Applied Mathematics, 2011, 2, 904-907
doi:10.4236/am.2011.27121 Published Online July 2011 (http://www.SciRP.org/journal/am)
Research of Neuron Growth Prediction and Influence of Its
Geometric Configuration*
Tao Sun, Liang Lin, Qiaoyu Huang
College of Science , Guilin University of Technolog y, Guilin, Ch ina
Received May 6, 2011; revised May 25, 2011; accepted May 28, 2011
Abstract
The neuron growth will bring series variation to the neuron characteristics of geometric configuration. Espe-
cially the growth of dendrite and axon can obviously change the space characteristic and geometric charac-
teristic of neuron. This article is to build the prediction model of neuron growth through knowing the statis-
tics rules of neuron geometric characteristics, better imitate the neuron growth, and clearly analyze the
growth influence of geometric configuration.
Keywords: Neuron, Growth Prediction, Geometric Configuration
1. Introduction
Neuron space geometric configuration research of is one
important project of Human Brain Project (HBP). As the
basic brain unit, there have many elements in neuron
structure and function. Neuron geometric configuration
characteristic and electric physical property are the two
importance. Electrical characteristics include different po-
tential issue mode of neuron. Geometric characteristics
involve neuron space conformation, specifically dendrites
to receive information, somas to manage information and
axons to come out information. With regard to the hot re-
search of geometric characteristic, different experts place
extra emphasis on different index to describe the morpho-
logical characteristic of neurons. In the Research of Neuron
Typological Classification and Questions Identification [1],
we have classified the relatively stable neuron at normal
intervals through geometric configuration characteristics
and got the better effects. However, the dendrite and axon
growth of neurons are various with the passes of time. This
article will point at the neuron growth prediction and ana-
lyze these morphological changes to ensure the geometric
characteristics effects.
2. Neuron Growth Prediction
The variation of neuron growth reflects in the soma area
and axon length. Moreover, it is also the growth process
from one soma to the tree dendrite gradually. The data
information provide from Neuronmorpho.org [2] do not
arrange follow the time regularity. However, the present
data is only the single neuron form without the growth
process record. In addition, if we search for the growth
regulations that we need to start from various neuron
morphological characteristics. Especially analyze from
the given microcosmic statistic of each room and bifur-
cation such as length, local branch angle, local dip angle
and other geometric characteristics.
As we know, there will have a new bifurcation to
growth with once neuron growth. The local branch angle,
local dip angle and other geometric characteristics of
different types of neurons, there need to satisfy the de-
terminate statistics regulations. If we can find the dis-
tributed regularity about the neuron crotch, it will be
possible to take the advantage of stochastic simulation to
create the correct regulation of growth direction, length
and so on. Imitate the entire growth process of neuron
growth to reach the variety prediction of neuron modal.
Here we not only point at regulation abstraction of
neuron growth but also research the physiological proc-
ess of neuron structure, then to do the mechanism-based
study of neuron structure.
2.1. Theory Research
In the conference [3], based on test description, take the
hypothalamus neuron of rat, and continuously observe
the change regulation of neuron somas diameter, axon
*Supported by the Innovation Project of Guangxi Graduate Education
(Grant No. 2011105960202M31)

T. SUN ET AL.905
length and numbers. Through the observation in the cul-
ture solution, we can find the dispersed hypothalamus
neurons adherences in 3 hours with the shape of round-
ness or egg. After 12 hours, the cells aggregate to cluster
and disperse growth at the same time. After 24 hours, the
cells will change into triangle or polygon with special
soma enation. After 36 hours growth, the shape become
clearly with enation. After 48 hours, the visible soma can
send out several tiny dendrites. After 3 days, the growth
speed of dendrite increase every day. After 6 days, there
will have thick axon connection among soma clusters
with clear-cut neuron. Moreover, the soma is fullness
with roundness or fusiform shape. On the seventh day,
the growth of neuron soma and dendrite length will reach
the peak value. On the tenth day, the vacuoles will ap-
pear in the soma and the dendrite is shrinking. Experi-
ments shows, cultivate rat hypothalamus (CRH) growth
the most fast from the third day to the sixth day. During
the seventh day to the tenth day, the neuron number, so-
ma diameter, dendrite length and CRH coloration
strength reach the peak. After the twelfth day, part neu-
ron appears back change, the somas become shrinking,
the rounding glow is fading, the number is reducing and
the coloration is weakening.
From the above data, we can predict the growth varia-
tion of neuron. During the growth process, the growth
rate from slow to fast and then gradually slow to stop.
Moreover, the neuron has the process from small to large
then to the last shrink. The predict growth curve is Fig-
ure 1.
2.2. Growth Imitation Predicti on
In order to achieve the computer imitation of neuron
growth, we can discrete the growth time. During each
section of growth period, all the termination point will
appear fixed rate growth. The offspring of termination
could be one or two then will appear the branch growth.
This kind of growth occurrence time suppose as the
Figure 1. Growth cycle curve of neuron.
primary time of growth period. While in the computer
imitation, the growth can also predict as:
 In the system, only consider each level growth of
branch direction, diverge and length bout the motor
neuron but ignore the dendrite diameter, soma di-
ameter change during the growth, there things cannot
be ignored while analyzing.
 The characteristics of neuron growth direction and
length need to satisfy the normality distribute random.
 The neurons always grow in the imitation period
without limitation.
 In once growth, the characteristic that has room will
not change (length, direction). Moreover, the external
surface rooms grow the filial generation room.
Here we chose the neuron with big soma, huge trunk
and similar to the ball growth. It only has dendrite with-
out axon characteristics as reference. Next will introduce
the prediction implement through prediction model of
neuron growth.
The process description is:
There has only soma in the initial growth. The soma is
a ball, the branch has to grow from the cell and the
branch number is the random number of obeyed normal-
ity distribution N1. Branch length is one obeyed normal-
ity distribution N
2. The direction is random; the most
external surface room has probability p to growth the
new room. Moreover, the branch probability is q .The
most external surface room and part dip angle of new-
born room is the obeyed normality distribution N3. If it is
branch, the first newborn room and the second angle is
the random number of obeyed normality distribution N4.
The growth number of times is Num. The Process model
of neuron growth prediction is Figure 2.
 Get one random number of obeyed N1 is the number
of gronw room. The length abstract one obeyed nor-
mality distribution N of random number and grows
level one room.
 2,3, 4,k

 Judge whether k can reach the
growth number or not. The time is Num . If reach the
number, stop doing that.
 Judge whether k level room can grow the room or
not


2, 3, 4, If grow, jump to 4 meters, if not,
1kk
k

 then to 2.
 Judge the k level room is branch or not: if not,
jump to 5. If it is, jump to 6.
 The part dip angle of 1k level room and k level
room chose one random number to obey N
3, the
length can chose one random number to obey N2, and
it should grow 1k

level room. 1kk , jump to 2.
 The part dip angle from first level of 1k room and
k level room that can chose one random number to
obey N3, the length from the random number to obey
N2 then to grow the first room of 1k level.

T. SUN ET AL. 906
 The part branch angle of second room and the first
room is a random number to obey N4. The length is a
random number to obey N2. When grow the second
room of 1k level, jump to 2.
Note 1: if it is branch, the part dip angle of first
growth room is less than the second growth room.
Note 2: 2-7 steps is the growth process of level
room, all the level rooms are same as this.
k
k
Note 3: the incidental system of this article, N1 nor-
mality distribution average and variance is all the neuron
branch average and variance between A and B. the nor-
mality distribution average of N2, N3 and N4 is the aver-
age and variance of neuron room length, part dip angle
and part branch angle.
The system imitates the neuron growth and the system
operation get three imitation growth neurons, such as
Figures 3-5 shows:
At the closer soma part, the dendrite growth gets better
imitation.
Figure 2. The Process model of neuron growth pre diction.
Figure 3. Neuron growth imitation 1.
Figure 4. Neuron growth imitation 2.
Figure 5. Neuron growth imitation 3.

T. SUN ET AL. 907
Not all the crazy growth of trees is suit with the neuron
growth regulations. This is created by the suppose 4. In
the growth of real neuron, each tree will not be limited
until reach the certain degree. The most external surface
growth is random so this is the most important reason.
The length of some rooms is too long. If set one thresh-
old to chose from the obeyed random number of normal-
ity distribution, it can avoid this unmoral condition.
Nevertheless, the threshold cannot determine that not set
this subject.
3. Neuron Growth Prediction and Its
Influence of Geome tric Characteristics
According to the research of neuron morphologic, dif-
ferent function of neuron has huge differences in size,
shape and complexity [4]. The axon is long in common.
It is separate from axon hillock with uniformity diameter.
The commence part is the begin part. Apart from the
soma some distances, we will get the myelin sheath,
which called nerve fiber. The soma differences are huge.
The small diameter is only 5 - 6 and the large one
could be even 100 and more. The dendrite form,
number and length are different. Dendrite most be branch,
it can transform to the somas after stimulation. Axons are
funicular. The terminal have branches and called axon
terminal. Axons transform from soma to the terminal.
Usually, one neuron has one or more dendrites. Never-
theless, axon has only one. The bigger neuron is the
longer the axon is. Now divide the neuron growth proc-
ess into exponential phase, stationary phase and death
phase. Target is as the length of neuron dendrite. Sepa-
rately describe the growth change and impact of geomet-
ric characteristic in different phases. Here we predict the
following things:
μm
μm
Exponential phase: The half diameter is small. Never-
theless, it will grow more branches with obviously
changes. With the increase of the diameter, the broadcast
consume of neuron signal will increase all the same. At
the same time, the metabolic costs also increase the same.
The change of form will influence the geometrical form
and it might have mistakes.
Stationary phase: the space form of neuron is ensuring.
Under the rich growth, there will not have a change in a
period [5]. However, on the limited environment, the
neuron will limit the growth even grow back. So the en-
sure form data should reflects the geometric form. It is
the best periods of neuron form and functional predic-
tion.
Death phase: when the neuron and neighboring somas
is same to the certain extent, the neuron growth will be
limited. Some will back growth and the whole neuron
structure will change more and not suit for the neuron
identification and classification.
4. Conclusions
Neuron growth will bring the series change of geometri-
cal characteristics. Especially the growth of dendrite and
axon will change the space characteristic and geometric
characteristic obviously. This article is through the iden-
tification of spastics regulations and builds the prediction
model. The growth prediction of combine neuron struc-
ture knowledge, take the advantage of growth period and
describe the form structure and function such as growth,
death, branch and so on. Use the rate distribution and
random process theory to analyze the neuron topological
structure regulation. Through the model identification
and abstract the growth regulation. The model applies
Monte Carlo to imitate the neuron growth. For the close
soma part, dendrite growths get the better imitation.
However, far side room growth cannot control reason-
able. There has no whole reflect condition of neuron
growth. If want to do the further research, the initial
thinking is increasing with the growth configuration and
reduction.
5. References
[1] T. Sun, L. Lin and Q. Y. Huang, “Research of Neuron
Typological Classification and Identification Questions,”
(Committed)
[2] NeuroMorpho.Org. 2010.
http://neuromorpho.org/neuroMorpho/index.jsp
[3] Y. D. Zhang, P. F. Zhu and Z. G. Wang, “Research of
Neuron Regulation about Cultivate Rat Hypothalamus,”
Journal of Traumatic Surgery, Vol. 6, No. 1, 2004, pp.
45-47.
[4] M. B. Kerry, “Quantifying Neuronal Size: Summing up
Trees and Splitting the Branch Difference,” Seminars in
Cell & Developmental Biology, Vol. 19, No. 6, 2008, pp.
485-493. doi:10.1016/j.semcdb.2008.08.005
[5] G. A. Ascoli, et al., “Generation, Description and Storage
of Dendritic Morphology Data,” Philosophical Transac-
tions of the Royal Society B, Vol. 356, No. 1412, 2001, pp.
1131-1145. doi:10.1098/rstb.2001.0905