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Thus, the residual energy of the node n(n=1,2,…,N) is as follows: E n re t = E n init - E n sens t - E n rece + E n tran · D n t - E n tran · M n t = E n init - τ n P n sens t - 2 P n elec + P n tran KLD n t r - P n elec + P n tran KLM n t r, (18).
where M n and M n ′ are non-negative integers described as M n = E n init - τ n P n sens t - E th r P n elec + P n tran KL, ∀ n ∈ 1, 2 …, N, (27) M n, k ′ = E n init - τ n P n sens t - E th r - kKL P n elec + P n tran 2 P n elec + P n tran KL, ∀ n ∈ 1, 2 …, N. (28).
Specially, if Λ n (t) does not change over time, Equation 3 can be rewritten as E E n init t ≈ τ n P n sens + P n elec + P n tran KL r λ n + 2 P n elec + P n tran KL r ∑ m = 0 n - 1 R m, n L · λ m t. (38).
Without loss of generality, when M n (t) = k,k ≤ M n, we have D n (t) ∈ {0,1,…,Mn,k′} where M n,k′ can be described as M n, k ′ = E n init - τ n P n sens t - E th r - kKL P n elec + P n tran 2 P n elec + P n tran KL, ∀ n ∈ 1, 2, …, N. (59).
Obviously, when D n (t) = 0, M n (t) may take the maximum value M n which can be expressed as M n = E n init - τ n P n sens t - E th r P n elec + P n tran KL, ∀ n ∈ 1, 2, …, N. (56).
Thus, the expected value of the initial energy for the relay node n can be calculated as E E n init t ≈ E E n cons t = τ n P n sens t + P n elec + P n tran KL r Λ n t + 2 P n elec + P n tran KL r ∑ m = 0 n - 1 R m, n L · Λ m t. (37).
The energy consumption for transmitting one packet can be defined as E n tran = P n elec + P n tran KL r ∀ n ∈ 0, 1, …, N, (8).
Similar to the source node, from Equation 18, the expected value of energy consumption for the relay node n at time t can be obtained as E E n cons t = τ n P n sens t + P n elec + P n tran KL r E M n t + 2 P n elec + P n tran KL r E D n t = τ n P n sens t + P n elec + P n tran KL r Λ n t + 2 P n elec + P n tran KL r ∑ m = 0 n - 1 R m, n L · Λ m t. (36).
In case of the 6.1-Mb interval (Fig. S7), the frequency of double-positive cells after 7 days of OHT stimulation was significantly lower than that seen with the 1.1-Mb interval: (1.2±0.6 ×10−3 (cis, n = 4) and (3.0±1.7 ×10−5 (trans, n = 8).
