as black lines across the image [83]. Solutions to artifacts include the incorporation of software to correct the motion artifacts [108].

Visual acuity is still viewed as the gold standard in clinical settings for assessing vision using the Snellen or ETDRS charts, but it does not entirely reflect functional vision [109, 110]. Functional vision depicts the impact of sight on the quality of life as expressed by the patient [109]. Various visual function disturbances such as waviness, relative scotoma, and reduction in contrast sensitivity are known to precede loss of visual acuity in patients with DME. However, they are not assessed and quantified during a routine eye examination. For assessing these abnormalities, microperimetry is used to identify vision-threatening retinopathy before visual acuity is affected. Microperimetry is a diagnostic tool used to assess retinal sensitivity while the fundus is directly examined; it enables exact topographic correlation between macular pathology and corresponding functional abnormality [109, 110]. It is rapid, safe, and non-invasive [110]. Microperimetry is of value in prognosticating the functional outcome as foveal thickness returns to normal following the treatment of DME [109]. Microperimetry has been used to demonstrate low retinal sensitivity present in the areas of capillary drop out in eyes with ischemic DME [111].

Multifocal electroretinogram is an electrophysiologic test. It is used to objectively identify functional changes of the retina in the early phases of DR and DME [112] and is also helpful for objectively monitoring eyes on intravitreal antiVEGF treatment such as Ranibizumab for DME [113].


**8. Summary**

Therapy for HCV has seemed to exponentially grow over the past 4 years. Because of DAAs, IFN-free as well as all-oral regimens are being used to treat HCV. In addition to this, ribavirinfree regimens are also available. Thus far, these highly effective therapies have proven to provide fewer side effects and achieve better results, all the while in less time. Hope for cure and eradication remains paramount and is now achievable. With appropriate allocation of resources, physician training, and available treatment, the cure of HCV is possible. Doing so will drastically decrease overall health care costs, improve quality of life, and decrease the number of liver transplants needed.