**Author details**

**Figure 16(b)** shows that action potentials are generated, because the input frequency is 13 Hz, which is close to the resonance frequency of this neuron model. Thus, the maximum amplitude of membrane potentials exceeds the threshold by the effect of the subthreshold resonance property. In the case of **Figure 16(c)**, for 30 Hz input frequency, no action potentials are generated, because the membrane potential is less than the threshold. On the other hand, if a

generated for 13 Hz input frequency input than the case of no DC bias input. This indicates the effect of a DC bias current on generation of action potentials. Comparing **Figure 16(b)** and **(d)**, it is clarified that the more spikes are observed than the case of no DC bias current input.

input frequency, as shown in **Figure 16(e)**. As no action potential is generated for the case of

Until now, it has been mainly proposed that the cell membrane and neurons are modeled by an RC circuit. However, from the fact that many neurons in various regions of the brain have band pass properties, a neuron should be modeled by an RLC circuit. In this chapter, an equivalent RLC circuit was developed for a neuron model with *h* and *NaP* channels, and it was clarified that the subthreshold resonance property of this neuron model comes from inductive properties of *h* and *NaP* channels, especially, *h* channel. Furthermore, by incorporating the Hodgkin-Huxley dynamics into this neuron model, we showed the relation between the subthreshold resonance oscillation and the generation of action potentials. By computer simulations, it was shown that the amplitude of an AC input and a DC bias current input strongly play a role in the generation of action potentials, coupled with AC input frequencies.

It is presumed that the subthreshold resonance phenomena may relate closely to various practical neuron activities and behaviors in our brain, such as the sensitivity to external noises in sensory system. So, it is very important and interesting to study firing patterns of a neuron or properties of burst oscillations by using computer simulations, in order to clarify the

Needless to say, mutual collaboration of experimental research and modeling research is of large significance, in order to create more sophisticated models based on the most recent findings from experiments, and in order to develop new experimental methods to verify the

mechanisms of higher information processing in the brain.

We thank Mr. Babak V. Ghaffari for preparing figures.

facts suggested from simulation results.

**Acknowledgements**

, this is also caused by the effect of a DC bias current input.

, as **Figure 16(d)** shows, more action potentials are

,a neuron model can also generate an action potential for 30Hz

DC bias current input increases to 1μA/cm2

72 Numerical Simulation - From Brain Imaging to Turbulent Flows

For the case of *id*= 1 μA/cm2

*id*= 0 μA/cm2

**4. Conclusion**

Tatsuo Kitajima1\*, Zonggang Feng2 and Azran Azhim3

\*Address all correspondence to: tatsuo.kitajima@gmail.com

1 Malaysia-Japan International Institute of Technology (MJIIT), UTM KL Campus, Kuala Lumpur, Malaysia

2 Yamagata University, Yonezawa-shi, Yamagata, Japan

3 International Islamic University Malaysia, Kuantan Campus, Kuantan, Malaysia
