Page 114 - ITU Journal Future and evolving technologies Volume 2 (2021), Issue 3 – Internet of Bio-Nano Things for health applications

ITU Journal on Future and Evolving Technologies, Volume 2 (2021), Issue 3

frequency domain analysis of the system to quantify channel
attenuation and compare the results with the classical ca‑
ble model to show the effect of paranodal regions on infor‑
mation transmission. Then, we derive the rate per chan‑
nel use and channel capacity when different forms of bio‑
logical noise sources exist in the environment.

The rest of the paper is organized as follows. First, in Sec‑
tion 2, we describe the system model. Secondly, in Sec‑
tion 3, we ine noise sources affecting the internodal
channel and derive bounds on rate per channel use and
capacity. Next, in Section 4, we provide numerical analy‑
sis of the channel’s frequency domain properties. Finally,
in Section 5, conclusions and future directions are sum‑
marized.

2. SYSTEM MODEL

Fig. 1 – Paranodal and nodal regions of the myelin sheath.
A myelinated axon consists of active and passive compart‑
impulse‑like potential changes in the neuron membrane, ments that sustain the active and passive spread of ac‑
called Action Potential (AP). Myelination increases the tion potential through the axon, respectively. The nodes
speed of signal propagation along the axon considerably of Ranvier, which contain dense ion channels, are ac‑
by a process called saltatory conduction, which is simply tive compartments. In contrast, electrically neutral myeli‑
the jumping of APs between the consecutive nodes of Ran‑ nated segments, i.e., internodes, with low ion channel den‑
vier. Successful saltatory conduction is strongly related to sity constitute passive compartments [17] as shown in
the structure and integrity of the myelin sheath [14]. In Fig. 2. Due to the stochastic opening and closing of ion
an intact and suf iciently thick sheath, ion leakage from channels, which can be described via nonlinear differen‑
the neuron membrane is minimal. As a result, attenua‑ tial equations of Hodgkin Huxley formalism, membrane
tion at the membrane potential is also minimal. However, resistance is time‑varying at the nodes of Ranvier. On
demyelination, which is the loss of myelin sheath, can in‑ the other hand, since passive compartments have only a
crease ion leakage from the axon membrane to a level negligible number of ion channels, membrane resistance
that the membrane potential attenuates too much when does not depend on time, and the axon acts linearly at in‑
it reaches the next node. In this case, low membrane po‑ ternodes.
+
tential may not be suf icient to open Na channels in the
node, and consequently, AP propagation is blocked [15]. To investigate the linear response of an internode, we take
paranodal regions into account. In this respect, classical
The myelin sheaths generally form in multiple layers. The cable theory, which is proven to be successful at explain‑
sheath is wrapped around the axon starting from its short ing the behavior of AP propagation through the cylindrical
edge as shown in Fig.1. This structure of myelin forms in‑ structures such as dendrites and axons, is utilized [18].
termediary regions called the paranodal regions between
the nodes of Ranvier and the nodal regions of the myelin 2.1 The cable equation
sheath. Assuming that the n‑fold myelin sheath begins
abruptly following a node of Ranvier causes inaccuracy
According to cable theory, the membrane voltage is given
when modeling the leakage resistance and capacitance of
by the following differential equation [13]
the region. Bearing in mind that there may be hundreds,
even thousands of nodal and paranodal regions in a sin‑ 2
1
gle axon, the importance of inaccuracy caused by oversim‑ = + , (1)
2
plistic modeling becomes apparent. Moreover, as shown
in [16], even minor changes in the structure of paranodal
where , and are the membrane resistance, for‑
regions can affect AP propagation icantly. This evi‑
ward resistance and membrane capacitance of the axon,
dence shows that we should also consider paranodal re‑
gions to obtain a realistic model of myelinated axons. respectively. Using the length constant, = √ and

the time constant, = , Eq. (1) becomes
In this paper, we propose a detailed model for the intern‑
ode in a myelinated axon by taking paranodal regions into 2
account, based on experimental evidence from the liter‑ 2 2 = + . (2)
ature. Our aim is to investigate the frequency response
properties of a single internodal channel. We perform

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