8. Conclusions

In this paper fuzzy inductive modeling method FGMDH is considered.

The algorithms of FGMDH with different membership functions and different partial descriptions, including orthogonal polynomials, were presented and analyzed.

The experimental investigations of GMDH and fuzzy GMDH in problems of macroeconomic index forecast in Ukrainian economy were carried out.

The comparative investigations of FGMDH with ARIMA and neural network backpropagation were performed.

Experimental result analysis has confirmed the high accuracy of fuzzy GMDH in problems of forecasting in macroeconomy.

Investigation of Fuzzy Inductive Modeling Method in Forecasting Problems DOI: http://dx.doi.org/10.5772/intechopen.86348


**Composite Electrolyte & Electrode Membranes for Electrochemical Energy Storage & Conversion Devices**

Editor

**Giovanni Battista Appetecchi**

MDPI • Basel • Beijing • Wuhan • Barcelona • Belgrade • Manchester • Tokyo • Cluj • Tianjin

*Editor* Giovanni Battista Appetecchi ENEA, SSPT-PROMAS-MATPRO Technical Unit Italy

*Editorial Office* MDPI St. Alban-Anlage 66 4052 Basel, Switzerland

This is a reprint of articles from the Special Issue published online in the open access journal *Membranes* (ISSN 2077-0375) (available at: https://www.mdpi.com/journal/membranes/special issues/electrochemical energy).

For citation purposes, cite each article independently as indicated on the article page online and as indicated below:

LastName, A.A.; LastName, B.B.; LastName, C.C. Article Title. *Journal Name* **Year**, *Volume Number*, Page Range.

**ISBN 978-3-0365-0738-5 (Hbk) ISBN 978-3-0365-0739-2 (PDF)**

c 2021 by the authors. Articles in this book are Open Access and distributed under the Creative Commons Attribution (CC BY) license, which allows users to download, copy and build upon published articles, as long as the author and publisher are properly credited, which ensures maximum dissemination and a wider impact of our publications.

The book as a whole is distributed by MDPI under the terms and conditions of the Creative Commons license CC BY-NC-ND.


3. Results and discussion

#### 3.1. Estimation of ET using Penman-Monteith method

The Penman-Monteith method is the main approach recommended internationally to estimate ET; it requires the use of meteorological parameters, such as radiation, air temperature, relative humidity, and wind speed. These parameters might be difficult to obtain and measure in many meteorological stations, with the exception of temperature. Using Taiwan as an example, only a few meteorological stations had complete data of all meteorological parameters, and still there were missing data in the observation materials. Yeh et al. [13] evaluated the ET difference between the Penman-Monteith method and evaporation pan in southern Taiwan. They used six meteorological stations in the southern part of Taiwan as case studies and collected meteorological data over a span of 15 years from 1990 to 2004 to estimate ET and ET of evaporation pans. In addition, a coefficient of evaporation pans was established. The results showed that the Penman-Monteith method and evaporation pan were highly correlated. Therefore, this study used longterm meteorological data from 1961 to 2013 from Tainan Weather Station provided by Central Weather Bureau for estimation. The estimation results calculated using the Penman-Monteith method were taken as the standard, which were named PM1. In cases where radiation data were missing or incomplete, Eq. (3) was used for substitution, which was called PM2. When wind speed data were missing or incomplete, the average wind speed of 1.83 m s1 in Taiwan was used for calculation [15], which was called PM3. Eq. (2) was used for substitution in cases where relative humidity data were missing or incomplete, which was named PM4. Finally, when radiation, wind speed, and relative humidity data were all missing, all of the above substitutes were used, which was called PM5. Statistical methods of MBE, RMSE, and R2 were applied to this study. In addition, the four models, namely PM2, PM3, PM4, and PM5, were used to estimate ET, and the results were compared with those of model PM1.

The characteristics of the ET at Tainan Weather Station estimated using different models are shown in Table 1. This demonstrates that maximum values are mainly concentrated in July, while minimum values are primarily concentrated in January or December. The average value was within the range of 3.42–3.61 mm/day. In addition, the ET estimated by PM models at Tainan Weather Station is shown in Figure 2, and the results indicate that the trend of each PM model was roughly the same as that of PM1. The comparison results between each PM model and PM1 are shown in Figure 3. This suggests that ET was underestimated by PM2 from July to September, while it was overestimated during other months; PM3 underestimated ET in

Table 1. Various scenarios for calculating evapotranspiration using the Penman-Monteith method (mm d1 ).

Figure 2. Comparison of monthly mean values of the Penman-Monteith method from various scenarios.

3. Results and discussion

10 Current Perspective to Predict Actual Evapotranspiration

3.1. Estimation of ET using Penman-Monteith method

estimate ET, and the results were compared with those of model PM1.

The characteristics of the ET at Tainan Weather Station estimated using different models are shown in Table 1. This demonstrates that maximum values are mainly concentrated in July, while minimum values are primarily concentrated in January or December. The average value was within the range of 3.42–3.61 mm/day. In addition, the ET estimated by PM models at Tainan Weather Station is shown in Figure 2, and the results indicate that the trend of each PM model was roughly the same as that of PM1. The comparison results between each PM model and PM1 are shown in Figure 3. This suggests that ET was underestimated by PM2 from July to September, while it was overestimated during other months; PM3 underestimated ET in

Scenarios Min. Min. (month) Max. Max. (month) Mean Standard deviation

PM1 2.26 January 4.72 July 3.54 0.92 PM2 2.35 January 4.55 July 3.61 0.85 PM3 2.22 January 4.78 July 3.58 0.95 PM4 2.15 December 4.56 July 3.42 0.89 PM5 2.24 December 4.38 July 3.49 0.81

Table 1. Various scenarios for calculating evapotranspiration using the Penman-Monteith method (mm d1

).

The Penman-Monteith method is the main approach recommended internationally to estimate ET; it requires the use of meteorological parameters, such as radiation, air temperature, relative humidity, and wind speed. These parameters might be difficult to obtain and measure in many meteorological stations, with the exception of temperature. Using Taiwan as an example, only a few meteorological stations had complete data of all meteorological parameters, and still there were missing data in the observation materials. Yeh et al. [13] evaluated the ET difference between the Penman-Monteith method and evaporation pan in southern Taiwan. They used six meteorological stations in the southern part of Taiwan as case studies and collected meteorological data over a span of 15 years from 1990 to 2004 to estimate ET and ET of evaporation pans. In addition, a coefficient of evaporation pans was established. The results showed that the Penman-Monteith method and evaporation pan were highly correlated. Therefore, this study used longterm meteorological data from 1961 to 2013 from Tainan Weather Station provided by Central Weather Bureau for estimation. The estimation results calculated using the Penman-Monteith method were taken as the standard, which were named PM1. In cases where radiation data were missing or incomplete, Eq. (3) was used for substitution, which was called PM2. When wind speed data were missing or incomplete, the average wind speed of 1.83 m s1 in Taiwan was used for calculation [15], which was called PM3. Eq. (2) was used for substitution in cases where relative humidity data were missing or incomplete, which was named PM4. Finally, when radiation, wind speed, and relative humidity data were all missing, all of the above substitutes were used, which was called PM5. Statistical methods of MBE, RMSE, and R2 were applied to this study. In addition, the four models, namely PM2, PM3, PM4, and PM5, were used to

January, February, and December, and it was overestimated in the remaining months; ET was underestimated by PM4 in all months; PM5 underestimated ET in June, July, August, September, October, and December and overestimated ET in other months.

In this study, the estimated ET of PM2, PM3, PM4, and PM5 models were compared with that of the PM1 model using the statistical methods of MBE, RMSE, and R2 . Statistical verification

Figure 3. Monthly evapotranspiration comparison between the PM1 and the calculated values by using the various scenarios. (a) PM2; (b) PM3; (c) PM4; (d) PM5.

results of MBE showed that the MBE value was within the range of 0.12 to 0.07 mm d1 , while the value of RMSE ranged from 0.09 to 0.31 mm d1 . There is slight overestimation in PM2 and PM3. In contrast, there is slight underestimation in PM4 and PM5. In addition, R2 was optimal in PM3 based on the statistical verification results. Therefore, according to the calculation results of MBE, RMSE, and R2 , the PM3 model had the optimal performance. Given the above comparison, the results of this study showed that wind speed had little effect on the assessment of ET with the Penman-Monteith method as the standard (PM1), which was similar to the conclusion drawn by Jabloun et al. [25]. The results obtained by Popova et al. [26] using the global average wind speed of 2 m s1 were similar to PM1 as well. In addition, compared to missing radiation or wind speed data, the absence of relative humidity data exerted a larger impact on the estimation of ET when Penman-Monteith method was used.

### 3.2. The results of ET estimation using different empirical formulas

Compared with other meteorological parameters, namely radiation, relative humidity, and wind speed, temperature is relatively easy to obtain. Apart from that, radiation can be accurately measured, and yet existing measurement methods are unable to acquire precise wind speed data, especially in dry areas where the error would be relatively larger. Because the mixed evaluation methods, such as the Penman-Monteith method, require many meteorological parameters, there are some difficulties in the funding, maintenance, and construction of meteorological stations, making it difficult to acquire certain data. Therefore, it is essential to develop ET estimation methods that require fewer or a single meteorological parameter [27]. A number of scholars have proposed various methods or experiential formulas and compared them to the Penman-Monteith method in the hope of finding a relatively simple method and experiential formula to measure ET [28]. This study selected six radiation-based methods and four temperature-based methods to explore their applicability in the study area.

#### 3.2.1. Estimation of monthly average ET using radiation-based methods

According to the radiation-based estimation methods that are used internationally, this study selected six methods, including Makkink [4], Turc [16], Jensen and Haise [17], Priestley and Taylor [5], Doorenbos and Pruitt [18], and Abtew [19]. A commonly used statistical mean error percentage was applied to the estimation so as to discuss the basic statistical differences. The data recorded by Tainan Weather Station from 1961 to 2013 were substituted into the formula, and the results are shown in Table 2. This demonstrates that minimum values were mainly concentrated in December and January, while maximum values were primarily concentrated in July. The mean value indicated a significant underestimation in ET calculated by the Makkink method, with an average value of 2.99 mm d1 and an error percentage of 15.5%. The results of the Turc method showed a slight overestimation, with an average value of 3.66 mm d1 and an error percentage of 3.4%. ET was significantly overestimated by the Jensen-Haise method, with a mean value of 5.16 mm d1 and an error percentage of 45.8%. The results of the Priestley-Taylor method suggested an overestimation, with an average value of 3.96 mm d1 and an error percentage of 11.9%. ET calculated by the Doorenbos-Pruitt method was the closest to the mean value of the Penman-Monteith method, with an average value of 3.43 mm d1 and an

Table 2. Performance evaluation of the radiation-based methods against Penman-Monteith (mm d1 ).

results of MBE showed that the MBE value was within the range of 0.12 to 0.07 mm d1

PM2 and PM3. In contrast, there is slight underestimation in PM4 and PM5. In addition, R2 was optimal in PM3 based on the statistical verification results. Therefore, according to the

the above comparison, the results of this study showed that wind speed had little effect on the assessment of ET with the Penman-Monteith method as the standard (PM1), which was similar to the conclusion drawn by Jabloun et al. [25]. The results obtained by Popova et al. [26] using the global average wind speed of 2 m s1 were similar to PM1 as well. In addition, compared to missing radiation or wind speed data, the absence of relative humidity data exerted a larger

Compared with other meteorological parameters, namely radiation, relative humidity, and wind speed, temperature is relatively easy to obtain. Apart from that, radiation can be accurately measured, and yet existing measurement methods are unable to acquire precise wind speed data, especially in dry areas where the error would be relatively larger. Because the mixed evaluation methods, such as the Penman-Monteith method, require many meteorological parameters, there are some difficulties in the funding, maintenance, and construction of meteorological stations, making it difficult to acquire certain data. Therefore, it is essential to develop ET estimation methods that require fewer or a single meteorological parameter [27]. A number of scholars have proposed various methods or experiential formulas and compared them to the Penman-Monteith method in the hope of finding a relatively simple method and experiential formula to measure ET [28]. This study selected six radiation-based methods and four temperature-based methods to explore their applicability

According to the radiation-based estimation methods that are used internationally, this study selected six methods, including Makkink [4], Turc [16], Jensen and Haise [17], Priestley and Taylor [5], Doorenbos and Pruitt [18], and Abtew [19]. A commonly used statistical mean error percentage was applied to the estimation so as to discuss the basic statistical differences. The data recorded by Tainan Weather Station from 1961 to 2013 were substituted into the formula, and the results are shown in Table 2. This demonstrates that minimum values were mainly concentrated in December and January, while maximum values were primarily concentrated in July. The mean value indicated a significant underestimation in ET calculated by the Makkink method, with an average value of 2.99 mm d1 and an error percentage of 15.5%. The results of the Turc method showed a slight overestimation, with an average value of 3.66 mm d1 and an error percentage of 3.4%. ET was significantly overestimated by the Jensen-Haise method, with a mean value of 5.16 mm d1 and an error percentage of 45.8%. The results of the Priestley-Taylor method suggested an overestimation, with an average value of 3.96 mm d1 and an error percentage of 11.9%. ET calculated by the Doorenbos-Pruitt method was the closest to the mean value of the Penman-Monteith method, with an average value of 3.43 mm d1 and an

while the value of RMSE ranged from 0.09 to 0.31 mm d1

impact on the estimation of ET when Penman-Monteith method was used.

3.2. The results of ET estimation using different empirical formulas

3.2.1. Estimation of monthly average ET using radiation-based methods

calculation results of MBE, RMSE, and R2

12 Current Perspective to Predict Actual Evapotranspiration

in the study area.

,

. There is slight overestimation in

, the PM3 model had the optimal performance. Given

error percentage of 3.1%. The results of the Abtew method showed a slight overestimation, with an average value of 3.68 mm d1 and an error percentage of 4.0%.

The trend of monthly average ET at Tainan Weather Station calculated by various radiation-based methods were all consistent with that of the Penman-Monteith method, which was taken as the standard, as shown in Figure 4. As shown in Figure 5, the monthly average ET was underestimated by the Makkink method, with an error percentage ranging from 16.9 to 13.7%; the Turc method slightly overestimated all the monthly average ET, with an error percentage of 1.1 to 11.1%; and the monthly average ET was significantly overestimated by the Jensen-Haise method. Especially in summer, the overestimation was far more significant, and the error percentage was up to 54.2%. The results of the Priestley-Taylor method suggest underestimation only in December and January, and overestimation in other months, with an error percentage of 4.4 to 17.2%. The Doorenbos-Pruitt method slightly underestimated ET in May, August, and September, while in other months ET was overestimated with an error percentage ranging from 11.7 to 16.8%. Compared with the Penman-Monteith method, ET was overestimated by the Abtew method, and the error percentage was within the range of 4.7 to 19%. The above results suggest that the Doorenbos-Pruitt method was the least biased in estimating ET, while the Jensen-Haise method was the most biased.

Figure 4. Monthly evapotranspiration computed by the Penman-Monteith method and six radiation-based methods.

Figure 5. Monthly evapotranspiration comparison between the Penman-Monteith method and the calculated values by using the radiation-based methods ((a) Makkink; (b) Turc; (c) Jensen-Haise; (d) Priestley-Taylor; (e) Doorenbos-Pruit; (f) Abtew).

In addition, three statistical methods, namely MBE, RMSE, and R2 , were used in this study to compare the estimation results of the Makkink, Turc, Jensen-Haise, Priestley-Taylor, Doorenbos-Pruitt, and Abtew methods with the Penman-Monteith method. The statistical verification results of MBE indicated that the value of MBE was within the range of 0.55 to 0.41 mm d1 and the value of RMSE ranged from 0.23 to 1.78 mm d1 . Figure 6(a) shows that the Makkink method underestimated ET, and the MBE value was 0.55. Furthermore, the other five methods, Turc, Jensen-Haise, Priestley-Taylor, Doorenbos-Pruitt, and Abtew methods, all overestimated ET, and the MBE values were respectively 0.12, 1.62, 0.41, 0.49, and 0.14. In particular, the overestimation of the Jensen-Haise method was the most significant. Figure 6(b) suggests that all six methods overestimated ET, and the values of RMSE were respectively 0.60, 0.23, 1.78, 0.55,

Figure 6. (a) MBE and (b) RMSE for evapotranspiration comparison between the Penman-Monteith method and six radiation-based methods.

In addition, three statistical methods, namely MBE, RMSE, and R2

and the value of RMSE ranged from 0.23 to 1.78 mm d1

14 Current Perspective to Predict Actual Evapotranspiration

compare the estimation results of the Makkink, Turc, Jensen-Haise, Priestley-Taylor, Doorenbos-Pruitt, and Abtew methods with the Penman-Monteith method. The statistical verification results of MBE indicated that the value of MBE was within the range of 0.55 to 0.41 mm d1

Figure 5. Monthly evapotranspiration comparison between the Penman-Monteith method and the calculated values by using the radiation-based methods ((a) Makkink; (b) Turc; (c) Jensen-Haise; (d) Priestley-Taylor; (e) Doorenbos-Pruit; (f) Abtew).

(e) Doorenbos-Pruit (1977) (f) Abtew (1996)

(a) Makkink (1957) (b) Turc (1961)

(c) Jensen-Haise (1963) (d) Priestley-Taylor (1972)

method underestimated ET, and the MBE value was 0.55. Furthermore, the other five methods, Turc, Jensen-Haise, Priestley-Taylor, Doorenbos-Pruitt, and Abtew methods, all overestimated ET, and the MBE values were respectively 0.12, 1.62, 0.41, 0.49, and 0.14. In particular, the overestimation of the Jensen-Haise method was the most significant. Figure 6(b) suggests that all six methods overestimated ET, and the values of RMSE were respectively 0.60, 0.23, 1.78, 0.55,

, were used in this study to

. Figure 6(a) shows that the Makkink

0.53, and 0.37. Evapotranspiration was most significantly overestimated by the Jensen-Haise method as well. The statistical results showed that R2 was within the range of 0.90–0.97. Therefore, judging from the statistical results of MBE, RMSE, and R2 , the Turc method was optimal at the Tainan Weather Station, followed by the Abtew method; the method with the worst performance was the Jensen-Haise method. Previously, Tabari et al. [29] used 31 methods to evaluate ET at a meteorological station named Rasht in a humid area of Iran. The results showed that, compared to the Penman-Monteith method, the Jensen-Haise method severely overestimated ET with a relative error of about 30%. It was also found to significantly overestimate ET in this study area, and the relative errors were respectively around 59 and 48%. Such overestimation also occurred in the humid regions of Serbia [30] and Florida of the USA [31].

#### 3.2.2. Estimation of monthly average ET using temperature-based methods

Among the temperature-based methods that are commonly used internationally, this chapter selected four methods, including Thornthwaite [20], Blaney and Criddle [21], Hamon [22], and Linacre [23]. To begin with, the commonly used statistical mean value and error percentage were used for estimation; then this chapter discusses the basic statistical error. After the data recorded by Tainan Weather Station from 1961 to 2013 were substituted into the formulas to calculate the daily ET, the average monthly ET was calculated with month as the unit, and the results are shown in Table 3. At the Tainan Weather Station, minimum values were mainly concentrated in January and maximum values were primarily concentrated in July. The mean value suggests that the Thornthwaite method severely underestimated ET, with a mean value of 1.95 mm d1 and an error percentage of 44.9%. The Blaney-Criddle method significantly underestimated ET as well. Its mean value was 1.61 mm d1 and the error percentage was 54.5%. The Hamon method underestimated ET, with a mean value of 2.72 mm d1 and an error percentage of 23.2%. Evapotranspiration was overestimated by the Linacre method, with a mean value of 4.05 mm d1 and an error percentage of 14.4%.

This chapter compared the ET of Tainan Weather Station as calculated by the temperaturebased methods with that of the Penman-Monteith method, and the results are as shown in Figure 7. The trends of the Thornthwaite, Hamon, and Linacre methods were consistent with the Penman-Monteith method, while Blaney-Criddle method suggested otherwise. The monthly average ET at Tainan Weather Station estimated by the temperature-based estimation methods was compared with Penman-Monteith method, as shown in Figure 8. Evapotranspiration was underestimated by Thornthwaite method, with an error percentage of 70.4 to 31.1%. The maximum error occurred in March and April. The Blaney-Criddle method underestimated monthly average ET, and the error percentage was within the range of 60.6 to 38.9%. Evapotranspiration was also underestimated by the Hamon method. The underestimation in winter was insignificant, with an error percentage of 23.5 to 18.1%. In May, the percentage reached its maximum. The Linacre method overestimated the monthly average ET. The error percentage ranged from 5.1 to 23.9% and reached maximum value in November. In light of the above results, the error percentage of Thornthwaite method was the largest.

This study used three statistical methods, namely MBE, RMSE, and R2 , to compare ET at the Tainan Weather Station estimated by the Thornthwaite, Blaney-Criddle, Hamon methods with that of the Penman-Monteith method. The value of MBE ranged from 1.93 to 0.51 mm d1 and RMSE was within the range of 0.63–2.08 mm d1 . The statistical results of R2 indicated that

Table 3. Performance evaluation of the temperature-based methods against Penman-Monteith (mm d1 ).

3.2.2. Estimation of monthly average ET using temperature-based methods

16 Current Perspective to Predict Actual Evapotranspiration

with a mean value of 4.05 mm d1 and an error percentage of 14.4%.

This study used three statistical methods, namely MBE, RMSE, and R2

Penman-Monteith 2.26 January 4.72 July 3.54 0.92 Thornthwaite (1948) 0.67 January 3.25 July 1.95 1.02 Blaney-Criddle (1959) 1.38 January 1.86 July 1.61 0.32 Hamon (1961) 1.85 January 3.61 July 2.72 0.80 Linacre (1977) 2.80 January 4.96 July 4.05 0.82

Table 3. Performance evaluation of the temperature-based methods against Penman-Monteith (mm d1

and RMSE was within the range of 0.63–2.08 mm d1

Among the temperature-based methods that are commonly used internationally, this chapter selected four methods, including Thornthwaite [20], Blaney and Criddle [21], Hamon [22], and Linacre [23]. To begin with, the commonly used statistical mean value and error percentage were used for estimation; then this chapter discusses the basic statistical error. After the data recorded by Tainan Weather Station from 1961 to 2013 were substituted into the formulas to calculate the daily ET, the average monthly ET was calculated with month as the unit, and the results are shown in Table 3. At the Tainan Weather Station, minimum values were mainly concentrated in January and maximum values were primarily concentrated in July. The mean value suggests that the Thornthwaite method severely underestimated ET, with a mean value of 1.95 mm d1 and an error percentage of 44.9%. The Blaney-Criddle method significantly underestimated ET as well. Its mean value was 1.61 mm d1 and the error percentage was 54.5%. The Hamon method underestimated ET, with a mean value of 2.72 mm d1 and an error percentage of 23.2%. Evapotranspiration was overestimated by the Linacre method,

This chapter compared the ET of Tainan Weather Station as calculated by the temperaturebased methods with that of the Penman-Monteith method, and the results are as shown in Figure 7. The trends of the Thornthwaite, Hamon, and Linacre methods were consistent with the Penman-Monteith method, while Blaney-Criddle method suggested otherwise. The monthly average ET at Tainan Weather Station estimated by the temperature-based estimation methods was compared with Penman-Monteith method, as shown in Figure 8. Evapotranspiration was underestimated by Thornthwaite method, with an error percentage of 70.4 to 31.1%. The maximum error occurred in March and April. The Blaney-Criddle method underestimated monthly average ET, and the error percentage was within the range of 60.6 to 38.9%. Evapotranspiration was also underestimated by the Hamon method. The underestimation in winter was insignificant, with an error percentage of 23.5 to 18.1%. In May, the percentage reached its maximum. The Linacre method overestimated the monthly average ET. The error percentage ranged from 5.1 to 23.9% and reached maximum value in November. In light of the above results, the error percentage of Thornthwaite method was the largest.

Tainan Weather Station estimated by the Thornthwaite, Blaney-Criddle, Hamon methods with that of the Penman-Monteith method. The value of MBE ranged from 1.93 to 0.51 mm d1

Min. Min. (month) Max. Max. (month) Mean Standard deviation

, to compare ET at the

).

. The statistical results of R2 indicated that

Figure 7. Monthly evapotranspiration computed by the Penman-Monteith method and four temperature-based methods.

Figure 8. Monthly evapotranspiration comparison between the Penman-Monteith method and the calculated values by using the temperature-based methods ((a) Thornthwaite; (b) Blaney-Criddle; (c) Hamon; (d) Linacre).

it was within the range of 0.36–0.83. As shown in Figure 9(a), the results of Thornthwaite, Blaney-Criddle, and Hamon methods suggest underestimation, and the values of MBE were 1.58, 1.93, and 0.82, respectively. Results of the Linacre method, however, indicated overestimation with an MBE of 0.51. Figure 9(b) suggests overestimation in Thornthwaite,

Figure 9. (a) MBE and (b) RMSE for evapotranspiration comparison between the Penman-Monteith method and four temperature-based methods.

Blaney-Criddle, Hamon, and Linacre methods, with RMSE values of 1.63, 1.31, 1.15, and 1.12, respectively. In summary, according to the statistical results of MBE, RMSE, and R2 , the Linacre method was optimal for estimating ET at the Tainan Weather Station, followed by the Hamon method. The Blaney-Criddle method was the least fit.

According to relevant studies and literature, Fontenot [32] declared that for meteorological stations near the coast, the Linacre method overestimated ET by 18.46% compared to the Penman-Monteith method. It was also pointed out that this method could be greatly affected by the dew point temperature. Compared with the Penman-Monteith method, the results of Thornthwaite, Hamon, and Blaney-Criddle methods all suggest underestimation, as these three temperaturebased formulas all took daylight hours into consideration. In spite of the high temperature, the results would still be lower than the actual amount when daylight hours were insufficient, causing underestimation. Even if the daylight hours were insufficient, ET still occurred. The results of this study show that the Blaney-Criddle method underestimated ET in Tainan because it is strongly influenced by the annual daylight percentage of every month. Cruff and Thompson [33] used the Thornthwaite and Blaney-Criddle methods to estimate ET in the desert areas of the southwestern United States, and the results suggested underestimation as well.

This study compared the results of radiation-based methods with that of Penman-Monteith method and discovered that the empirical formulas of radiation-based methods were better than those of temperature-based methods. In addition, the errors of ET calculated by temperature-based methods were larger than those of the radiation-based methods. The reason is as follows: it is most likely that temperature is the only meteorological parameter used in empirical formulas of temperature-based methods. Therefore, it could be easily affected by the data of meteorological station, which would easily cause inaccuracy. Such a conclusion is similar to that of Lu et al. [34], Sentelhas et al. [8], and Gebhart et al. [35]. Moreover, the estimation results of Tukimat et al. [36] in Malaysia showed that three radiation-based methods, namely Makkink [4], Turc [16], and Priestley and Taylor [5], were more accurate than two temperature-based methods, the Thornthwaite [20] and Blaney and Criddle [21] methods. In terms of temperature-based estimation methods, many scholars have found that ET was underestimated by the Thornthwaite [20] method in humid areas compared to the Penman-Monteith method. For instance, the results of Alkaeed et al. [37] in Fukuoka of Japan, Trajkovic and Kolakovic [30] in six meteorological stations of Balkan Peninsula, and Sentelhas et al. [8] in Ontario of Canada, all showed the same conclusion. Some scholars, however, have pointed out that compared with the Penman-Monteith method, the performance of R2 in the Thornthwaite [20] method was worse, and yet its trend was consistent with the Penman-Monteith method. The evaluation of ET conducted by [36] in Kedah of Malaysia suggested same result.


3. Pharmacological aids to enhance regeneration after nerve root reimplantation

time the regenerating axonal sprouts reach the motor end plates [72, 73]. In rats, functional recovery is seen only in cervical but not in lumbosacral avulsion models as the distance to cover is much shorter for the cervical NRs [9, 40, 85–87], and in any case only proximal limb muscle recovery is seen [86–89]. Third, the regenerating fibers may reach the wrong target due to misrouting [53], and in the absence of NG or conduit, the regenerating axons will grow along the surface of the SC [27, 43, 53, 83, 87]. The misrouting is responsible for simultaneous contractures in agonist and antagonist muscles leading to ineffective limb movements [30]. Fourth, there is severe muscular atrophy due to lack of use [74]. Hence, for a successful clinical result, MN survival must be improved, axonal regeneration has to be enhanced and accelerated, misrouting should be minimized and muscle atrophy should be prevented [15, 72].

Although the MN cell body can regenerate and grow a new axon after this is torn [69, 90], many MNs apoptose [13, 65, 69], and only 80% of the surviving MNs do finally project a regenerating axon in the reimplanted ventral root or NG [26, 27, 31, 86]. Reimplantation of avulsed NRs either directly or by means of a peripheral NG helps to reduce the number of MNs undergoing apoptosis, probably because of local NF production [69, 77, 89, 91–93]. Exogenous NFs can be administered to enhance the regenerating capacity of cells [47, 94, 95]. Historically, the first attempts were directed at motor recovery with ventral rootlet reimplantantion [96], but recently sensory recovery has been proved possible by reimplanting dorsal rootlets [97]. The results of dorsal rootlet repair are dismal because the SC glial proliferation creates barriers that prevent the regenerating DRG axons from reaching the posterior SC horn [81]. The lack of sensory recovery induces chronic neuropathic pain [49, 98], and the lack of proprioception causes limb clumsiness [30]. This has been partially avoided by direct implantation of the dorsal rootlets or their NGs' extensions inside the posterior horn itself rather than on the surface of the SC [81, 99]. The repair of both motor and sensory NRts leads to better functional results with more accurate movements and less muscular synkinesis [100]. Functional MRI studies have corroborated affected limb sensory cortex function recovery in

The timing of NR reimplantation is crucial, as a longer waiting period will correlate with a greater amount of MNs undergoing apoptosis [20, 27, 91, 93, 101–103]. The percentage of dead MNs increases from 20% by 10–12 days post-avulsion [13, 65, 69] to 50% by 4 weeks [104, 105], 85% by 6 weeks [106] and 90% by 20 weeks [27, 83, 93, 107]. Early NR reimplantation seems to have neuroprotective effects [27, 83, 89, 93, 108, 109], but some MN loss will happen even if repair occurs immediately after avulsion [93, 101]. In animal models, NRA followed by immediate reimplantation in the same surgical procedure minimizes MN apoptosis and achieves muscle reinnervation with some limited functional recovery, which is better in the brachial plexus than in the lumbosacral plexus [27, 69, 83, 110]. Ideally, the surgical repair must be performed no later than 10 days post-injury [65] as a delay over 2 weeks will lead to poor clinical results [20, 26, 27]. In clinical practice, patients suffering from brachial or lumbosacral plexus avulsions often experience other concomitant injuries, sometimes quite serious, that force delaying NR repair [111]. Another common scenario is that the precise diagnosis takes weeks or even months [3]. In any case, in human beings NRA repair has to occur no later than 1 month after the injury to allow any motor function recovery [45, 74, 97, 100]. NGs are almost

the area corresponding to the reimplanted NR [100].

48 Treatment of Brachial Plexus Injuries

Several pharmacological aids have been introduced to improve MN survival and axonal regeneration after anterior spinal NRt reimplantation. They can be classified into NFs, drugs and cell-derived products (Table 1).

NF administration improves MN survival as well as synaptic and axonal regrowth [87, 112–115] improving the NR reimplantation results. NFs enhance Schwann cell migration, axonal regeneration and myelination [8, 16, 69, 93, 105, 116–120] and delay MN apoptosis—by 6 weeks 80–90% of them are still alive [8, 69, 116, 118–121]. To be maximally effective, they must be administered locally at the SC-NR interface within the first 3 days and no later than 2 weeks post-avulsion [20, 87, 93, 116]. NFs ought to be applied with Gelfoam or fibrin glue to avoid dilution in the CSF [72], but free intrathecal application by means of an injecting pump is not recommended [122]. Their short half-life limits their use, particularly because NFs have to be applied directly to a surgically exposed SC [123]. Although NFs increase MN survival and axonal regeneration, their effect on muscle recovery and final functional results is very limited [4, 7, 18, 20, 27, 37, 93, 105]. It has been observed that in areas where the concentration of NFs is high, the regenerating axons get trapped and do not grow to reach their final distal targets [18, 102]. Some have cautioned against the possible adverse effects of using NFs in human clinical practice [124]. The currently used NFs are brain-derived neurotrophic factor (BDNF) [115], glial-derived neurotrophic factor (GDNF) [8, 18, 20, 37, 102, 105, 125], ciliary neurotrophic factor (CNTF) [87] and intracellular sigma peptide (ISP) [126]. GDNF shows the strongest action and a single direct application to the SC are enough, provided that they are applied within the first 2 weeks after NRA [18, 20, 37, 102, 116, 127]. GDNF delays MN cell death for 6 weeks, therefore broadening the window for avulsed NR reimplantation [20]. Similarly, the intracellular sigma peptide (ISP) blocks astrocytic inhibitory action, thus facilitating axonal regeneration [126].

Moreover, the distance to cover by the regenerating axons from the SC avulsion site to the muscular end plates is so long that by the time the axons reach their destination, the muscles are atrophic and fibrotic [20, 128]. To avoid and delay this muscle atrophy as much as possible, several strategies have been attempted: manipulating the molecular pathways involved in muscle atrophy [129–131], nerve transfers from neighboring functioning nerves [132–136], direct electrical stimulation of the affected muscles [137–139] and neuronal transplantation inside the denervated muscle [20, 140–142]. In rats, the combination of GDNF at the SC-NR injury site and embryonic spinal foetal neuron transplant inside the target muscles provided the best possible functional result [20]. These embryonic neurons reinnervate the muscle end plates just after the injury, preventing muscle atrophy while the regenerating axons arrived

Agent Lithium Minocycline

Tetracyclyne

Inhibits glial

Orally

Motoneuron

Improves axonal

Neurotoxic

doses.

Prevents and reverses

hypersensitivity

 at high

Rat,

Bacterial infections,

mice

Stroke

sprouting and

migration

survival

487% at

5 weeks. Autonomic

neurons ∅

effect

Recombinant

Drug

 Counteracts

Subcutaneously

survival

51.7 0.8%

at 12 days

postavulsion

Motoneuron

Suppresses

Induces a pro-

Rat

 Anemia

thrombotic

 state. Neuroprotective

microglia

proliferation.

Protects axon

effect NOT long-

regeneration

lasting

glutamate's

effect

 cytotoxic

erythropoietin

FK506-tacrolimus

 Drug

Target heat shock

protein 90

Immunosuppression.

Sublingual

survival not

axons

reported.

penetrating

reaching the

posterior horn

 and

> Used ONLY

in dorsal

nerve root

repair

Geldamycin Acamprosate

 Drug

⇓

Synaptic glutamate

 Orally

Ansamycin

On heat shock protein

Parenteral

⇑ dorsal

axonal

ganglion

regeneration

Toxic at high doses

neuron.

Motoneuron

not studied

Associated

Associated

ribavirin

accelerates

 with

Side effects if ethanol

Rat

 Alcoholism 51

consumption

with

ribavirin ⇑

Survival

Accelerates

No

Rat

 Cancer

Nerve Root Reimplantation in Brachial Plexus Injuries http://dx.doi.org/10.5772/intechopen.82431

immunosuppression.

injection

antibiotic

90. NOT immunosuppression

Motoneuron

⇑

Regenerating

Immunosuppression.

Rat

 Organ transplant immunosuppression

Long-term

administration

needed

derivative

proliferation.

 Strong

anti-inflammatory

effect

Drug

⇑

Endogenous

secretion

 BDNF

Orally

Group

Mechanism

 of action

Administration

Motoneuron

Axonal

Observation

 Applied

Current human

to

clinical use

regeneration

survival

post-injury

Motoneuron

⇑

Myelinated

Helps prevent muscle

Rat

 Bipolar disorder

atrophy

survival 69%

axons inside reimplanted nerve

by 12 weeks

postavulsion

root

route

Agent Brain-

NF

Reverses cholinergic

Intrathecal

survival 53%

by 16 weeks

fibers reaching

cord-avulsed

root interface

Motoneuron

Abundant regenerating

Active against many

Rat

 None

50 Treatment of Brachial Plexus Injuries

neurodegenerative

disorders

transmitter-related

enzyme deficiency

derived-neurotrophic-

factor (BDNF)

Glial-

NF

⇑

Survival of

Direct

Completely

⇑ Axonal

Strongest NF.

combined with

Riluzole

Administration

⇑ Effect

Rat

 None

prevents

regeneration

motoneuron

and coiling and

regeneration

Schwann cells

before 2 week post-

avulsion

loss at 16 weeks postavulsion

administration

dopaminergic

neurons

on spinal cord

derived-neurotrophic-

factor (GDNF) Ciliary NF (CNTF)

 NF

Activates motor

Direct

Motoneuron

⇑ Axon

Conjugation

transferrin prolongs

 it with

Rabbit

 None

administration

survival 23

4.3% by 3 weeks post-

avulsion

regeneration

across interface

its action

> spinal cord/

nerve root

neuron signal

transducer

 and

on spinal cord

transcription

activator(STAT3)

Intracellular

peptide (ISP)

Resveratrol

Riluzole

Drug

 Inhibitor presynaptic

Orally

Motoneuron

⇑

Myelinated

Administration

Rat

sclerosis, Nervous

Depression,

Cord Injury

 Spinal

Amyotrophic

 lateral

> before 2 week after

injury. Maximum

survival 70%

axons in reimplanted nerve

> by 5 weeks

postavulsion

root.

⇓ hypersensitivity

and allodynia

Sensory

effect combined with

GDNF

glutamate release

Drug

inhibitor

Topoisomerase

 II

Added to nerve

Motoneuron

⇑ Axonal

Only tried on

Rat

 Cancer, Chronic

diseases, Aging

autologous

graft cultures

 nerve

survival 69%

regeneration,

Schwann cell migration and

myelination

at 8 weeks

postavulsion

graft culture

 sigma

NF

⇓

Inhibition of

Subcutaneous

Motoneuron

⇑

Amount and

Act as synapse

Rat

 None

organizing

 agent

survival

size of regenerated

axons

61.2% at 12 weeks postavulsion

injection

astrocyte secreted

chon-droitin

proteoglycans

 sulfate

 3

Group

Mechanism

 of action

Administration

Motoneuron

Axonal

Observation

 Applied

Current human

to

clinical use

regeneration

survival

post-injury

route

Table 1. NFs (neurotrophic factors) and drugs used in nerve root reimplantation with their effects.

[20]. However, when the regenerating axons reached the muscular end plates, they had to compete with the already existing axons coming from the locally injected embryonic foetal

Some drugs have been administered to minimize MN apoptosis and improve NR regenera-

zothiazole) [8, 69, 121], lithium [146, 147], minocycline [119], recombinant erythropoietin

[154], N-acetyl cysteine [155] and glatiramer [156]. Some researchers have administered combinations such as acamprosate and ribavirin [154] or riluzole and GDNF [8]. The main advantage of acamprosate, ribavirin, and riluzole is that they can be administered orally

Resveratrol has been added to the autologous NG culture for a week in the rat experimental C6 NRA and reimplantation model [145], finding that it improves axonal regeneration,

In experimental brachial plexus avulsion (BPA) rat models, riluzole has been proved to improve MN survival, prolonging the time period at which reimplantation can be successful [65, 69, 101, 121]. If administered within 2 weeks post-avulsion, riluzole helps to keep 70% of the MNs [65, 69, 121] alive and minimizes the sensory hypersensitivity and allodynia [119]. Its maximum effect is achieved when combined with GDNF [8], and it can be administered

In rat, experimental avulsion models and at doses used in the treatment of mood disorders, lithium improves neuronal survival, axonal regeneration and myelination, allowing an earlier and better functional recovery [146, 147]. One of its mechanisms of action is by increasing endogenous BDNF secretion [158]. Its effect on growing axon myelination starts 4 weeks post-NR reimplantation, reaching its pinnacle at 6 weeks and slowing down by 12 weeks [146].

properties [120]. In rats, it has been administered intraperitoneally and intrathecally, with better results through the latter route [106]. At low doses, minocycline has neuroprotective properties, but at high concentrations it is neurotoxic [164], among other reasons, because glial proliferation and Wallerian degeneration are a sine qua non for nerve regeneration [106].

Recombinant erythropoietin injected subcutaneously once a day for 3 days has shown neuroprotective properties in a rat NRA experimental model [118]. These neuroprotective properties are short lasting but can help to delay motor neuron apoptosis after NRA, increasing the period in which a NR reimplantation can be undertaken [118]. Recombinant erythropoietin seems to counteract the cytotoxic effect of glutamate, block free radicals, increase the release of neurotransmitters and decrease microglial activation [165]. The positive effects of recombinant erythropoietin are maximal when its administration is started within 96 hours (4 days) after NRA and reimplantation [118]. The side effects related with the administration of

Minocycline is a tetracycline derivative that inhibits glial proliferation [159]

Schwann cell migration and myelination and MN survival

,5-trihydroxystilbene) [145], riluzole (2-amino-6-trifluoromethoxyben-

–151], geldanamycin [152, 153], acamprosate [67, 154], ribavirin

—and decreases neuronal [161] and oligodendrocyte cell loss

–brain barrier and has anti-inflammatory

—69% surviving 8 weeks after

Nerve Root Reimplantation in Brachial Plexus Injuries http://dx.doi.org/10.5772/intechopen.82431 53

—a barrier against

neurons [20, 140, 143, 144].

[118], FK506-tacrolimus [148

.

axonal and dendrite growth [160]

[120, 162, 163]. Minocycline can cross the blood

tion: resveratrol (3,40

[67, 154, 157]

NR repair.

orally [157].

[20]. However, when the regenerating axons reached the muscular end plates, they had to compete with the already existing axons coming from the locally injected embryonic foetal neurons [20, 140, 143, 144].

Some drugs have been administered to minimize MN apoptosis and improve NR regeneration: resveratrol (3,40 ,5-trihydroxystilbene) [145], riluzole (2-amino-6-trifluoromethoxybenzothiazole) [8, 69, 121], lithium [146, 147], minocycline [119], recombinant erythropoietin [118], FK506-tacrolimus [148–151], geldanamycin [152, 153], acamprosate [67, 154], ribavirin [154], N-acetyl cysteine [155] and glatiramer [156]. Some researchers have administered combinations such as acamprosate and ribavirin [154] or riluzole and GDNF [8]. The main advantage of acamprosate, ribavirin, and riluzole is that they can be administered orally [67, 154, 157].

Resveratrol has been added to the autologous NG culture for a week in the rat experimental C6 NRA and reimplantation model [145], finding that it improves axonal regeneration, Schwann cell migration and myelination and MN survival—69% surviving 8 weeks after NR repair.

In experimental brachial plexus avulsion (BPA) rat models, riluzole has been proved to improve MN survival, prolonging the time period at which reimplantation can be successful [65, 69, 101, 121]. If administered within 2 weeks post-avulsion, riluzole helps to keep 70% of the MNs [65, 69, 121] alive and minimizes the sensory hypersensitivity and allodynia [119]. Its maximum effect is achieved when combined with GDNF [8], and it can be administered orally [157].

In rat, experimental avulsion models and at doses used in the treatment of mood disorders, lithium improves neuronal survival, axonal regeneration and myelination, allowing an earlier and better functional recovery [146, 147]. One of its mechanisms of action is by increasing endogenous BDNF secretion [158]. Its effect on growing axon myelination starts 4 weeks post-NR reimplantation, reaching its pinnacle at 6 weeks and slowing down by 12 weeks [146].

Minocycline is a tetracycline derivative that inhibits glial proliferation [159]—a barrier against axonal and dendrite growth [160]—and decreases neuronal [161] and oligodendrocyte cell loss [120, 162, 163]. Minocycline can cross the blood–brain barrier and has anti-inflammatory properties [120]. In rats, it has been administered intraperitoneally and intrathecally, with better results through the latter route [106]. At low doses, minocycline has neuroprotective properties, but at high concentrations it is neurotoxic [164], among other reasons, because glial proliferation and Wallerian degeneration are a sine qua non for nerve regeneration [106].

Recombinant erythropoietin injected subcutaneously once a day for 3 days has shown neuroprotective properties in a rat NRA experimental model [118]. These neuroprotective properties are short lasting but can help to delay motor neuron apoptosis after NRA, increasing the period in which a NR reimplantation can be undertaken [118]. Recombinant erythropoietin seems to counteract the cytotoxic effect of glutamate, block free radicals, increase the release of neurotransmitters and decrease microglial activation [165]. The positive effects of recombinant erythropoietin are maximal when its administration is started within 96 hours (4 days) after NRA and reimplantation [118]. The side effects related with the administration of

Agent

Group

Mechanism

 of action

Administration

Motoneuron

Axonal

Observation

 Applied

Current human

to

clinical use

52 Treatment of Brachial Plexus Injuries

regeneration

survival

post-injury

motoneuron

axonal

regeneration

survival by

64.62% at

>4 weeks

> 1 week

> > Ribavirin

Drug

 Synthetic guanosine

Orally

Associated

Associated

 with

Can induce anemia

 Rat

 Hepatitis virus C

Acamprosate

accelerates

axonal

with

acamprosate

⇑

motoneuron

regeneration

survival by

>4 weeks

> 64.62% at

1 week

> N-acetyl cysteine

Glatiramer Table 1. NFs

(neurotrophic

 factors) and drugs used in nerve root

Drug

Immunomodulator

Subcutaneously

⇑

Reduction in

⇑ Risk of infection

Rat

 Multiple sclerosis

> and malignancy

Motoneuron

astrocyte

proliferation

survival but

NOT

quantified

reimplantation

 with their effects.

 Drug

 Stabilizes oxidative

Orally

Neuron

Facilitates

Vitamin C

Rat

 Mucolytic

counteracts

effects

 side

survival 26%

axonal

motor, 95%

regeneration

sensory

metabolism

antiviral properties

route

this drug—increase in erythrocyte production and a prothrombotic state—are not problematic because this drug is only administered for 3 days [118]. Perhaps administering this drug for a longer period of time could provide additional neuroprotective effects, but 3 days are enough to prolong the period in which a successful NR reimplantation can be performed [118].

A word of caution is to be said about the materials used to glue the peripheral NGs to the SC. Only Tisseel® causes no long-term histological reaction [180, 181], while other preparations available in the market (BioGlue®, Adherus®) induce local fibrous reaction with SC adherences and at times neurological sequelae [181]. BioGlue® when applied close or in contact with nervous tissues can create serious damages [182]. In rats, some researchers have used snake (Crotalus durissus terrificus) venom-derived fibrin glue and reported excellent results [183, 184].

Nerve Root Reimplantation in Brachial Plexus Injuries http://dx.doi.org/10.5772/intechopen.82431 55

On the other hand, conduits can be used to substitute autologous NGs. They have been extensively tried in peripheral nerve repairs [186, 187], but in NR reimplantation the data available are more limited [188, 189]. In peripheral nerve repair, these conduits have proved useful up to distances of 70 mm in length [37, 38, 190]. Certainly, the central-peripheral nervous tissue interface is a place in which autologous NFs provided by the autologous NGs play a pivotal role in regeneration of the reimplanted NR [69, 77, 89, 91–93]. Some researchers have tried nerve conduits enriched with BDNF that have had a good result in a rabbit experimental model [191]. In human clinical practice, there are currently no published

However, the applicability of all these studies is limited since they were generated with experimental animal models and with reimplantation immediately following the avulsion. On top of that, the regenerating capacities of the human nervous system are much less than that observed in research animals (the rat especially [73]), and the reimplantation of an avulsed NR has to be delayed weeks or even months until the patient is stabilized from other traumatic

Surgical techniques can be useful, particularly in complete BPA and with a delay between the injury and the surgical repair of no longer than 4 weeks [45]. Some significant problems are that MN apoptosis is greater as the time goes by [20, 27, 91, 93, 101–103] and that by 4 weeks, there is a dense scar around the BP as well as the avulsed NRs and in their intervertebral

The surgical approaches described can be summarized into posterior subscapular [192], lateral [193], anterolateral [194, 195] and single-stage combined anterior (first) and posterior

With the patient in the prone position, a longitudinal incision is made halfway between the spine and the scapula [39, 192, 196]. The trapezius muscle is sectioned transversally in the direction of its fibers. The rhomboid major and minor muscles are also divided following the direction of their fibers. The T1 transverse process is identified and removed with the aid of a drill. A section of the first rib is also removed. A laminectomy and facetectomy are needed to

lesions and when an adequate diagnosis and treatment strategy are well defined [111].

4. Surgical technique of human NR reimplantation

foramina that hinders any surgical manoeuvres [45, 74].

In clinical practice, fibrin glue from human origin is usually used [15, 30, 33, 45, 185].

reports [45, 74].

(second) [33].

4.1. Posterior subscapular approach

FK506-tacrolimus improved the amount of regenerating posterior NR axons penetrating the SC and reaching the posterior horn [151].

Acamprosate is a taurine analogue used to prevent relapse in alcoholic patients that acts as neuroprotective and accelerates axonal regeneration [154, 166].

Ribavirin is a nucleoside antimetabolite antiviral agent that blocks nucleic acid synthesis that is administered together with acamprosate to encourage axonal regeneration [154].

N-Acetyl cysteine administered intraperitoneally and intrathecally in rats enhances the rate of MN survival and facilitates regeneration in case of NR reimplantation [155].

Glatiramer is a polymer of L-alanine, L-glutamic acid, L-lysine and L-tyrosine that structurally resembles the myelin basic protein and that when administered daily reduces the gliosis and the avulsed MN synaptic stripping [156].

To summarize, in NRA reimplantation GDGF applied directly to the anterior SC—to the point where the motor rootlets go out—associated with oral riluzole provides the highest rate of MN survival and axonal regeneration [8]. For the dorsal root, CNTF [87] applied directly to the section of the posterior SC where the sensory rootlets get in combined with oral N-acetyl cysteine [155] allows maximal sensory neuron survival. Other agents could be added, such as oral minocycline [106, 120], tacrolimus [151] or recombinant erythropoietin [118, 165]to reduce the reactive glial proliferation that impairs the axonal regeneration. ISP should be administered subcutaneously to minimize astrocyte inhibition of axonal regeneration [126, 167]. The data are summarized in Table 1.

Another strategy has been to apply pluripotent cells at the SC avulsion site to improve MN survival and axonal regeneration. These have been particularly useful in minimizing neuronal apoptosis.  The human embryonic stem cells overexpressing human fibroblast growth factor 2 (FGG2) applied at the injury site improved MN survival and reduced the glial reactivity, thus improving the regenerating capacities [95]. However, it has unknown effectivity, only shown in animal experimental studies, and its application in the human being creates ethical issues.

Some researchers have found in vivo that a week time gap between NG harvest and its subsequent use in nerve repair improves the regenerating capacities [175] by increasing the number of Schwann cells and macrophages inside the NG [145, 176, 177] as well as by inducing the local GDNF release [145, 178, 179]. This is another possibility but difficult to use in clinical practice.

A word of caution is to be said about the materials used to glue the peripheral NGs to the SC. Only Tisseel® causes no long-term histological reaction [180, 181], while other preparations available in the market (BioGlue®, Adherus®) induce local fibrous reaction with SC adherences and at times neurological sequelae [181]. BioGlue® when applied close or in contact with nervous tissues can create serious damages [182]. In rats, some researchers have used snake (Crotalus durissus terrificus) venom-derived fibrin glue and reported excellent results [183, 184]. In clinical practice, fibrin glue from human origin is usually used [15, 30, 33, 45, 185].

On the other hand, conduits can be used to substitute autologous NGs. They have been extensively tried in peripheral nerve repairs [186, 187], but in NR reimplantation the data available are more limited [188, 189]. In peripheral nerve repair, these conduits have proved useful up to distances of 70 mm in length [37, 38, 190]. Certainly, the central-peripheral nervous tissue interface is a place in which autologous NFs provided by the autologous NGs play a pivotal role in regeneration of the reimplanted NR [69, 77, 89, 91–93]. Some researchers have tried nerve conduits enriched with BDNF that have had a good result in a rabbit experimental model [191]. In human clinical practice, there are currently no published reports [45, 74].

However, the applicability of all these studies is limited since they were generated with experimental animal models and with reimplantation immediately following the avulsion. On top of that, the regenerating capacities of the human nervous system are much less than that observed in research animals (the rat especially [73]), and the reimplantation of an avulsed NR has to be delayed weeks or even months until the patient is stabilized from other traumatic lesions and when an adequate diagnosis and treatment strategy are well defined [111].