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A Modified Hodgkin-Huxley model to Show the Effect of Motor Cortex Stimulation on the Trigeminal Neuralgia Network

09 Nov 2018-bioRxiv (Cold Spring Harbor Laboratory)-pp 467100
TL;DR: The results showed that by decreasing the conductivity of the slow sodium channels (pain channels) and applying tDCS over the M1, the activity of the somatosensory cortex would be reduced, and this reduction can cause pain relief.
Abstract: Background Trigeminal neuralgia (TN) is a severe neuropathic pain, which has an electric shock like characteristic. There are some common treatments for this pain such as medicine, microvascular decompression or radio frequency. In this regard, transcranial direct current stimulation (tDCS) is another therapeutic method to reduce the pain, which has been recently attracting the therapists’ attention. The positive effect of tDCS on TN was shown in many previous studies. However, the mechanism of tDCS effect has remained unclear Objective This study aims to model the neuronal behavior of the main known regions of the brain participating in TN pathways to study the effect of transcranial direct current stimulation Method The proposed model consists of several blocks (block diagram): 1) trigeminal nerve, 2) trigeminal ganglion, 3) PAG (Periaqueductal gray in the brainstem), 4) thalamus, 5) motor cortex (M1) and 6) somatosensory cortex (S1). Each of these components represented by a modified Hodgkin-Huxley (HH) model (a mathematical model). The modification of the HH model was done based on some neurological facts of pain sodium channels. The input of the model is any stimuli to ‘trigeminal nerve,’ which cause the pain, and the output is the activity of the somatosensory cortex. An external current, which is considered as electrical current, was applied to the motor cortex block of the model Result The results showed that by decreasing the conductivity of the slow sodium channels (pain channels) and applying tDCS over the M1, the activity of the somatosensory cortex would be reduced. This reduction can cause pain relief Conclusion The proposed model provided some possible suggestions about the relationship between the effects of tDCS and associated components in TN, and also the relationship between the pain measurement index, somatosensory cortex activity, and the strength of tDCS.

Summary (3 min read)

Introduction

  • There are some common treatments for this pain such as medicine, microvascular decompression or radio frequency.
  • The input of the model involves any stimuli to the ‘trigeminal nerve,’ which cause the pain, and the output is the activity of the somatosensory cortex.
  • Electrical stimulation (e.g., tDCS) of an appropriate area can play a role similar to that of the medial brain in reducing pain [4].
  • The results of the simulation of the proposed model, considering the effect of tDCS, are described in the Results section.

2 Method

  • The stages of modeling have been described.
  • This model, which has been explained in [6] in detail, consists of some important brain regions involved in TN.
  • At the last step, an external current stimulation has been applied over M1 to show the effect of external stimuli on TN.

2.1 Trigeminal neuralgia pathway

  • Many studies have investigated the brain regions involved in pain processing [1, 8, 16–18].
  • According to the results of these studies, there are a wide variety of brain areas that are involved in pain processing that can form a vast network with complex interactions.
  • In their previous work [6], the authors have described this complicated network as a pain neuromatrix diagram.
  • A simplified version of this neuromatrix is proposed that consists of the leading and substantial blocks of pain network in TN processing system from the initial noxious stimuli of TN to somatosensory cortex [11, 19–23].
  • As shown in Fig. 1, this model includes the following blocks.

2.1.1 Trigeminal ganglion

  • Trigeminal neuralgia begins from the root of the nerve and trigeminal ganglion (TG) that is involved in the pain processing pathway.
  • The signals come from the face, and trigeminal afferents project using the TG, thereby they directly go to the brainstem and then project to the brain [16, 24].

2.1.2 Brainstem

  • After TG, the nociceptive signals reach to different parts of the brainstem [25, 26].
  • 1.3 Periaqueductal gray (PAG) Periaqueductal gray is one of the substantial main parts of the pain-mediating process, which is in the middle part of the brainstem.
  • It receives signals from thalamus [32], insula, and hypothalamus [31].

2.1.5 Motor cortex

  • Many studies signify the importance and effects of the tDCS over M1 and put emphasis on the role of motor cortex stimulation in pain intensity reduction or increase in the pain threshold [1, 8, 14, 25, 26, 46–49].
  • Such pain-relief effects may exist because of sub-cortical and thalamocortical connections [44].

2.2 Mathematical modeling of the simplified pain neuromatrix

  • The Hodgkin–Huxley model gives the ability to investigate the chemical reactions and activity changes of neuronal response.
  • It has been shown that some ion channels, such as the Nav1.8 slow sodium channels, play a role in pain pathway and pain intensity modification.
  • Moreover, the equations presented for the HH model can take into account the activity variation of neuronal behaviors.
  • At last, the output potential of the block was obtained by considering the (I)-form of MHH (Eq. (11)) and the input stimuli (or current for other blocks except the first one).
  • The proposed model has been simulated considering parameters amounts that have been reported in the next part.

3 Results

  • In the equations which were described in the previous section, the values of the parameters have been selected as indicated in Table 2.
  • The numbers are based on some formula and the amounts reported in previous studies, which have been mentioned next to each value.
  • According to Fig. 3, the peak to peak value of the output decreased by increasing the input stimulus.
  • Different values have been considered for input current from I0 = –80 to 80 in order to observe the behavior of S1 behavior with a fixed value of conductivity of slow sodium channels (gNaS) for Fig.
  • Then for each gNaS the mentioned value and the related column of the output potential of S1 with the whole row of that column, the figure was plotted.

3.1 Nonlinear dynamic analysis of the model

  • Different types of bifurcations have been considered previously in the bifurcation of HH equations study by Guckenheimer [58] in which a qualitative depiction of the different regimes of the bifurcation diagrams for HH in the two-dimensional I-VK parameter plane, limit cycles, diagrams and phase portraits on the two-dimensional invariant manifold for HH on the I-VK plane have been obtained.
  • When I0 = –49.126377 is reached two pairs of complex conjugate eigenvalues and a Hopf bifurcation occur.
  • By adding another current as an external input current, which can be regarded as a tDCS current to M1 block (see Fig. 2), the results of simulations can show the effect of on the output behaviors.
  • The circular point shows the mean level of VAS when ItDCS = 2 mA obtained from [15] pain changes the pattern of the activities of the neurons [52].

4 Discussion

  • Today, different treatment methods such as drugs, microvascular decompression, or surgeries are applied to reduce TN pain.
  • The complexity of the computations for considering an MHH for each neuron would definitely prevent us even from getting such available results.
  • The outputs of the TG and S1 regions, corresponding to the two different pain channels’ conductivity, are shown in Fig.
  • In the current study, the onset of Hopf bifurcation points (shown in Fig. 8) can be controlled.
  • As shown in Fig. 11, by applying ItDCS , the somatosensory cortex (S1) potential activity is reduced.

5 Conclusion

  • By the current version of the model, the possible effect of increasing the pain strength and also the external current stimulus on the TN neuromatrix components were investigated.
  • MK wrote the first draft of the manuscript and interpreted the findings as a significant contributor.
  • DaSilva AF, Becerra L, Makris N, Strassman AM, Gonzalez RG, Geatrakis N, et al.
  • Hofbauer RK, Rainville P, Duncan GH, Bushnell MC. Cortical representation of the sensory dimension of pain.
  • Transcranial direct current stimulation (tDCS) for the treatment of chronic pain.

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Khodashenas et al. Journal of Mathematical Neuroscience (2019) 9:4
https://doi.org/10.1186/s13408-019-0072-5
SHORT REPORT OpenAccess
A modified Hodgkin–Huxley model to show
the effect of motor cortex stimulation on the
trigeminal neuralgia network
Mohammadreza Khodashenas
1*
, Golnaz Baghdadi
1
and Farzad Towhidkhah
1
*
Correspondence:
mreza.khodashenas@gmail.com
1
Department of Biomedical
Engineering, Amirkabir University of
Technology, Tehran, Iran
Abstract
Background: Trigeminal neuralgia (TN) is a severe neuropathic pain, which has an
electric shock-like characteristic. There are some common treatments for this pain
such as medicine, microvascular decompression or radio frequency. In this regard,
transcranial direct current stimulation (tDCS) is another therapeutic method to reduce
pain, which has been recently attracting the therapists’ attention. The positive effect
of tDCS on TN was shown in many previous studies. However, the mechanism of the
tDCS effect has remained unclear.
Objective: This study aims to model the neuronal behavior of the main known
regions of the brain participating in TN pathways to study the effect of transcranial
direct current stimulation.
Method: The proposed model consists of several blocks: (1) trigeminal nerve,
(2) trigeminal ganglion, (3) PAG (periaqueductal gray in the brainstem), (4) thalamus,
(5) motor cortex (M1) and (6) somatosensory cortex (S1). Each of these components is
represented by a modified Hodgkin-Huxley (HH) model. The modification of the HH
model was done based on some neurological facts of pain sodium channels. The
input of the model involves any stimuli to the ‘trigeminal nerve, which cause the pain,
and the output is the activity of the somatosensory cortex. An external current, which
is considered as an electrical current, was applied to the motor cortex block of the
model.
Result: The results showed that by decreasing the conductivity of the slow sodium
channels (pain channels) and applying tDCS over the M1, the activity of the
somatosensory cortex would be reduced. This reduction can cause pain relief.
Conclusion: The proposed model provided some possible suggestions about the
relationship between the effects of tDCS and associated components in TN, and also
the relationship between the pain measurement index, somatosensory cortex
activity, and the strength of tDCS.
Keywords: Computational modeling; Pain network; Neuropathic pain; Transcranial
direct current stimulation
1 Background
The TN (trigeminal neuralgia) is a rare facial pain disorder that leads to a sudden, short,
and severe sense of pain in the face [1, 2]. It is one of the most severe neuropathic forms
of pain [3]. This pain does not have a regular and normal behavior with a specific pattern.
© The Author(s) 2019. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License
(http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, pro-
vided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and
indicate if changes were made.

Khodashenas et al. Journal of Mathematical Neuroscience (2019) 9:4 Page 2 of 23
Therefore,the predictionof itsoccurrence is in acertain measure impossible. Itmay occur
either spontaneously without doing any particular activity or by doing some routine tasks
such as chewing, brushing teeth or even shaving, which can trigger the pain attack [1, 2].
Physiological factors (e.g., superior cerebellar artery compression) and plasticity of the
nervous system have roles in TN to play [4]. Many diverse regions of the brain such as
the thalamus, motor cortex (M1), brainstem, primary somatosensory cortex are included
in the TN processing [5, 6], and connections and communications between these regions
processing the TN, result in the TN network or the TN neuromatrix.
Carbamazepine, as one of the TN medicine treatments, can reduce the pain. However,
the side effects of this medicine (e.g., drowsiness and confusion) usually result in discon-
tinuation of its usage [1, 7]. Surgical interventions such as microvascular decompression
or radiotherapies are other options that may be suggested to the patient with TN. Pa-
tients often do not tend to have surgery, because it has a high risk of face mutilation [1].
Transcranial direct current stimulation (tDCS) is another therapeutic method that was
recently used in the field of pain and shows positive effect [1, 8]. This method is cheapand
non-invasive. No serious side effect has been reported for this method.
ThetDCS is a low direct current (usually 1 or 2 mA) which is applied to a specific region
of the brain using two electrodes, which are placed on the superficial part of the brain.
Motor cortex (M1) stimulation is more prevalent than in other regions of the brain. In
this regard, M1 stimulation is utilized for pain relief, depression, addiction and so on [9,
10]. It was suggested that, by applying tDCS, pain perception is modulated by shifts of
the resting membrane potential [1] and consequently results in the modification of the
neuronal excitability at the stimulationsite [1, 11]. Electrical stimulation(e.g., tDCS) of an
appropriate area can play a role similar to that of the medial brain in reducing pain [4].
Despite the positive results of the effect of stimulation in pain relief, it is still unknown
how tDCS can reduce the symptoms of TN. Modeling the pain pathway can provide a tool
to understand some aspects of TN and to investigate the mechanism of tDCS effect. No
computationalmodel has been suggested for TN. However, there are some models of pain
based on gate control theory [4] and artificial neural networks [12].
In the current study, we simplified a conceptual model of TN pathways that is proposed
in the previous study [6]. Then we represented this conceptual model by a mathematical
formula based on a modified version of the Hodgkin-Huxley (HH) equations. By using
this model, the possible effects and mechanism of the influence of an external input such
as tDCS were investigated. To evaluate the outcomes of our model, as we may not able
to understand the meaning of S1 output potential or S1 activity outcome clearly, which
is essential for investigating any modification in neuronal behavior in our model, we can
change it to a more tangible and practical scale, such as visual analog scale (VAS) to com-
prehend the intensity of pain and the activity of S1. As a result, interpreting the output
of our model, S1 activity is turned to VAS display, a method which is indeed efficient and
practical for subjective measuring of pain, including TN. This self-evaluation scale ranges
from 0 to 10 as visually described in centimeter units: 0 cm indicates no pain, and 10 cm
means the worst pain possible. Participants will be asked to rate their pain during the pre-
vious 24 hours to get a baseline pain. This scale has been widely used in studies to evaluate
pain as an outcome [13]. There are a few types of research which have done some experi-
mentsonTNpatientsbyapplyingtDCSoverM1[1, 8, 14, 15].

Khodashenas et al. Journal of Mathematical Neuroscience (2019) 9:4 Page 3 of 23
In the next section, the details of the proposed conceptual and computational mod-
els are presented. The results of the simulation of the proposed model, considering the
effect of tDCS, are described in the Results section. In the last part, the discussion and
interpretation of the obtained results are provided as regards different computational and
physiological aspects.
2 Method
Inthissection,thestagesofmodelinghavebeendescribed. Atfirst,a simplifiedconceptual
model of TN pathway has been introduced. This model, which has been explained in [6]
in detail, consists of some important brain regions involved in TN. Then each part of the
TN pathway has been modeled by a modified version of the HH model. At the last step,
an external current stimulation has been applied over M1 to show the effect of external
stimuli on TN.
2.1 Trigeminal neuralgia pathway
Manystudies haveinvestigated the brain regions involved in pain processing [1, 8, 1618].
According to the results of these studies, there are a wide variety of brain areas that are
involvedinpainprocessing thatcan form avast networkwithcomplexinteractions. In our
previous work [6], we havedescribed this complicated network as a pain neuromatrix dia-
gram. A simplified version of thisneuromatrix is proposed that consists of the leading and
substantial blocks of pain network in TN processing system from the initial noxious stim-
uli of TN to somatosensory cortex [11, 1923]. The simplified pain neuromatrix model is
showninFig.1.
As shown in Fig. 1, this model includes the following blocks.
2.1.1 Trigeminal ganglion
Trigeminal neuralgia begins from the root of the nerve and trigeminal ganglion (TG) that
is involved in the pain processing pathway. Somas of face neurons are in TG. The signals
come from the face, and trigeminal afferents project using the TG, thereby they directly
go to the brainstem and then project to the brain [16, 24].
Figure 1 Concise TN pathway block diagram. PAG: periaqueductal gray, VPL: ventral posterolateral nucleus
(reprinted from [6])

Khodashenas et al. Journal of Mathematical Neuroscience (2019) 9:4 Page 4 of 23
2.1.2 Brainstem
After TG, the nociceptive signals reach to different parts of the brainstem [25, 26]. The
brainstem consists of trigeminal nuclei [16, 18, 2730], the para brachial (PB) nucleus,
and PAG (periaqueductal gray). The brainstem projects signals to different nuclei of the
thalamus [29, 31] especially the VPL (ventral posterolateral nucleus) and VPM (ventral
posteromedial nucleus) regions [16, 19, 30].
2.1.3 Periaqueductal gray (PAG)
Periaqueductal gray is one of the substantial main parts of the pain-mediating process,
which is in the middle part of the brainstem. Itreceives signals from thalamus [32], insula,
andhypothalamus[31]. Periaqueductalgrayinvolvesthe secretion ofendogenous opioids,
such as encephalin, for relieving pain [12, 19, 26, 28, 3137].
2.1.4 Thalamus
The thalamus is one of the major structures that receives pain signals from diverse pain
pathways [18, 19, 25, 26, 2832, 3443]. The thalamus processes the nociceptive informa-
tion coming from the brainstem [29, 31] especially to the VPL and VPM regions [16, 19,
30] and projects them to different parts of the brain such as S2 (secondary somatosen-
sory cortex) [37, 39, 40], primary somatosensory cortex(S1) [19, 30, 31, 37, 39, 40, 42
]and
PAG [32]. It has a reciprocal interaction with some parts of the M1 [35], especially the VL
(ventral lateral nucleus) and anterior nuclei [36]. In this regard, it has been suggested that
the thalamus may play a role in the inhibitory pain pathway by applying anodal tDCS over
M1, which may result in a probable pain-relief effect [44].
2.1.5 Motor cortex
Although the primary motor cortex (M1) is not considered regularly as part of the pain
neuromatrix, it plays a crucial role in modulating the pain in different chronic pain syn-
dromes [25, 28, 3537, 41, 45]. It has some reciprocal connections with S1 [28, 37, 45].
It receives direct information from the ACC (anterior cingulate cortex) [41] and sends it
to the prefrontal cortex [25], brainstem [25, 26] and thalamus [25, 26], and especially VPL
[28].Manystudiessignify theimportanceand effectsofthe tDCSover M1 andputempha-
sis on the role of motor cortex stimulation in pain intensity reduction or increase in the
pain threshold [1, 8, 14, 25, 26, 4649]. Although the mechanism of the effect of the M1
anodal tDCS has remained somewhat unclear, such pain-relief effects may exist because
of sub-cortical and thalamocortical connections [44].
2.1.6 Somatosensory cortex
The primary somatosensory cortex is also one of the main cortical regions in the pain or
TN neuromatrix [5, 16, 19, 2831, 3537, 3942, 45, 50, 51]. The primary somatosensory
cortex has some mutual interaction with M1 [28, 37
, 45]andS2[37]. The primary so-
matosensory cortex receives nociceptive information from S2 [41], and the thalamus [19,
30, 31, 37, 39, 40, 42].
In the above paragraphs, a brief review of the simplified pain neuromatrix model was
provided. More details can be found in [6]. In the next section, this model has been for-
mulated by mathematical equations.

Khodashenas et al. Journal of Mathematical Neuroscience (2019) 9:4 Page 5 of 23
2.2 Mathematical modeling of the simplified pain neuromatrix
The Hodgkin–Huxley model gives the ability to investigate the chemical reactions and
activity changes of neuronal response. The equations that describe the HH model can be
found in textbooks.
It has been shown that some ion channels, such as the Na
v
1.8 slow sodium channels,
play a role in pain pathway and pain intensity modification. In this regard, their synthesis
and activity mayalso cause different neuronal potential and behavior [52]. The HH model
has the capability to model and describe the effect of diverse factors influencing the ion
channels. Moreover, the equations presented for the HH model can take into account the
activity variation of neuronal behaviors. Importantly, use-dependent sodium channel in-
hibitors are clinically effective in the treatment of many types of chronic pain [53]. Hy-
peralgesia is removed by factors decreasing impulse activity of Na
v
1.8 channels. That is
why these factors are believed to be of use in highly selective pain-killing medicine [52].
Considering the physiological role of the activation gating structure of the slow sodium
channels Na
v
1.8 in impulse coding of nociceptive information [54], and observing that the
modification of specified slow sodium channels in the membrane of nociceptive neurons
is the basis of the pain perception [52], it seems that the HH model is able to be a proper
candidate for modeling the pain modulation process. However, it needs some modifica-
tions for using in our pain processing study. A voltage-gated slow Na
+
current needs to
be added into the HH equations. In other words, despite HH original model being useful
for modeling the behavior of neurons, it is a general model and should be specialized for
our use in pain-related neurons and simulating their behavior. Considering one more ion
channel will definitely result in a more realistic simulation, since we have separated the
current and gating variables related to it in our model. Besides, it is necessary to under-
stand what parameters cause the possibility of the nociceptive neuron to affect generating
or preventing a painful signal. As a result, the extra current for pain intensity plus its cor-
responding activity fluctuation needs tobe considered in the HH model.In fact, the added
currentis theNa
v
1.8 slow sodium channel current specified for pain and pain modulation
processing [52]. Therefore,the modifications havebeen appliedby adding two more equa-
tions to the main HH equations (Eqs. (5)and(6)). Themodified version of theHH (MHH)
model is described by Eqs. (1)–(16):
C
m
dE
dt
= I g
Naf
m
3
h(E E
Na
)–g
k
n
4
(E E
K
)–g
L
(E E
L
)–g
NaS
m
3
S
h
S
(E E
Na
), (1)
dm
dt
= α
m
(E)(1 m)–β
m
(E)m,(2)
dh
dt
= α
h
(E)(1 h)–β
h
(E)h,(3)
dn
dt
= α
n
(E)(1 n)–β
n
(E)n,(4)
dm
s
dt
= α
m
s
(E)(1 m
s
)–β
m
s
(E)m
s
,(5)
dh
s
dt
= α
h
s
(E)(1 h
s
)–β
h
s
(E)h
s
,(6)

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TL;DR: In this paper , the application of phenomenological and biophysical models in non-invasive brain stimulation is discussed, through the lens of four case studies, and the authors provide an account of the questions these models can address, commonalities and limitations across studies.

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Abstract: Central Pattem Generators (CPG) are neuronal network generating proper commands for motor behaviors like walking, running, breathing, and etc. These neuronal networks are responsible for making suitable rhythms for the limbs to reach proper tasks. Nonlinear oscillators have been widely used as models of CPGs. Different structures were used for generating suitable rhythm (attractor), but less attention has been paid to the design of a basin of attraction. It has been shown different kinds of nonlinear oscillators have different properties and the shape of the basin of attractions can affect their transient response time and their capability of noise rejection. In this work, a new method based on a neural network is proposed to design a proper oscillator with a proper basin of attraction and attractor. Besides, for this method, a pre-train approach is introduced that makes training for this function much faster. Results show that the proposed neural network with pre-training can properly learn Van der Pol oscillator attractor and basin of attraction. It is shown that the mentioned pre-training strategy can considerably speed up the training procedure and thus gaining a better training error.

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  • ...Some studies have focused on CPGs networks by coupling HH or HRs equations, while the others have tried to model and regenerate variety of behaviors of periodic and chaotic bursting of a CPG neuron(s) by modifying equations [10], changing parameters [11], or adding complex stimulation [12] to HH or HR....

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TL;DR: In this paper , a systematic review in accordance with the Preferred Reporting Items for Systematic Reviews and Meta-analyses (PRISMA) guideline was performed using PubMed, Embase, and Cochrane Central Registry of Controlled Trials databases.
Abstract: Abstract Background This study aims to systematically review the treatment outcomes of percutaneous balloon compression (PBC) and microvascular decompression (MVD) in patients with trigeminal neuralgia. Methods A systematic review in accordance with the Preferred Reporting Items for Systematic Reviews and Meta-analyses (PRISMA) guideline was performed using PubMed, Embase, and Cochrane Central Registry of Controlled Trials databases. Only those articles with more than 5 years' follow-up length were included in this investigation. To uniformly assess the postoperative outcome, we defined pain relief as totally pain free, while the postoperative hospitalization and last follow-up period were defined as early and long term , respectively. The facial numbness was quantified with Barrow Neurological Institute Pain Intensity Score (BNI). Results After database searching and screening, 7,797 cases were finally included according to the criteria. The early pain relief rates were 94.1% (1,551/1,649) and 89.9% (4,962/5,482) following PBC and MVD (odds ratio [OR] = 0.603; p < 0.05), while the long-term rates were 58.1% (921/1,566) and 74.9% (4,549/6,074; OR = 2.089; p < 0.05), respectively. Although a significant higher facial numbness occurred in the PBC group in the early stage, it was mostly diminished 5 years later compared with the MVD group. At long-term follow-up, hypoacusis and facial palsy occurred more often in the MVD group ( p < 0.05). Conclusions Both MVD and PBC provide a satisfactory outcome for the patients in the long term. As a simple, safe, and reliable technique, PBC should be considered as a viable alternative.
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Abstract: Hypersensitivity to low temperature is a common problem due to the increased spontaneous activity of C fibers following nerve injuries. In addition, nerve damage can lead to the loss of A-beta fibers. Pain modulation following these abnormalities is still poorly understood. In this study, we modified the latest model of pain processing circuits in the dorsal horn of the spinal cord to investigate two cases of neuropathic pain: 1) The effect of exposure to cold and 2) The reduction in the number of Aβ fibers. Results indicate that the mere increased spontaneous activity of the nociceptive fibers in a neuropathic condition does not lead to the arousal of pain. But it has sensitized the projection (P) neurons to an upcoming stimulus. Interestingly in the second case, despite keeping the firing frequency of Aβ fibers intact, decreased efficiency of tactile stimulation or TENS was seen. This reduction was only due to a reduction in the number of fibers entering the dorsal horn. Our results provide considerable insights into the mechanisms of pain processing in the dorsal horn concerning the consequences of receptor injuries, which might be beneficial for clinical interventions.
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References
More filters
Book
01 Oct 2006
TL;DR: This book explains the relationship of electrophysiology, nonlinear dynamics, and the computational properties of neurons, with each concept presented in terms of both neuroscience and mathematics and illustrated using geometrical intuition, providing a link between the two disciplines.
Abstract: This book explains the relationship of electrophysiology, nonlinear dynamics, and the computational properties of neurons, with each concept presented in terms of both neuroscience and mathematics and illustrated using geometrical intuition In order to model neuronal behavior or to interpret the results of modeling studies, neuroscientists must call upon methods of nonlinear dynamics This book offers an introduction to nonlinear dynamical systems theory for researchers and graduate students in neuroscience It also provides an overview of neuroscience for mathematicians who want to learn the basic facts of electrophysiology "Dynamical Systems in Neuroscience" presents a systematic study of the relationship of electrophysiology, nonlinear dynamics, and computational properties of neurons It emphasizes that information processing in the brain depends not only on the electrophysiological properties of neurons but also on their dynamical properties The book introduces dynamical systems starting with one- and two-dimensional Hodgkin-Huxley-type models and continuing to a description of bursting systems Each chapter proceeds from the simple to the complex, and provides sample problems at the end The book explains all necessary mathematical concepts using geometrical intuition; it includes many figures and few equations, making it especially suitable for non-mathematicians Each concept is presented in terms of both neuroscience and mathematics, providing a link between the two disciplines Nonlinear dynamical systems theory is at the core of computational neuroscience research, but it is not a standard part of the graduate neuroscience curriculum - or taught by math or physics department in a way that is suitable for students of biology This book offers neuroscience students and researchers a comprehensive account of concepts and methods increasingly used in computational neuroscience

3,683 citations

Journal ArticleDOI
TL;DR: A systematic review of the literature regarding how activity in diverse brain regions creates and modulates the experience of acute and chronic pain states, emphasizing the contribution of various imaging techniques to emerging concepts is presented in this paper.

2,686 citations

Journal ArticleDOI
TL;DR: An overview of the state of the art for transcranial direct current stimulation (tDCS) is offered, which suggests that it can induce beneficial effects in brain disorders and facilitate and standardize future tDCS studies.

2,539 citations

ReportDOI
01 Jan 1996
TL;DR: In this paper, a database of dielectric data based on measurements using recently developed techniques is presented, and the new data are evaluated by comparison with corresponding data from the literature where available.
Abstract: : Knowledge of the dielectric properties of biological materials is of importance in solving electromagnetic interaction problems. There is, as yet, no consensus on such data among scientists dealing with these issues. This project is geared towards producing a database of dielectric data based on measurements using recently developed techniques. This has been achieved through measurement over a wide frequency range. The new data were evaluated by comparison with corresponding data from the literature where available. To facilitate the incorporation of the dielectric data in numerical solutions, their frequency dependence was modelled to a spectrum characterised by 4 dispersion regions. The conductivity of tissues below 100 Hz was estimated from the recent measurements mitigated by data from the literature and used to estimate the body and of various body parts.

1,995 citations


Additional excerpts

  • ...01*10 7 (55) εr (all blocks except TG) 4....

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Frequently Asked Questions (2)
Q1. What have the authors contributed in "A modified hodgkin–huxley model to show the effect of motor cortex stimulation on the trigeminal neuralgia network" ?

This study aims to model the neuronal behavior of the main known regions of the brain participating in TN pathways to study the effect of transcranial direct current stimulation. The proposed model provided some possible suggestions about the relationship between the effects of tDCS and associated components in TN, and also the relationship between the pain measurement index, somatosensory cortex activity, and the strength of tDCS. 

For future work, other interventions ( e. g., transcranial alternating current stimulation ( tACS ) ) to other blocks of the model are suggested.