# Modeling the Growth of Neurology Literature

• Hadagali, Gururaj S. (Department of Library and Information Science Karnataka University) ;
• Anandhalli, Gavisiddappa (Department of Library and Information Science Karnataka State Women’s University)
• Accepted : 2015.07.21
• Published : 2015.09.30

#### Abstract

The word ‘growth’ represents an increase in actual size, implying a change of state. In science and technology, growth may imply an increase in number of institutions, scientists, or publications, etc. The present study demonstrates the growth of neurology literature for the period 1961-2010. A total of 291,702 records were extracted from the Science Direct Database for fifty years. The Relative Growth Rate (RGR) and Doubling Time (Dt.) of neurology literature have been calculated, supplementing with different growth patterns to check whether neurology literature fits exponential, linear, or logistic models. The results of the study indicate that the growth of literature in neurology does not follow the linear, or logistic growth model. However, it follows closely the exponential growth model. The study concludes that there has been a consistent trend towards increased growth of literature in the field of neurology.

# 1. INTRODUCTION

One of the features of modern research in recent years has been the spectacular development of scientific discoveries and growth of knowledge, say Gupta et al. (2002). This has caused an unprecedented accumulation of information and has become a major concern for scientists and researchers (Meera & Sangam, 2010). Hence, there is a need to study the growth of scientific knowledge and its dynamics in every field of activity.

The word ‘growth ’ represents an increase in actual size, implying a change of state. In science and technolgy, growth may imply an increase in number of in stitutions, scientists, or publications, etc. Ravichandra Rao (1998) says that a change in the size of literature over a specific period of time is termed as ‘growth of literature. ’ One of the features of modern research in the twenty-first century has been the unprecedented and spectacular development in scientific inventions, discoveries, and the growth of knowledge. This has caused an unexpected accumulation of information (Gupta et al., 2002). Hence, there is a need to study this growth of knowledge and its dynamics. Price (1966 & 1975) was one of the pioneering researchers who studied the growth of science and found that the exponential model holds well with high accuracy in the majority of growth data of publications. The fitting of growth models, distributions, and curves to the data on exponentially growing literature and identifying the best fitting one to explain the growth of literature is an important aspect of growth study. The present study is aimed to study the growth of neurology literature published in the Science Direct database.

# 2. REVIEW OF LITERATURE

The understanding of the process of growth of knowledge in research specialties and its modeling has challenged bibliometricians and sociologists for a long time, say Gupta et al. (1997). Gilberts ’ (1978) work reveals the existing literature on the indicators of growth of knowledge in scientific specialties and lists many ways of measuring it. The analysis of Gupta et al. (1999) suggests that the growth of Indian physics literature follows a logistic model, while the growth of world physics literature is explained by the combination of logistic and power models.

Seetharam and Ravichandra Rao (1999) in their work compare trends in the growth of Food Science and Technology (FST) literature produced by CFTRI scientists, by food scientists in India, and by food scientists of the world, covering a period between 1950 and 1990. Further, the authors identify the best fitting growth models for actual and cumulative growth of data through various growth models. Different approaches are introduced by Gupta and Karisiddappa (2000) in their paper for studying the growth of scientific knowledge as reflected through publications and authors. The selected growth models are applied to the cumulative growth of publications and authors in theoretical population genetics from 1907-1980. It is concluded that the power model is observed to be the only model among the models studied which best explains the cumulative growth of publication and author counts in theoretical population genetics.

Karki et al. (2000) investigate Indian Organic Chemistry research activity during 1971-1989 using Chemical Abstracts. The authors conclude that the growth trends for India and world for organic chemistry follow the same patterns and the output in the three sub-fields is not going to saturate in the near future. Gupta et al. (2002) apply selected growth models to the growth of publications in six sub-disciplines of social sciences, namely economics, history, political science, psychology, and sociology in the world. The results show that the power model ( α>0, γ>1) followed by logistic models are best describing the cumulative growth of publications in all sub-disciplines. Both power and logistic models are applicable: the power model (as reflected in trend values of α1) and logistic model (as reflected in trend values of α2) in the case of cumulative growth of publications in history, political sciences, and psychology.
Tsay (2008) explores the characteristics of hydrogen energy literature from 1965-2005 based on the database of Science Citation Index Expanded (SCIE). The study reveals that the cumulative literature on hydrogen energy may be fitted relatively well by an exponential fit. Szydlowski and Krawiec (2009) present a description of knowledge more realistic than simple exponential growth. The study also reveals that the data on symbolic logic exhibit an exponential trend with some periodic oscillation. Ramakrishna (2009) examines the growth of references over the past fifteen years (1994-2008). The results show that the linear growth model provides better fits to the observed data, whereas the exponential model provided the poorest fit.
Sangam et al. (2010) study the growth and dynamics of Indian and Chinese publications in the field of liquid crystals research (1997-2006) by applying growth models as suggested by Egghe and Ravichandra Rao (1992). The authors conclude that these power and growth models are likely to be fully applicable in the growth of Indian, and linear, power, and growth models applicable in the growth of Chinese liquid crystals literature. Bouabid (2011) proposes a model which is proved to be suitable to represent observed citation distribution over time and to interestingly identify with accuracy when the major loss of citations happens. The model fits the observed data from Science Citation Index (SCI) according to R which is greater than 98.9 %. Zhao and Guan (2012) assess the dynamic associations between scientific activity and technological output. The authors use the simultaneous equations model to analyze the reciprocal dependence between science and technology. The result shows that there is no significant connection between R&D expenditures and actual practices of research in terms of publications.

# 3. OBJECTIVES OF THE STUDY

The specific objectives of the study are

1. to study the growth of neurology literature (RGR) and also compare the growth rate as reflected in the Science Direct database among the world, China, and India.
2. to examine the Doubling Time (Dt.) of the rology literature.
3. to analyze the fit of neurology literature for cumulative numbers of publications in terms of different models.

# 4. DATA AND METHODOLOGY

The dataset was collected from the Science Direct database for the period 1961-2010. A total of 291,702 records were received for fifty years. Science Direct is one of the most comprehensive database covering all subjects. Most of the research output on neurology is covered under the Science Direct Database. Hence, the same database is selected as a source for the present study. The keyword ‘neurology ’ has been used for extracting the number of records available in the said database. The retrieved records were examined, classified, and analyzed keeping the objectives in view. Further, the data is analyzed using MS Excel spreadsheet and SPSS software (15 version). Relative Growth Rate (RGR) and Doubling Time (Dt.) of neurology literature have been calculated, supplementing with different growth patterns to check whether the neurology literature is fit for exponential, linear, or logistic models.

Relative Growth Rate (RGR) and Doubling Time (Dt.)

The Relative Growth Rate (RGR) is the increase in number of articles / pages per unit of time. This definition is derived from the definition of relative growth rates in the study of growth analysis of individual plants and is effectively applied in the field of botany (Hunt, 1978 & 1982; Poorter & Garnier, 1996; Hoffmann & Poorter, 2002). The mean Relative Growth Rate (RGR) over the specific period of interval can be calculated from the following equation:

$1-2 \mathrm{R}=\frac{\log _{\mathrm{e} 2} \mathrm{W}-\log _{\mathrm{e} 1} \mathrm{W}}{2^{\mathrm{T}}-1^{\mathrm{T}}}$

Whereas

$1-2R$ = mean relative growth rate over the specific period of interval

$\log _{e 1} \mathrm{W}$ = log of initial number of articles

$\log _{e 2} \mathrm{W}$ = log of final number of articles after a specific period of interval

$2^T-1^T$ = the unit difference between the initial time and the final time

Doubling Time (Dt.)

There exists a direct equivalence between the relative growth rate and the doubling time (Bradford, 1934). If the number of articles / pages of a subject double during a given period then the difference between the logarithms of numbers at the beginning and end of this period must be logarithms of number 2. If natural logarithm is used this difference has a value of 0.693. Thus, the corresponding doubling time for each specific period of interval and for both articles and pages can be calculated by the formula;

$\text { Doubling Time (Dt.) }=\frac{0.693}{\mathrm{R}}$

# 5. RESULTS AND DISCUSSION

## 5.1. Year Wise Distribution of Literature (1961-2010)

Table 1 depicts the year wise distribution of papers in neurology literature. The world output in neurology literature is 286,001 (98.05 %) records and that of China is 3,730 (1.28 %), followed by India with 1,971 (0.68 %) records. A total of 291,702 records were extracted from the database for the period 1961-2010. It is observed that there is a steady growth of publications for world (except 1997) and China. A fluctuating trend was observed for India during the study period. An average of 5,720 papers were published per year at the global level, followed by China ’s average at 74 and India ’s average at 39. The maximum world contribution is observed during 2009 (20,656 publications) and those of China and India were published during 2010 (769 and 219, respectively). China took 24 years to achieve double digit numbers of publications, whereas India took twelve years to achieve the same. However, China took only 20 years to achieve three-digit numbers of publications but India took 33 years to achieve the same. The Relative Growth Rate (RGR) and Doubling Time (Dt.) of China, India, and world is calculated and presented in successive tables.

Table 1. Year-Wise Distribution of Literature (1961-2010)

 Sl. No. Year World India China Total No. of articles Percentage No. of articles Percentage No. of articles Percentage No. of articles Percentage 1 1961 400 0.14 5.00 0.26 0 0 405 0.14 2 1962 395 0.14 2.00 0.11 0 0 397 0.14 3 1963 473 0.17 4.00 0.21 0 0 477 0.17 4 1964 624 0.22 2.00 0.11 0 0 626 0.22 5 1965 709 0.25 2.00 0.11 1 0.03 712 0.25 6 1966 673 0.24 1.00 0.06 0 0 674 0.24 7 1967 783 0.28 0.00 0 1 0.03 784 0.27 8 1968 870 0.31 4.00 0.21 0 0 874 0.3 9 1969 926 0.33 6.00 0.31 0 0 932 0.32 10 1970 1,083 0.38 4.00 0.21 1 0.03 1,088 0.38 11 1971 1,169 0.41 5.00 0.26 3 0.09 1,177 0.41 12 1972 1,212 0.43 9.00 0.46 2 0.06 1,223 0.42 13 1973 1,351 0.48 10.00 0.51 1 0.03 1,362 0.47 14 1974 1,428 0.5 9.00 0.46 1 0.03 1,438 0.5 15 1975 1,682 0.59 12.00 0.61 0 0 1,694 0.59 16 1976 1,790 0.63 11.00 0.56 1 0.03 1,802 0.62 17 1977 1,846 0.65 11.00 0.56 0 0 1,857 0.64 18 1978 2,046 0.72 9.00 0.46 1 0.03 2,056 0.71 19 1979 2,168 0.76 10.00 0.51 4 0.11 2,182 0.75 20 1980 2,488 0.87 13.00 0.66 4 0.11 2,505 0.86 21 1981 2,839 1.00 18.00 0.92 3 0.09 2,860 0.99 22 1982 3,264 1.15 13.00 0.66 6 0.17 3,283 1.13 23 1983 3,535 1.24 15.00 0.77 6 0.17 3,556 1.22 24 1984 3,567 1.25 21.00 1.07 8 0.22 3,596 1.24 25 1985 3,962 1.39 18.00 0.92 17 0.46 3,997 1.38 26 1986 4,110 1.44 16.00 0.82 12 0.33 4,138 1.42 27 1987 4,708 1.65 25.00 1.27 13 0.35 4,746 1.63 28 1988 4,496 1.58 25.00 1.27 15 0.41 4,536 1.56 29 1989 4,852 1.7 19.00 0.97 16 0.43 4,887 1.68 30 1990 5,397 1.89 18.00 0.92 21 0.57 5,436 1.87 31 1991 5,696 2.00 25.00 1.27 22 0.59 5,743 1.97 32 1992 6,106 2.14 21.00 1.07 22 0.59 6,149 2.11 33 1993 5,708 2.00 30.00 1.53 27 0.73 5,765 1.98 34 1994 6,904 2.42 36.00 1.83 26 0.7 6,966 2.39 35 1995 6,842 2.4 36.00 1.83 32 0.86 6,910 2.37 36 1996 7,442 2.61 43.00 2.19 29 0.78 7,514 2.58 37 1997 11,698 4.1 44.00 2.24 39 1.05 11,781 4.04 38 1998 7,847 2.75 50.00 2.54 39 1.05 7,936 2.73 39 1999 8,207 2.87 39.00 1.98 68 1.83 8,314 2.86 40 2000 8,964 3.14 62.00 3.15 56 1.51 9,082 3.12 41 2001 8,692 3.04 45.00 2.29 69 1.85 8,806 3.02 42 2002 9,388 3.29 65.00 3.30 82 2.2 9,535 3.27 43 2003 11,374 3.98 71.00 3.61 131 3.52 11,576 3.97 44 2004 12,586 4.41 93.00 4.72 153 4.11 12,832 4.4 45 2005 15,115 5.29 89.00 4.52 203 5.45 15,407 5.29 46 2006 15,153 5.3 149.00 7.56 271 7.27 15,573 5.34 47 2007 16,366 5.73 163.00 8.27 420 11.27 16,949 5.82 48 2008 17,183 6.01 165.00 8.38 529 14.19 17,877 6.13 49 2009 20,656 7.23 209.00 10.61 606 16.25 21,471 7.37 50 2010 19,228 6.73 219.00 11.12 769 20.62 20,216 6.94 Total 286,001 (98.05) 100 1,971 (0.68) 100.00 3,730 (1.28) 100 291,702 (100) 100

Table 2. Descriptive Statistics of Neurology Literature

 Descriptive Statistics World India China Mean 5720 39.42 74.6 Standard Error 766.51 7.5276 23.212 Standard Deviation 5420 53.228 164.13 Range 20261 219 769 Minimum 395 0 0 Maximum 20656 219 769 Confidence Level (95.0%) Kurtosis Skewness 1,540.4 0.635 1.205 15.127 4.098 2.162 46.646 8.622 2.976

## 5.2. Relative Growth Rate (RGR) and Doubling Time (Dt.) (India)

The Relative Growth Rate (RGR) and Doubling Time (Dt.) of publications in India have been presented in Table 3. It indicates that the value of Relative Growth Rate (RGR) of publications decreased from 0.337 in the year 1962 to 0.119 in 2010. Simultaneously, the values of Doubling Time (Dt.) increased from 2.056 in 1962 to 5.823 in 2010. It is evident from the study that research in the field of neurology in India has increased over a period of time.

Table 3. Relative Growth Rate (RGR) and Doubling Time (Dt.) (India)

 Sl. No. Year publications No. of Cumulative publications no. of W 1 W 2 RGR Dt. (P) 1 1961 05 05 1.609 2 1962 02 07 1.609 1.946 0.337 2.056 3 1963 04 11 1.946 2.398 0.452 1.533 4 1964 02 13 2.398 2.565 0.167 4.149 5 1965 02 15 2.565 2.708 0.143 4.846 6 1966 01 16 2.708 2.772 0.064 10.828 7 1967 00 16 2.772 2.772 0.000 00.00 8 1968 04 20 2.772 2.995 0.223 3.107 9 1969 06 26 2.995 3.258 0.263 2.635 10 1970 04 30 3.258 3.401 0.143 4.846 11 1971 05 35 3.401 3.555 0.154 4.500 12 1972 09 44 3.555 3.784 0.229 3.026 13 1973 10 54 3.784 3.988 0.204 3.397 14 1974 09 63 3.988 4.143 0.155 4.471 15 1975 12 75 4.143 4.317 0.174 3.982 16 1976 11 86 4.317 4.454 0.137 5.058 17 1977 11 97 4.454 4.574 0.120 5.775 18 1978 09 106 4.574 4.663 0.089 7.786 19 1979 10 116 4.663 4.753 0.090 7.700 20 1980 13 129 4.753 4.859 0.106 6.537 21 1981 18 147 4.859 4.990 0.131 5.290 22 1982 13 160 4.99 5.075 0.085 8.153 23 1983 15 175 5.075 5.164 0.089 7.786 24 1984 21 196 5.164 5.278 0.114 6.078 25 1985 18 214 5.278 5.366 0.088 7.875 26 1986 16 230 5.366 5.438 0.072 9.625 27 1987 25 255 5.438 5.541 0.103 6.728 28 1988 25 280 5.541 5.634 0.093 7.451 29 1989 19 299 5.634 5.700 0.066 10.500 30 1990 18 317 5.7 5.759 0.059 11.745 31 1991 25 342 5.759 5.835 0.076 9.118 32 1992 21 363 5.835 5.894 0.059 11.745 33 1993 21 384 5.894 5.950 0.056 12.375 34 1994 30 414 5.950 6.026 0.076 9.118 35 1995 36 450 6.026 6.109 0.083 8.349 36 1996 43 493 6.109 6.200 0.091 7.615 37 1997 44 537 6.200 6.200 0.086 8.058 38 1998 50 587 6.286 6.375 0.089 7.786 39 1999 39 626 6.375 6.439 0.064 10.828 40 2000 62 688 6.439 6.534 0.095 7.294 41 2001 45 733 6.534 6.597 0.063 11.000 42 2002 65 798 6.597 6.682 0.085 8.153 43 2003 71 869 6.682 6.767 0.085 8.153 44 2004 93 962 6.767 6.869 0.102 6.794 45 2005 89 1,051 6.869 6.957 0.088 7.875 46 2006 149 1,200 6.957 7.090 0.133 5.210 47 2007 163 1,363 7.090 7.217 0.127 5.456 48 2008 165 1,528 7.217 7.332 0.115 6.026 49 2009 209 1,737 7.332 7.459 0.127 5.456 50 2010 219 1,956 7.459 7.578 0.119 5.823

## 5.3. Relative Growth Rate (RGR) and Doubling Time (Dt.) (China)

The Relative Growth Rate (RGR) and Doubling Time (Dt.) of publications in China have been presented in Table 4. The study reveals that the value of RGR of publications decreased from 0.693 in 1967 to 0.231 in the year 2010. However, the values of Doubling Time (Dt.) increased from 1.00 in 1967 to 3.00 in 2010. It is also observed from the study that research in the field of neurology in China has increased over a period of time.

Table 4. Relative Growth Rate (RGR) and Doubling Time (Dt.) (China)

 Sl. No. Year publications No. of Cumulative publications no. of W 1 W 2 RGR Dt. (P) 1 1961 00 00 00 2 1962 00 00 00 00 00 00 3 1963 00 00 00 00 00 00 4 1964 00 00 00 00 00 00 5 1965 01 01 00 00 00 00 6 1966 00 01 00 00 00 00 7 1967 01 02 00 0.693 0.693 1.00 8 1968 00 02 0.693 0.693 00 00 9 1969 00 02 0.693 0.693 00 00 10 1970 01 03 0.693 1.098 0.405 1.711 11 1971 03 06 1.098 1.791 0.693 1.00 12 1972 02 08 1.791 2.079 0.288 2.406 13 1973 01 09 2.079 2.197 0.118 2.406 14 1974 01 10 2.197 2.302 0.105 6.600 15 1975 00 10.000 2.302 2.302 00 00 16 1976 01 11.000 2.302 2.397 0.095 7.294 17 1977 00 11.000 2.397 2.397 00 00 18 1978 01 12.000 2.397 2.485 0.088 7.875 19 1979 04 16.000 2.485 2.772 0.287 2.414 20 1980 04 20.000 2.772 2.995 0.223 3.107 21 1981 03 23.000 2.995 3.135 0.140 4.950 22 1982 06 29.000 3.135 3.367 0.232 2.987 23 1983 06 35.000 3.367 3.555 0.188 3.686 24 1984 08 43.000 3.555 3.761 0.206 3.364 25 1985 17 60.000 3.761 4.094 0.333 2.081 26 1986 12 72.000 4.094 4.276 0.182 2.807 27 1987 13 85.000 4.276 4.442 0.166 4.174 28 1988 15 100.000 4.442 4.605 0.163 4.251 29 1989 16 116.000 4.605 4.753 0.148 4.682 30 1990 21 137.000 4.753 4.919 0.166 4.174 31 1991 22 159.000 4.919 5.068 0.149 4.651 32 1992 22 181.000 5.068 5.198 0.130 5.330 33 1993 27 208.000 5.198 5.337 0.139 4.985 34 1994 26 234.000 5.337 5.455 0.118 5.872 35 1995 32 266.000 5.455 5.583 0.128 5.414 36 1996 29 295.000 5.583 5.687 0.104 6.663 37 1997 39 334.000 5.687 5.811 0.124 5.588 38 1998 39 373.000 5.811 5.921 0.110 6.300 39 1999 68 441.000 5.921 6.089 0.168 4.125 40 2000 56 497.000 6.089 6.208 0.119 5.823 41 2001 69 566.000 6.208 6.338 0.130 5.330 42 2002 82 648.000 6.338 6.474 0.136 5.095 43 2003 131 779.000 6.474 6.658 0.184 3.766 44 2004 153 932.000 6.658 6.837 0.179 3.871 45 2005 203 1135.000 6.837 7.034 0.197 3.517 46 2006 271 1406.000 7.034 7.248 0.214 3.238 47 2007 420 1826.000 7.248 7.509 0.261 2.655 48 2008 529 2355.000 7.509 7.764 0.255 2.717 49 2009 606 2961.000 7.764 7.993 0.229 3.026 50 2010 769 3730.000 7.993 8.224 0.231 3.000

# 6. GROWTH MODELS OF NEUROLOGY LITERATURE

The authors briefly introduce three growth models, viz. the Linear Growth Model, the Exponential Growth Model, and the Logistic Growth Model, which are generally used in the literature for analyzing the growth of literature in different subjects.

## 6.1. Linear Growth Model

The Linear Growth Model describes growth to be constant or similar from year to year. Thus, a graphic representation of the yearly data accumulated would be a straight line.

Hypothesis 1

The growth of publications in the field of neurology literature follows the Linear Growth Model.

Testing of Hypothesis

To find out the growth pattern in the field of neurology literature, publications over the last fifty years (1961-2010) were considered as a sample for the analysis in order to fit the data to test whether the growth of literature in neurology follows the Linear Growth pattern or not. The expected numbers of publications (y) or (p) were computed using the following formula:

$Y=a+b^x$
Where a and b are constants
X is the unit of time

Inference

The results of a Chi-Square test of goodness of fit

Fig. 1 Doubling time of Neurology literature

Table 5. Fit into Linear Growth of Neurology Literature

 X Year Observed publications no. of Y (f) XY X2 Expected publications no. of Y= a+b P x f-p (f-p)2 $\frac{(f-p)^{2}}{p}$ 1 1961 405 405 1 -2740.1 3145.1 9,891,654 -3610 2 1962 397 794 4 -2390.2 2787.2 7,768,484 -3250.1 3 1963 477 1,431 9 -2040.3 2517.3 6,336,799 -3105.8 4 1964 626 2,504 16 -1690.4 2316.4 5,365,709 -3174.2 5 1965 712 3,560 25 -1340.5 2052.5 4,212,756 -3142.7 6 1966 674 4,044 36 -990.6 1664.6 2,770,893 -2797.2 7 1967 784 5,488 49 -640.7 1424.7 2,029,770 -3168.1 8 1968 874 6,992 64 -290.8 1164.8 1,356,759 -4665.6 9 1969 932 8,388 81 59.1 872.9 761,954 12892.6 10 1970 1,088 10,880 100 409 679 461,041 1127.24 11 1971 1,177 12,947 121 758.9 418.1 174,808 230.343 12 1972 1,223 14,676 144 1108.8 114.2 13,042 11.7619 13 1973 1,362 17,706 169 1458.7 -96.7 9,351 6.41043 14 1974 1,438 20,132 196 1808.6 -370.6 137,344 75.9396 15 1975 1,694 25,410 225 2158.5 -464.5 215,760 99.9584 16 1976 1,802 28,832 256 2508.4 -706.4 499,001 198.932 17 1977 1,857 31,569 289 2858.3 -1001.3 1,002,602 350.769 18 1978 2,056 37,008 324 3208.2 -1152.2 1,327,565 413.804 19 1979 2,182 41,458 361 3558.1 -1376.1 1,893,651 532.209 20 1980 2,505 50,100 400 3908 -1403 1,968,409 503.687 21 1981 2,860 60,060 441 4257.9 -1397.9 1,954,124 458.941 22 1982 3,283 72,226 484 4607.8 -1324.8 1,755,095 380.897 23 1983 3,556 81,788 529 4957.7 -1401.7 1,964,763 396.305 24 1984 3,596 86,304 576 5307.6 -1711.6 2,929,575 551.958 25 1985 3,997 99,925 625 5657.5 -1660.5 2,757,260 487.364 26 1986 4,138 107,588 676 6007.4 -1869.4 3,494,656 581.725 27 1987 4,746 128,142 729 6357.3 -1611.3 2,596,288 408.395 28 1988 4,536 127,008 784 6707.2 -2171.2 4,714,109 702.843 29 1989 4,887 141,723 841 7057.1 -2170.1 4,709,334 667.319 30 1990 5,436 163,080 900 7407 -1971 3,884,841 524.482 31 1991 5,743 178,033 961 7756.9 -2013.9 4,055,793 522.863 32 1992 6,149 196,768 1024 8106.8 -1957.8 3,832,981 472.811 33 1993 5,765 190,245 1089 8456.7 -2691.7 7,245,249 856.747 34 1994 6,966 236,844 1156 8806.6 -1840.6 3,387,808 384.69 35 1995 6,910 241,850 1225 9156.5 -2246.5 5,046,762 551.167 36 1996 7,514 270,504 1296 9506.4 -1992.4 3,969,658 417.577 37 1997 11,781 435,897 1369 9856.3 1924.7 3,704,470 375.848 38 1998 7,936 301,568 1444 10206.2 -2270.2 5,153,808 504.968 39 1999 8,314 324,246 1521 10556.1 -2242.1 5,027,012 476.219 40 2000 9,082 363,280 1600 10906 -1824 3,326,976 305.059 41 2001 8,806 361,046 1681 11255.9 -2449.9 6,002,010 533.232 42 2002 9,535 400,470 1764 11605.8 -2070.8 4,288,213 369.489 43 2003 11,576 497,768 1849 11955.7 -379.7 144,172 12.0589 44 2004 12,832 564,608 1936 12305.6 526.4 277,097 22.518 45 2005 15,407 693,315 2025 12655.5 2751.5 7,570,752 598.218 46 2006 15,573 716,358 2116 13005.4 2567.6 6,592,570 506.91 47 2007 16,949 796,603 2209 13355.3 3593.7 1.30E+07 967.008 48 2008 17,877 858,096 2304 13705.2 4171.8 1.70E+07 1269.88 49 2009 21,471 1,052,079 2401 14055.1 7415.9 5.50E+07 3912.86 50 2010 20,216 1,010,800 2500 14405 5811 3.40E+07 2344.17

a = -3,090, b = 349.9, X = 10,094.5
For India: a= -33.25, b= 2.85, X = 408.399
For China: a=-108.9, b= 7.199, X = 2,982.08

indicated that the calculated Chi-Square value (X = 10,094.5) is much higher than the critical Chi-Square value of 31.41 for 49 degrees of freedom ( df ) at 0.05 (5%) level of significance. Hence, Hypothesis 1 has been rejected and it is concluded that the growth of literature in neurology does not follow the Linear Growth Model. Similar Growth Models have also been calculated for China and India. In both cases the calculated Chi-Square values (X = 408.399 for India, X = 2,982.08 for China) are much more than the critical Chi-Square value of 31.41 for 49 degrees of freedom ( df ) at 0.05 (5%) level of significance. In both cases the growth of literature in neurology does not follow the Linear Growth Model. The application of the Linear Growth Model in terms of R (0.854) is shown in Fig. 2. The fit statistics indicate a poor fit for the Linear Growth Model in the data sets. A graphical presentation of observed and estimated data values obtained is also shown in Fig. 2.

## 6.2. Exponential Growth Model

The Exponential Growth Model describes an unlimited exponential growth. This model not only provides a rate of growth (the exponential parameter) but also the rate at which the size of the literature doubles, and its doubling time. The exponential growth has been linked to compound interest.

Hypothesis 2

The growth of publications in the field of neurology literature better fit the Exponential Growth Model.

Testing of Hypothesis

In order to fit the data to test whether the growth of literature in neurology follows the exponential growth pattern or not, the expected number of publications (y) were computed using the following formula:

$Y=K+ab^x$
Where a and b are constants
$K$= is the asymptote or the upper limit
$X$ is the unit of time

Fig. 2 Linear growth pattern of neurology literature

Inference

The results of a Chi-Square test of goodness of fit indicated that the calculated Chi-Square value is (X = 3,631.96), higher than the critical Chi-Square value of 31.41 for 49 degrees of freedom ( $df$ ) at 0.05 level of significance. Hence, Hypothesis 2 has been rejected and it is concluded that the growth of literature in neurology does not exactly follow the Exponential Growth Model. The Exponential Growth model was also applied for China and India. In both cases the calculated Chi-Square value (X = 100.9477 for India, and X = -5,017.79 for China) is greater than the critical Chi-Square value of 31.41 for 49 degrees of freedom ( df ) at 0.05 (5%) level of significance. In both cases, the growth of literature in neurology does not exactly follow the Exponential Growth Model. However, it nearly follows this growth model.

However, the application of the Exponential Growth Model in terms of R (0.984) is shown in Fig. 3.

Table 6. Fit into Exponential Growth of Neurology Literature

 X Year Observed publications no. of Y (f) Expected no. of publication Y=K+abx f-p (f-p)2 $\frac{(f-p)^{2}}{p}$ 1 1961 405 273.27 131.73 17,354 63.505 2 1962 397 357.12 39.883 1,590.7 4.4542 3 1963 477 445.31 31.694 1,004.5 2.2557 4 1964 626 538.06 87.941 7,733.7 14.373 5 1965 712 635.61 76.39 5,835.4 9.1807 6 1966 674 738.21 -64.21 4,122.9 5.5849 7 1967 784 846.12 -62.12 3,858.5 4.5603 8 1968 874 959.61 -85.61 7,328.8 7.6373 9 1969 932 1,079 -147 21,601 20.02 10 1970 1,088 1,204.5 -116.5 13,575 11.27 11 1971 1,177 1,336.5 -159.5 25,455 19.045 12 1972 1,223 1,475.4 -252.4 63,712 43.183 13 1973 1,362 1,621.5 -259.5 67,322 41.519 14 1974 1,438 1,775.1 -337.1 113,618 64.008 15 1975 1,694 1,936.6 -242.6 58,869 30.398 16 1976 1,802 2,106.5 -304.5 92,748 44.029 17 1977 1,857 2,285.3 -428.3 183,401 80.254 S1= 17,522 18 1978 2,056 2,473.2 -417.2 174,062 70.379 19 1979 2,182 2,670.9 -488.9 239,011 89.487 20 1980 2,505 2,878.8 -373.8 139,723 48.535 21 1981 2,860 3,097.5 -237.5 56,387 18.204 22 1982 3,283 3,327.4 -44.44 1,974.8 0.5935 23 1983 3,556 3,569.3 -13.32 177.37 0.0497 24 1984 3,596 3,823.7 -227.7 51,853 13.561 25 1985 3,997 4,091.3 -94.27 8,886.6 2.1721 26 1986 4,138 4,372.7 -234.7 55,070 12.594 27 1987 4,746 4,668.6 77.37 5,986.1 1.2822 28 1988 4,536 4,979.9 -443.9 197,051 39.569 29 1989 4,887 5,307.3 -420.3 176,639 33.282 30 1990 5,436 5,651.6 -215.6 46,485 8.2251 31 1991 5,743 6,013.7 -270.7 73,299 12.189 32 1992 6,149 6,394.6 -245.6 60,324 9.4336 33 1993 5,765 6,795.2 -1,030 1E+06 156.18 34 1994 6,966 7,216.5 -250.5 62,748 8.6951 S2= 72,401 35 1995 6,910 7,659.6 -749.6 561,901 73.359 36 1996 7,514 8,125.6 -611.6 374,094 46.039 37 1997 11,781 8,615.8 3,165.2 1E+07 1162.8 38 1998 7,936 9,131.3 -1,195 1E+06 156.46 39 1999 8,314 9,673.5 -1,359 2E+06 191.05 40 2000 9,082 10,244 -1,162 1E+06 131.74 41 2001 8,806 10,843 -2,037 4E+06 382.82 42 2002 9,535 11,474 -1,939 4E+06 327.74 43 2003 11,576 12,138 -561.6 315,402 25.986 44 2004 12,832 12,835 -3.338 11.145 0.0009 45 2005 15,407 13,569 1,837.8 3E+06 248.92 46 2006 15,573 14,341 1,232 2E+06 105.84 47 2007 16,949 15,153 1,796.3 3E+06 212.94 48 2008 17,877 16,006 1,870.6 3E+06 218.6 49 2009 21,471 16,904 4,566.6 2E+07 33.7 50 2010 20,216 17,849 2,367.3 6E+06 313.97 S3= 201,779 3,631.96

The fit statistics indicate that it nearly follows the Exponential Growth Model in the data sets. A graphical presentation of observed and estimated data values obtained is also shown in Fig. 3.

Fig. 3 Expontial Growth Pattern of Neurology Literature

## 6.3. Logistic Growth Model

Hypothesis 3

The growth of publications in the field of neurology literature follows the Logistic Growth Model.

Testing of Hypothesis

In order to fit the data to test whether the growth of literature in neurology follows the logistic growth pattern or not, the expected number of publications (y) were computed using the following formula:

1/Y= K+ab

Where a and b are constants
K= is the asymptote or the upper limit
X is the unit of time

Inference

The results of the Chi-Square test of goodness of fit show that the calculated Chi-Square value is ($X^2$ = 5,821.7), much higher than the critical Chi-Square value of 31.41 for 49 degrees of freedom ( $df$ ) at .05 level of significance. Hence, Hypothesis 3 has been rejected and it is concluded that the growth of literature in neurology does not follow the Logistic Growth Model.

The Logistic Growth model was also applied for China and India. In both cases the calculated Chi-Square value ($X^2$ = 199.669504 for India, $X^2$ = -89,291.47204 for China) is much greater than the critical Chi-Square value of 31.41 for 49 degrees of freedom ( $df$ ) at 0.05 (5%) level of significance. In both cases the growth of literature in neurology does not follow the Logistic Growth Model.

# 7. CONCLUSION

The bibliometric technique is considered as the most powerful technique for conducting such quantitative studies in this direction. An attempt was made in the present study to measure the trends in various aspects of published literature in the field of neurology literature.

The study is based on 291,702 research papers published between 1961-2010 as reflected in Science Direct, which is one of the most comprehensive databases covering all subjects. The data were collected, tabulated, and analyzed. The study reveals some factual factorial data through bibliometric analysis. Research articles have been analyzed for finding the year wise trend, Relative Growth Rate, Doubling Time, and examining the different types of growth rate models. The outcome of the present study shows that there is a steady growth of publications for world (except 1997) and China, and a fluctuating trend was observed for India during the study period. Averages of 5,720 papers were published per year at the global level, followed by China ’s average which is 74 and India ’s average at 39. The maximum world contribution is observed during 2009 (20,656 publications) and those of China and India were published during 2010. China took 24 years to achieve double digit numbers of publications, whereas India took twelve years to achieve the same. The research in the field of neurology in India and China has increased over a period of time. The growth of literature in neurology does not follow either the Linear Growth Model or Logistic Growth Model. However, it nearly follows the Expo nential Growth Model. The study concludes that there has been a consistent trend towards increased growth of literature in the field of neurology.

Table 7. Fit into Logistic Growth of Model of Neurology Literature

 X Year Y 1/Y Expected no. of publications 1/Y=K+abx f-p (f-p)2 $\frac{(f-p)^{2}}{p}$ 1 1961 405 0.00247 469.09 -64.0894 4,107.44948 8.756219 2 1962 397 0.00252 516.22 -119.22 14,213.31824 27.53347 3 1963 477 0.0021 567.97 -90.9688 8,275.322192 14.57003 4 1964 626 0.0016 624.77 1.234815 1.524767453 0.002441 5 1965 712 0.0014 687.07 24.92833 621.4217341 0.90445 6 1966 674 0.00148 755.39 -81.3875 6,623.919766 8.768903 7 1967 784 0.00128 830.25 -46.2497 2,139.03512 2.576376 8 1968 874 0.00114 912.24 -38.2347 1,461.895382 1.602543 9 1969 932 0.00107 1,001.96 -69.9592 4,894.290061 4.88472 10 1970 1,088 0.00092 1,100.08 -12.0806 145.9408986 0.132664 11 1971 1,177 0.00085 1,207.30 -30.2974 917.9336117 0.760321 12 1972 1,223 0.00082 1,324.35 -101.349 10,271.5322 7.755913 13 1973 1,362 0.00073 1,452.01 -90.012 8,102.16351 5.579956 14 1974 1,438 0.0007 1,591.10 -153.102 23,440.37362 14.73216 15 1975 1,694 0.00059 1,742.47 -48.468 2,349.148287 1.348173 16 1976 1,802 0.00055 1,906.99 -104.985 11,021.87541 5.779739 17 1977 1,857 0.00054 2,085.55 -228.553 52,236.28849 25.04674 S1= 0.02076 18 1978 2,056 0.00049 2,279.08 -223.083 49,766.23102 21.83607 19 1979 2,182 0.00046 2,488.50 -306.495 93,939.25715 37.74942 20 1980 2,505 0.0004 2,714.70 -209.697 43,973.00579 16.19812 21 1981 2,860 0.00035 2,958.58 -98.5786 9,717.739615 3.284597 22 1982 3,283 0.0003 3,220.99 62.01099 3,845.363017 1.193845 23 1983 3,556 0.00028 3,502.72 53.27738 2,838.479262 0.810364 24 1984 3,596 0.00028 3,804.50 -208.496 43,470.7656 11.42615 25 1985 3,997 0.00025 4,126.93 -129.928 16,881.31098 4.090527 26 1986 4,138 0.00024 4,470.51 -332.512 110,564.1821 24.73188 27 1987 4,746 0.00021 4,835.59 -89.5941 8,027.100512 1.660003 28 1988 4,536 0.00022 5,222.35 -686.347 471,072.7936 90.20327 29 1989 4,887 0.0002 5,630.75 -743.747 553,159.502 98.2391 30 1990 5,436 0.00018 6,060.55 -624.547 390,059 64.3603 31 1991 5,743 0.00017 6,511.26 -768.26 590,223 90.64654 32 1992 6,149 0.00016 6,982.14 -833.142 694,125 99.41437 33 1993 5,765 0.00017 7,472.18 -1707.18 2,914,461 390.0416 34 1994 6,966 0.00014 7,980.08 -1014.08 1,028,368 128.8668 S2= 0.00452 35 1995 6,910 0.00014 8,504.30 -1594.3 2,541,791 298.8831 36 1996 7,514 0.00013 9,043.00 -1529 2,337,849 258.5257 37 1997 11,781 8.50E-05 9,594.13 2186.871 4,782,405 498.472 38 1998 7,936 0.00013 10,155.40 -2219.4 4,925,725 485.0352 39 1999 8,314 0.00012 10,724.30 -2410.34 5,809,753 541.7351 40 2000 9,082 0.00011 11,298.40 -2216.36 4,912,247 434.7753 41 2001 8,806 0.00011 11,874.70 -3068.74 9,417,189 793.0436 42 2002 9,535 0.0001 12,450.80 -2915.75 8,501,603 682.8185 43 2003 11,576 8.60E-05 13,023.60 -1447.64 2,095,662 160.9122 44 2004 12,832 7.80E-05 13,590.70 -758.732 575,674 42.35783 45 2005 15,407 6.50E-05 14,149.50 1257.547 1,581,424 111.7657 46 2006 15,573 6.40E-05 14,697.40 875.6138 766,699 52.1657 47 2007 16,949 5.90E-05 15,232.30 1716.694 2,947,039 193.4729 48 2008 17,877 5.60E-05 15,752.20 2124.788 4,514,724 286.6089 49 2009 21,471 4.70E-05 16,255.40 5215.646 27,202,964 1,673.477 50 2010 20,216 4.90E-05 16,740.20 3475.753 12,080,859 721.6655 S3= 0.00144

For China: a= 0.5924, b= 0.929, K= 0.03009, X = -89,291.47204

For India: a= 0.5113, b=0.9077, K = 0.0025, X = 199.669504

Table 8. Growth Models of Neurology Literature (R value)

 Growth models World China India Remark Linear 0.826 0.408 0.609 Not fit Exponential 0.984 0.861 0.765 Not fit Logistic 0.957 0.721 0.653 Not fit

Fig. 4 Logistic Growth Model

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