Objective. To explore the quantitative adjustment of ablation index (AI) under different baseline impedance to achieve similar lesion dimensions. Methods. (1) Keeping the AIs relatively constant, the lesion dimensions in different baseline impedances were studied. (2) According to Joule's law, Q = I2RT, keeping the current (I) unchanged, the powers corresponding to different baseline impedances can be obtained. Under different baseline impedances and corresponding powers, the swine hearts were ablated for 30 s in simulated human circumstances. The baseline impedances, the lesion dimensions, and AIs were recorded. And the derivation of empirical formula was achieved according to the AIs and baseline impedance values in similar lesions dimension. (3) Basic AI and baseline impedance (AI0/R0) were set as 400/120 Ω in the common AI groups and 550/120 Ω in the high AI groups, AI values in different baseline impedances were calculated using the empirical formula, and the corresponding lesion dimensions were measured to verify this formula. Results. (1) Higher baseline impedances were related to smaller lesion dimensions at similar AIs. (2) The lesion dimensions were roughly the same after modulating the baseline impedance and power to keep the electric current relatively constant. The relationship between AI and R fitted with experimental data is AI = 1.9933R + 203.61 (r = 0.9649), and the formula derived is ΔAI = (AI0 − 203)/R0 × ΔR. (3) Under the guidance of the empirical formula, there was no significant difference in lesion dimensions between the standard group and the formula guiding groups when AI0 = 400, but there was a shrinking tendence when AI > 700. Conclusion. The lesion depths are negatively correlated with baseline impedance at a certain AI. The relationship between baseline impedance and AI is “ΔAI = (AI0 − 203)/R0 × ΔR”. It is verified that when the AI is not too high, the empirical formula can be used to guide the quantitative adjustment of AIs at different baseline impedance, and the lesion depths achieved are roughly the same.

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In this paper, we consider a class of fractional Kirchhoff equations with L 2 critical exponents. By using the scaling technique and concentration-compactness principle we obtain the existence and nonexistence of ground state for fractional Kirchhoff equation with L 2 critical exponent.