# A Photolysis-Assist Molecular Communication for Tumor Biosensing
## 2 System Model
### Provitamin D3 Molecules Propagation Process  
In this paper, we assume that MC operates in a medium with an unbounded 1-D fluid environment, representing the tissues surrounding the tumor. As information molecules, provitamin D3 can be photocdecomposed by UV light. However, the nonphotodecomposed synchronization molecules can trigger the fluorescent. The transmitter releases impulses of provitamin D3 molecules, with a number \(Q\). We employ binary modulation with constant bit interval, where information molecules are released at the start of symbol \"1\", while synchronization molecules are released during the symbol \"0\". As different from conventional MC, where \"1\" or \"0\" are generated randomly, the symbol \"1\" or \"0\" here represents the coded pH information. A trigger signal can be generated once the receiver detects the synchronization molecules with a higher diffusion coefficient. Receivers are light-emitting components activated by trigger signals to emit light impulses of a specific wavelength when the transmitted symbol is \"0\". The information molecules released by the transmitter can be photocdecomposed by the light impulses; however, the nonphotodecomposed synchronization molecules can trigger the fluorescent. The MC system in the IoBNT for biosensing is illustrated in Figure 1. The biosensing signal, generated by the tumor sources, propagates from the transmitter to the receiver. While in the IoBNT network, the nodes are interconnected by way of the MC process, which implements the provitamin D3 molecules as the information carriers. The transmitter releases the information and synchronization molecules; meanwhile, the receiver receives information molecules and then triggers photolysis reactions once detecting the synchronization molecules with a higher diffusion coefficient. The system is characterized by the assumptions as follows:  
1. the propagation is unbounded,
2. the information transmitted is modulated by concentration and UV light,
3. the molecule reaching the receiver is considered to be fully absorbed and cannot be recycled. Molecular diffusion, thermal vibration and collision with other molecules in the fluid environment. The motion of molecules is called Brownian motion, that is, random motion without any priority direction leads to the concentration change of molecules in time and space, which is characterized by [PERSON]'s second diffusion law:  
\[\frac{\partial C(d,t)}{\partial t}=D\
abla^{2}C(d,t), \tag{1}\]  
where \(D\) is the diffusion coefficient, \(\
abla\) is the Laplace operator. The diffusion coefficient can be determined by the [PERSON] relation:  
\[D=\frac{k_{B}T}{6\pi\eta R_{p}}, \tag{2}\]where \(k_{B}\) is [PERSON]'s constant, \(T\) is the temperature in kelvin, \(\eta\) is the dynamic viscosity of the fluid, and \(R_{p}\) is the radius of the particle. Because the closed-form analytical solution can not always be attained, we can get the conditional solution by imposing some boundary conditions in the 1-D environment. CIR of the end-to-end channel, denoted by \(h(t)\), is defined as the probability of the output molecule at time \(t\) and at point distance from transmitter \(d\) when the transmitter is stimulated impulsively at time \(t_{0}=0\), which can be described as [30]:  
\[h_{1}(t)=\int_{d}^{d+R}\frac{1}{\sqrt{4\pi Dt}}\exp\biggl{(}-\frac{x^{2}}{4 Dt} \biggr{)}dx, \tag{3}\]  
where \(d\) is the distance from the transmitter to receiver, \(R\) is the receiver radius. The peak time \(t_{p}\) is calculated corresponding to the maximum value of the signal amplitude, which can be obtained by taking the first-order derivative of CIR in pure diffusion. In the 1-D environment, the peak time should be derived from formulation (3), denoted as:  
\[t_{p}=\frac{d^{2}}{2D}, \tag{4}\]  
According to Figure 2, the information and synchronization molecules are transmitted at different symbol slots. The high diffusion coefficient can lead to the rapid formation of the peak value so that synchronization molecules can be detected early than information molecules.