## 2 Multi-Hop Communications through the Human Body
\begin{table}
\begin{tabular}{l l} \hline
**Parameters** & **Value** \\ \hline \hline \multicolumn{2}{l}{Scenarios} \\ Area & 40 cm straight line \\ \multicolumn{2}{l}{Deployment} & Uniform distribution \\ \multicolumn{2}{l}{Number of hops} & 1–5 \\ \hline \hline \multicolumn{2}{l}{Path-loss model} & IEEE802.15.6 \\ \hline \hline \multicolumn{2}{l}{Energy model} \\ \multicolumn{2}{l}{Sensitivity} & –84 dBm \\ \multicolumn{2}{l}{Transmit power} & Sensitivity + path-loss \\ \multicolumn{2}{l}{Alpha} & 1 \\ \multicolumn{2}{l}{Circuitry power} \\ \multicolumn{2}{l}{Transmit mode} & 100 \(\mu\)W–15 mW \\ \multicolumn{2}{l}{Receive mode} & 100 \(\mu\)W–15 mW \\ \hline \hline \multicolumn{2}{l}{Application traffic} \\ \multicolumn{2}{l}{Data rate} & 2 packets/sec \\ \multicolumn{2}{l}{Packet size} & 200 bytes \\ \hline \hline \multicolumn{2}{l}{Simulation duration} & 30 s \\ \hline \end{tabular}
\end{table} 
Table 2: Simulation parameters for the evaluation of multi-hop communication. \[\mathrm{E_{1 hop}}=\left((1+\alpha)\times\mathrm{Pt1_{1 hop}}+\mathrm{Pct}\right) \times\mathrm{T_{D}} \tag{7}\] \[\mathrm{E_{2 hop}}=\left((1+\alpha)\times\mathrm{Pt1_{2 hop}}+\mathrm{ Pct}\right)\times\mathrm{T_{D}}+\left(\mathrm{Pcr}+(1+\alpha)\times\mathrm{Pt2_{2 hop}}+ \mathrm{Pct}\right)\times\mathrm{T_{D}}\] (8) \[\mathrm{E_{1 hop}}-\mathrm{E_{2 hop}}=\left((1+\alpha)\times\left( \mathrm{Pt1_{1 hop}}-\mathrm{Pt1_{2 hop}}-\mathrm{Pt2_{2 hop}}\right)-\left( \mathrm{Pct}+\mathrm{Pcr}\right)\right)\times\mathrm{T_{D}} \tag{9}\]  
For 1 mW circuitry power, it can be seen that 2-hop achieve the minimum energy consumption. As explained above, this is because the increase of circuitry power of 2-hop is smaller than the decrease of the transmission power component of 1 hop, and the increase of circuitry power from 2-hop to 3-hop is bigger than the decrease of the transmission power component. The minimum energy consumption shifts from 2-hop to 3-hop, 4-hop when the circuitry power becomes smaller. It is because when the circuitry power becomes smaller, the transmission power becomes dominant. Figure 3 shows the influence of \(\alpha\) to the total energy consumption with the circuitry power of 15 mW, 3 mW and 100 \(\upmu\)W. It can be seen that \(\alpha\) influences the total energy consumption significantly for 1 hop and 2 hops. It has little influence for 3 hops and after. The reason is that when 3 hops or above is adopted, the transmission power is very small. According to Equation (3), if Pt is small, then \(\alpha\) will have little influence on the whole energy consumption. For 1-hop and 2-hop, Pt is big, so \(\alpha\) will have an obvious influence on the whole energy consumption. For the available chipsets which have a circuitry power of 15 mW, multi-hop communication has no energy saving advantages. When the circuitry power reduces to 3 mW, 2-hop communication can achieve almost the same performance in terms of energy consumption. When the circuitry power reaches 100 \(\upmu\)W, which has already achieved in lab, multi-hop communication gives much better performance than single-hop communication for _in-vivo_ communication. The reason is the same as the explanation of Figure 2. Given the advancement of electronic technologies, multi-hop communications through the human body will become more and more reasonable and useful. Figure 2: Energy consumption _vs_. number of hops for different circuitry power. Figure 3: Energy consumption _vs._ number of hops for different \(\alpha\) when circuitry power is equal to **(a)** 15 mW; **(b)** 3 mW; **(c)** 100 \(\mu\)W.