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Anesth Analg 2008; 106:313-320
© 2008 International Anesthesia Research Society
doi: 10.1213/01.ane.0000296460.91012.51
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ANALGESIA

Section Editor:
Tony L. Yaksh

The Prolonged Analgesic Effect of Epidural Ropivacaine in a Rat Model of Neuropathic Pain

Chiyo Sato, MD*, Atsushi Sakai, MT, MHS{dagger}, Yumiko Ikeda, MT, MHS{dagger}, Hidenori Suzuki, MD, PhD{dagger}, and Atsuhiro Sakamoto, MD, PhD*

From the Departments of *Anesthesiology and {dagger}Pharmacology, Nippon Medical School, Bunkyo-ku, Tokyo, Japan.

Address correspondence and reprint requests to Hidenori Suzuki, MD, PhD, Department of Pharmacology, Nippon Medical School, 1-1-5, Sendagi, Bunkyo-ku, Tokyo, 113-8602, Japan. Address e-mail to hsuzuki{at}nms.ac.jp.

Abstract

BACKGROUND: In clinical practice, the analgesic effects of epidurally administered local anesthetics on chronic pain sometimes outlast the duration of drug action expected from their pharmacokinetics. To investigate the underlying mechanisms of this prolonged effect, we examined the effects of ropivacaine, a local anesthetic, on pain-related behavior in a rat model of neuropathic pain. We also analyzed changes in the expression of nerve growth factor (NGF), which is involved in plasticity of the nociceptive circuit after nerve injury.

METHODS: In a rat model of neuropathic pain produced by chronic constrictive injury (CCI) of the sciatic nerve, thermal hyperalgesia, and mechanical allodynia were observed from Day 3 after surgery. Ropivacaine or saline was administered through an epidural catheter once a day, every day, and from Days 7–13 after the CCI operation. NGF content was measured in the L4 dorsal root ganglion, the hindpaw skin, the L4/5 dorsal spinal cord, and the sciatic nerve, using enzyme immunoassay.

RESULTS: The latency to withdrawal from thermal stimuli on the ipsilateral paw pads of CCI rats was significantly increased 4 days after the beginning of ropivacaine treatment, and thermal hyperalgesia was almost fully relieved. Similarly, mechanical allodynia was partially reduced after ropivacaine treatment. NGF content was increased in the L4 dorsal root ganglion on the ipsilateral, but not the contralateral, side, in CCI rats treated with ropivacaine.

CONCLUSION: Repetitive administration of ropivacaine into the epidural space in CCI rats exerts an analgesic effect, possibly by inducing a plastic change in the nociceptive circuit.

Neuropathic pain is a persistent and intractable pain syndrome caused by trauma or disease affecting the nervous system, such as postherpetic neuropathy or diabetic neuropathy.1 It is characterized by spontaneous pain, increased responsiveness to noxious stimuli (hyperalgesia) and nociception induced by normally nonnoxious stimuli (allodynia). As neuropathic pain is often unresponsive to conventional analgesics, such as opiates and nonsteroidal antiinflammatory drugs, choice of treatment has been largely limited.

Local anesthetics block the activity of voltage-gated sodium channels, thereby reversibly inhibiting the conduction of nerve impulses along axons, and the excitation of neurons. In general, autonomic fibers, small unmyelinated C fibers, and small myelinated A{delta} fibers are more susceptible to local anesthetics than the larger myelinated A{gamma}, Aβ, and A{alpha} fibers.2 Based on these mechanisms of action, local anesthetics can be used to reduce acute nociception or sympathetic vasoconstriction for a short time in clinical practice. Furthermore, epidural administration of a single dose or repetitive doses of local anesthetics has also sometimes alleviated chronic pain in humans3–6 and experimental animals.7 The amelioration of pain by these drugs sometimes outlasts even the duration of Na+ channel blockade speculated to be from their pharmacological properties. Although the underlying mechanisms of this persistent analgesic effect are largely unknown, several hypotheses have been proposed: interrupting nociceptor activity with local anesthetics for a period might lead to a reversal of the sensitization of spinal cord neurons8; local anesthetics might induce plastic changes in primary sensory and dorsal horn neurons9; and sympathetic activation might be interrupted by local anesthetics.10 Identifying the mechanisms of action of local anesthetics to relieve chronic pain might lead to the development of a new strategy to treat neuropathic pain.

Neurotrophic factors regulate the survival, growth, or differentiation of a discrete population of neurons, and are involved in neural plasticity. Nerve growth factor (NGF), a neurotrophin, transmits its signals intracellularly via a specific member of the trk family of receptor tyrosine kinases, trkA.11 In adult rodents, trkA is expressed in approximately half of nociceptive primary afferent neurons with small diameter, unmyelinated fibers.12 NGF is not only critical for the survival of a population of sensory neurons during development, but it also plays a role in maintaining the phenotypes of adult dorsal root ganglion (DRG) neurons expressing trkA.12 Therefore, NGF is critically involved in hyperalgesia13 and the survival of DRG neurons.12

In the present study, we examined the effects of repetitive epidural administration of a local anesthetic, ropivacaine, on persistent pain in a rat model of neuropathic pain that is suitable for studying the mechanisms of drug action in detail. We also examined whether ropivacaine affects the expression of NGF, which is involved in plasticity of the nociceptive circuit after the nerve injury.

METHODS

Experimental Animals
Experimental procedures were approved by the institutional committee on laboratory animals (approved number 18-017) and were performed under the guidelines of the International Association for the Study of Pain.14 Rats were housed in clear plastic cages with sawdust bedding at standard room temperature, under a 12-h light–dark cycle. All rats received food and water ad libitum.

Production of a Neuropathic Pain Model
Male Sprague-Dawley rats (7–8 weeks of age and 250–300 g weight) were used for all experiments. All surgical procedures were performed on rats that were deeply anesthetized with sodium pentobarbital (50 mg/kg intraperitoneally). The left (ipsilateral) common sciatic nerve was exposed in the left mid-thigh and loosely ligated using 4-0 silk thread in four regions, at about 1-mm intervals, to cause chronic constrictive injury (CCI).15 The right (contralateral) sciatic nerve was left intact as a control. In sham-operated rats, the left sciatic nerve was exposed but not ligated.

Epidural Catheterization
For epidural administration of drugs, a polyethylene catheter (PE-10, Natsume, Japan) was implanted epidurally after the method described by Durant and Yaksh.16 Briefly, the catheter was gently introduced from the base of the L5 spinous process into the lumbar epidural space, to a length of 2 cm, so that its tip was located at the L3–4 level. The catheter was then flushed with 100 µL of saline containing 10 U/mL heparin to ensure no leakage into the surrounding tissue. The catheter was tied with a loose knot at the level between L5 and L6 vertebrae, and was secured to superficial lumbar muscles using 4-0 silk thread. The catheter was then tunneled subcutaneously to the surface of the neck skin and was fixed to its fascia using 4-0 silk thread. Catheter-implanted rats without obvious movement disturbances, such as paralysis, were used in the following experiments. Throughout the observation period, no rats suffered from late-occurring motor disturbance. After completion of the experimental series, we confirmed that the tip of the catheter was located at around the L3 level in the epidural space. Furthermore, we confirmed in preliminary experiments, using injection of a dye through the indwelling catheter, that the dye was delivered to the epidural, but not the subdural, space around the L3–4 level in rats showing transient motor paralysis after ropivacaine administration.

Epidural Administration of Drugs
One-hundred microliters of a drug, 0.2% ropivacaine (AstraZeneca, Japan) or saline, was slowly injected for 30 s through the epidural catheter, followed by 20 µL of saline. The drugs were administered once a day, every day, from Day 7 to 13 after the operation for CCI rats and on the corresponding days for sham-operated rats.

Behavioral Tests
Two behavioral tests (thermal and mechanical stimulation tests) were used to assess pain threshold on the day before surgery and on Days 3, 5, 7, 9, 11, and 13 after the surgery. The behavioral evaluation was done before drug administration between Days 7 and 13. The Plantar Test (Ugo Basile, Italy) was used to examine thermal hyperalgesia. Each rat was placed on a glass plate with radiant heat equipment (a 50 W halogen reflector bulb) underneath. After the acclimation period, radiation heat was applied to either the contralateral or ipsilateral hindpaw pad independently. The latency of paw withdrawal from thermal stimuli was measured three times at 5-min intervals, and its average value was used as the latency of the response. Mechanical allodynia was measured using a set of von Frey filaments (Muromachi Kikai, Japan) with bending forces ranging from 2.0 to 44.0 g. Each rat was placed on a metallic mesh floor, covered with a plastic box, and a von Frey filament was applied from under the mesh floor to the plantar surface of either the contralateral or ipsilateral hindpaw. Each paw was stimulated with each filament five times at 10-s intervals in the individual trial. The weakest force (g) inducing withdrawal of the stimulated paw at least three times in each trial was referred to as the paw withdrawal threshold.

Two-Site Enzyme Immunoassay for NGF
To perform a two-site enzyme immunoassay (EIA) for NGF, the L4 DRG, the hindpaw skin and the sciatic nerves, from both sides, and the L4/5 dorsal spinal cord, were dissected out at postoperative Day 14. The ipsilateral sciatic nerve was cut into three segments: injured, adjacent proximal and distal. The contralateral side was also cut into three pieces, at similar positions to the ipsilateral side. Proximal and distal segments of at about 5 mm in length were used for EIA. The skin from the hindpaws was dissected out, to a size of 1 cm2. The L4/5 dorsal spinal cord was further divided into contralateral and ipsilateral parts. The tissues were immediately frozen in liquid nitrogen and stored at –80°C. Each tissue was homogenized using a Polytron homogenizer in 500 µL of homogenizing buffer (50 mM Tris, 0.5 M NaCl, 0.3% Triton X-100, pH 7.5) containing protease inhibitors (Complete Mini, Roche Diagnostics, Germany). In the preparation of homogenates from skin, the tissues were ground into powder in liquid nitrogen, before homogenization, using a Cryopress (Microtech, Japan). The homogenate was centrifuged at 12,000 rpm for 30 min at 4°C, and the supernatant was used for the measurement of NGF.17 EIA titer plates (FluoroNunc Module plate, Nunc A/S, Denmark) were coated with a primary polyclonal antibody against NGF (20 ng/well, Promega) overnight and then blocked with EIA buffer (50 mM Tris, 0.5 M NaCl, 0.3% Triton X-100, 0.4% bovine albumin and 0.4% gelatin, pH 7.5) at 4°C for more than 3 h. One hundred microliters of each tissue extract or 1–1000 pg of NGF-β standard (recombinant human NGF-β, Roche Diagnostics) in EIA buffer was placed into each well and the plates were incubated for 7 h at room temperature. After three washes with Wash-buffer (EIA buffer without bovine serum albumin), 100 µL of anti-NGF monoclonal antibody conjugated to β-galactosidase (5 µg/mL, Boehringer Mannheim, Germany) in EIA buffer was added to each well and the plates were incubated for 12–18 h at room temperature. After subsequent incubation with 200 µM 4-methylumbelliferyl β-d-galactoside (Sigma, MO) in 50 mM sodium phosphate buffer (pH 7.3) containing 10 mM MgCl2 for either 45 h (for DRG) or 20 h (for skin, spinal cord, and sciatic nerve) in the dark at room temperature, β-galactosidase activity was measured in terms of the fluorescent products using a Spectraflour Plus microplate reader (Tecan, Salzburg, Austria) with excitation at 360 nm and emission at 465 nm.

Statistical Analysis
Values are expressed as means ± sem. An unpaired t-test was used to compare the latency or threshold values in behavioral tests between sham-operated rats and CCI rats on corresponding days, and to compare the latency or threshold value in ropivacaine-treated CCI rats with those in saline-treated CCI rats on the corresponding day. Dunnett’s test for multiple comparisons was used to compare latency or threshold values obtained in behavioral tests performed before the operations with those obtained in tests performed after the operations. Tukey-Kramer’s multiple comparison was used to compare the NGF content in each tissue in rats treated with ropivacaine or saline. P < 0.05 was considered to be statistically significant.

RESULTS

Behavioral Studies
In sham-operated rats, the latencies of withdrawal from heat stimulation were 12.8 ± 0.6 and 12.5 ± 0.5 s on the ipsilateral and contralateral sides of the paw, respectively, before surgery (n = 7; Fig. 1A). Paw withdrawal thresholds in response to mechanical stimulation were 24.2 ± 1.8 and 24.2 ± 1.8 g on the ipsilateral and contralateral sides of the paw, respectively, before the operation (n = 7; Fig. 1B). These values were almost unchanged during the period examined (Fig. 1). In CCI rats, on the other hand, the threshold of paw withdrawal to mechanical or thermal stimulation was significantly decreased at Day 3 on the ipsilateral, but not the contralateral, side (P < 0.001 compared with sham-operated rats; n = 7; Fig. 1). This increased sensitivity to both stimuli persisted at least until Day 13 after the operation (Fig. 1).


Figure 155
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  		Figure 1. Effect of the chronic constrictive injury (CCI) procedure on pain-related behaviors. Thresholds for foot withdrawal on the contralateral (left panels) and ipsilateral (right panels) sides in response to thermal (A) or mechanical (B) stimuli applied to the corresponding hindpaw pad in CCI rats (open circle) and sham-operated rats (filled circle). *P < 0.05 and ***P < 0.001 compared with the values in the rats treated with a sham procedure on the corresponding days, by an unpaired t-test; #P < 0.05, ##P < 0.01, and ###P < 0.001 compared with the values at the preoperative day by Dunnett’s multiple comparisons. n = 7.

 

Prolonged Analgesic Effect of Repetitive Epidural Administration of Ropivacaine on Neuropathic Pain
We next examined the effect of repetitive epidural administration of ropivacaine on the thermal hyperalgesia and mechanical allodynia in CCI rats. Epidural administration of ropivacaine or saline commenced at 7 days after the CCI operation, when hyperalgesia had become established, and it was continued once a day for 7 days. Motor paralysis was observed immediately after the epidural injection of ropivacaine, but this paralysis was limited to the hindlimbs in all rats examined, as described by Durant and Yaksh,16 and disappeared within about 30 min. Such behavioral changes confirmed that the drug had been delivered to the appropriate site, at around the L3 level in the epidural space. The tests for thermal hyperalgesia and mechanical allodynia were conducted before drug injection. The latency to withdrawal from the thermal stimulus on the ipsilateral side of CCI rats was significantly increased at 4 days after the beginning of ropivacaine treatment (P < 0.05 compared with CCI rats with saline treatment; Fig. 2A), when the thermal hyperalgesia was almost fully relieved. Similarly, the withdrawal threshold in response to a mechanical stimulus on the ipsilateral side of CCI rats was significantly, but only partially, increased, 4 days after the beginning of ropivacaine treatment (P < 0.05 compared with CCI rats with saline treatment at Day 11; Fig. 2B). Treatment with ropivacaine did not affect either the withdrawal threshold in response to mechanical stimulation, or the latency of withdrawal from a thermal stimulus, on the contralateral side (Fig. 2).


Figure 255
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  		Figure 2. Effect of ropivacaine administration in the rats treated with the chronic constrictive injury (CCI) procedure. Ropivacaine (open circle) or saline (closed circle) was epidurally administered once a day, every day, from Day 7 to 13, as indicated by the horizontal bars. Thresholds for foot withdrawal on the contralateral (left panels) and ipsilateral (right panels) sides in response to thermal (A) or mechanical (B) stimuli applied to the corresponding hindpaw pad in rats treated with the CCI procedure. *P < 0.05 and **P < 0.01 compared with the values in CCI rats treated with saline on the corresponding days, by an unpaired t-test. #P < 0.05, ##P < 0.01, and ###P < 0.001 compared with the values at the preoperative day by Dunnett’s multiple comparisons. n = 8–9.

 

Change in NGF Content in the Nociceptive Pathway After Ropivacaine Administration
To examine whether repetitive treatment with ropivacaine induced a change in the expression of NGF, we examined the NGF content of the tissues involved in the nociceptive pathway at Day 14 after ropivacaine treatment. There were no significant differences in NGF content in L4 DRGs on the ipsilateral and contralateral sides, between sham-operated and CCI rats (n = 6–7; Fig. 3). The epidural administration of saline did not affect NGF content in L4 DRGs in CCI rats (n = 13; Fig. 3). By contrast, NGF content in the L4 DRG on the ipsilateral, but not the contralateral, side of CCI rats was significantly increased after treatment with ropivacaine, by which thermal hyperalgesia was alleviated (P < 0.05; n = 14; Fig. 3). To determine whether this increase in NGF content in the DRG after ropivacaine treatment is also observed in sham-operated rats without thermal hyperalgesia, NGF content in the DRG was measured in sham-operated animals treated repetitively with ropivacaine. No difference in NGF content was observed in DRGs between sham-operated rats receiving ropivacaine treatment (n = 6) and those without drug treatment (Fig. 3).


Figure 355
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  		Figure 3. Changes in nerve growth factor (NGF) content in the L4 dorsal root ganglion (DRG) in chronic constrictive injury (CCI) rats treated with ropivacaine. NGF content in the L4 DRG on the contralateral (open column) and ipsilateral (closed column) sides were measured in rats treated with CCI, sham operation, sham operation plus epidural ropivacaine, CCI plus epidural saline, and CCI plus epidural ropivacaine. *P < 0.05 compared by Tukey-Kramer’s multiple comparison. n = 6–14.

 

NGF is normally produced in the skin and retrogradely transported to the cell bodies of DRG neurons by an axonal transport system.18 Therefore, we also examined the NGF content of the hindpaw skin, the dorsal spinal cord and the sciatic nerve to identify the site responsible for the increase in NGF level in the DRG after ropivacaine treatment. In the hindpaw plantar skin and the L4/5 spinal dorsal horn, NGF content was unchanged between ropivacaine- and saline-treated CCI rats (n = 4–7; Figs. 4A and 4B). NGF content was significantly increased in the distal segment of the ipsilateral, but not the contralateral, sciatic nerve after CCI operation (P < 0.001 for rats with ropivacaine treatment and P < 0.01 for those with saline; n = 6–7; Fig. 4C), reflecting an accumulation of NGF retrogradely transported from the periphery. However, ropivacaine treatment did not induce a further increase in NGF content in the distal segment. There was no difference in the NGF content of the proximal segment on the ipsilateral side, or the proximal or distal segments on the contralateral side, between ropivacaine- and saline-treated CCI rats (n = 6–7; Fig. 4C). Thus, ropivacaine treatment induced upregulation of NGF only in the DRG on the ipsilateral side of CCI rats.


Figure 455
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  		Figure 4. Nerve growth factor (NGF) content in the plantar skin, the dorsal spinal cord, and the sciatic nerve in chronic constrictive injury (CCI) rats treated with ropivacaine. NGF content in the plantar skin (A), the dorsal half of L4/5 spinal cord (B), the sciatic nerve (C) segments proximal and distal to the ligated area on the contralateral (open column) and ipsilateral (closed column) sides, were measured in CCI rats treated with epidural ropivacaine or saline. The NGF content in the distal segment of the sciatic nerve is significantly increased on the ipsilateral side after the CCI procedure, with and without ropivacaine. **P < 0.01 and ***P < 0.001 compared by Tukey-Kramer’s multiple comparison. n = 4–7.

 

DISCUSSION

The present study shows that repetitive administration of ropivacaine into the epidural space, which is used in clinical practice as an epidural block, causes a prolonged analgesic effect in CCI rats, a model of neuropathic pain. This treatment significantly ameliorated thermal hyperalgesia and, to a lesser extent, mechanical allodynia. In association with a reduction of hyperalgesia, the NGF content was increased in the ipsilateral DRG after ropivacaine treatment.

Sustained activation of nociceptive pathways causes activity-dependent neural plasticity.19 Such plastic changes occur in primary sensory neurons (peripheral sensitization) as well as dorsal horn neurons (central sensitization). Peripheral changes include: sympathetic sprouting,20 a decrease in resting cytosolic calcium concentration21 and calcium channel current,22 and abnormal expression of Na+ channels in DRG neurons.23 Central sensitization mechanisms include activation of glial cells24 and altered N-methyl-d-aspartate receptor-mediated neuronal transmission in the spinal cord.25,26 Local anesthetics block voltage-dependent Na+ channels and their epidural administration causes inhibition of nerve impulse propagation in sympathetic and somatic nociceptive neurons. Therefore, repetitive temporary conduction blockade of noxious inputs with ropivacaine may allow the sensitized nervous system to revert to a more normal function.

Ropivacaine exerted prolonged analgesia, and its effect persisted at least during the period examined. Previously, long-lasting analgesic effects of lidocaine have also been reported.27,28 Thus, since the half-life of ropivacaine is not sufficiently long (several hours on epidural administration) to suppress Na+ channel-dependent conduction over several days, ropivacaine may change the pathological neural circuit by acting on other molecules, directly or indirectly, through inhibition of Na+ channels. Indeed, several molecules have been reported to be targets of local anesthetics. For example, local anesthetics such as lidocaine and mexiletine not only inhibit K+29,30 and Ca2+ channels,29–32 TRPV1,33 and various G-protein coupled receptors such as B2 bradykinin receptors,34 but they also affect cytoskeletal dynamics, neurite outgrowth and axonal transport.35,36 Furthermore, low concentrations of local anesthetics have been reported to attenuate neutrophil functions, such as the chemotactic response.37 In in vivo experiments, systemic administration of lidocaine decreased sympathetic sprouting in DRGs ipsilateral and contralateral to the axotomy in spinal nerve-ligated rats.38

In this study, an increase in the level of NGF in the injured DRG, but not in the dorsal horn, was associated with the reduction in neuropathic pain induced by repetitive ropivacaine treatment. NGF is a neurotrophic factor essential for the differentiation, survival, and maintenance of a subpopulation of DRG neurons and sympathetic neurons.39 The involvement of NGF in neuropathic pain has been reported, but its role seems complicated. Spinal nerve ligation causes a transient reduction in NGF levels in DRGs,40 whereas CCI causes an increase41 or no change in NGF levels in DRGs.42 In the periphery, NGF acts as a mediator of inflammation to cause sensitization of primary nociceptive neurons, mast cell degranulation and neutrophil accumulation.11 Furthermore, local anesthetics suppress NGF-mediated neurite outgrowth in cultured neurons.43,44 These lines of evidence imply that NGF induces the peripheral sensitization or deterioration of a pain state. On the other hand, NGF sometimes functions to protect neurons against axonal damage and plays a role in the repair of injured peripheral nerves. The increase in the expression level of c-jun in small-diameter sensory neurons that occurs after axotomy can be prevented by treatment with NGF.45 NGF also ameliorates the increase in ATF3 expression that occurs in DRGs in response to peripheral nerve injury, resulting in the protection of a population of small- to medium-sized cells.46 Furthermore, administration of exogenous NGF onto the ligated nerve abolishes thermal and mechanical hyperalgesia in CCI rats,47 and NGF improves neuropathy in streptozotocin-induced diabetic rats.48 In the present study, the increase in NGF levels after ropivacaine treatment was observed in the injured DRG, but not in the skin, the sciatic nerve or the dorsal horn. Contrarily, either repeated ropivacaine treatment or the sustained activation of the nociceptive pathways caused by CCI alone did not affect NGF content in the DRG. Ropivacaine may act on neurons or glial cells of the injured, but normal, DRGs and subsequently induce ectopic production of NGF, which may contribute, in part, to the analgesia exerted by ropivacaine.

In contrast to the complete restoration of thermal hyperalgesia, ropivacaine treatment was less effective at treating mechanical allodynia. This discrepancy might have been due to a difference in pathogenesis between mechanical allodynia and thermal hyperalgesia. It has been speculated that mechanical allodynia is evoked by the activation of normally nonnociceptive tactile Aβ fibers, whereas thermal hyperalgesia results from the hyperactivity of nociceptive neurons.49 Local anesthetics may preferentially block C fibers rather than Aβ fibers.2 In addition, whole-cell patch-clamp recording from rat DRG neurons has revealed that ropivacaine preferentially blocks tetrodotoxin-resistant Na+ channels,50 which are dominantly expressed in C fibers.23

In conclusion, repetitive administration of ropivacaine into the epidural space in CCI rats exerts an analgesic effect, probably by inducing a plastic change in the nociceptive circuit. Further investigation of the effects of local anesthetics might lead to the development of a more effective strategy for the treatment of chronic pain using local anesthetics.

ACKNOWLEDGMENTS

This study was supported by a Grant-in-Aid for Science Research (C) (Project number 11672282) from the Ministry of Education, Culture, Sports, Science, and Technology, Japan, to H. S., a Grant-in-Aid for Science Research (C) (Project number 18591728) from the Ministry of Education, Culture, Sports, Science, and Technology, Japan, to A. S. and a Grant-in-Aid for Encouragement of Young Scientists (B) (Project number 18790184) from the Japan Society for the Promotion of Science to A. S.

Footnotes

Accepted for publication September 11, 2007.

Supported by Grant-in-Aid for Science Research (C) (Project number 11672282) from the Ministry of Education, Culture, Sports, Science, and Technology, Japan, to H. S.; a Grant-in-Aid for Science Research (C) (Project number 18591728) from the Ministry of Education, Culture, Sports, Science, and Technology, Japan, to A. S.; and a Grant-in-Aid for Encouragement of Young Scientists (B) (Project number 18790184) from the Japan Society for the Promotion of Science to A. S.

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