To present a very fast method of calculating core and local temperature throughout the human body in MRI considering SAR, respiration, perspiration, convection, conduction, and local perfusion rates.Absorption of electromagnetic RF energy can result in heating of tissues, and safety guidelines are provided by the IEC to set maximum temperature and maximum absorbed local SAR during MRI scans. Although temperature increase in tissues is more directly related to risk respect to SAR, SAR is still the quantity most used to respect safety guidelines, in part because temperature increase computation can be time consuming. Hence, methods for rapid temperature calculation have been developed^1-3. Specifically, one method² allows fast temperature calculation by convolving the temperature response to a short SAR segment with the series of power levels used throughout an MRI exam. The method is based on the linearity of the bioheat equation and can consider many thermoregulatory mechanisms related to the core body temperature (including whole body heat transfer through temperature-dependent perspiration, convection, respiration, radiation, and conduction)⁴, but not other spatially-varying temperature-dependent phenomena, most importantly thermoregulatory variation in local perfusion rates^5,6. Here we introduce a method to approximate the nonlinear effects of local changes in perfusion in this fast impulse response based method².

Temperature in the human body can be estimated with the Pennes’ bioheat equation:

$$\rho c\frac{\partial T}{\partial t} = \nabla \cdot(k\nabla T)-W\rho_{bl}c_{bl}(T-T_{bl})+Q+\rho SAR\;[1]$$

where T is temperature, W is rate of blood perfusion, k is thermal conductivity, ρ is density, c is heat capacity, Q is rate of metabolism, and the subscript bl denotes values for blood. This equation can be expressed to allow variation in core temperature T_bl without loss of linearity². Core temperature can be made a function of the whole body SAR and numerous physiological phenomena as listed above⁴. Local blood perfusion can be expressed as a function of temperature in a number of ways, including⁶

$$W(r)=\begin{cases}W_0(r) & T(r) \leq 39\,^{\circ}{\rm C} \\W_0(r)\left( 1+S_B \left( T(r)-39 \right) \right) & 39\,^{\circ}{\rm C} < T(r) \leq 44\,^{\circ}{\rm C} \\ W_0(r)\left( 1+5S_B \right) & T(r) > 44\,^{\circ}{\rm C} \end{cases} [2]$$

Let us define $$$W(r) = W_0(r)+\Delta W(r,t)\;[3]$$$, and substituting eq. [3] in eq. [1] yields

$$\rho c \frac{\partial T}{\partial t} = \nabla \cdot (k\nabla T)-W_0 \rho_{bl} c_{bl} (T-T_{bl})-\Delta W_0 \rho_{bl} c_{bl} (T-T_{bl})+Q+\rho SAR \;[4]$$

Let us define $$$T_C = T_{NC}+\Delta T\;[5]$$$, so that eq. [4] can be separated into

$$\rho c \frac{\partial T_{NC}}{\partial t} = \nabla \cdot (k\nabla T_{NC})-W_0 \rho_{bl} c_{bl} (T_{NC}-T_{bl})+Q+\rho SAR \;[6]$$

which is a linear equation which can be solved with the impulse response method previously presented², and

$$\rho c \frac{\partial T}{\partial t} = \nabla \cdot (k\nabla T)-W_0 \rho_{bl}c_{bl} (T-T_{bl})-\Delta W \rho_{bl} c_{bl} ((T_{NC}+\Delta T)-T_{bl}) \;[7]$$

which determines the value of Δt, a correction term that estimates the effect of the change in temperature due to the change in blood perfusion. Eq. [7] can be quickly solved by using a previously demonstrated method of applying a low-pass spatial filter³ that approximates the effects of thermal conduction. The filter is applied sequentially at time intervals Δt of 30s and longer.

When no nonlinear thermoregulatory effects are considered the maximum estimated local temperature is 47.3 °C, while with temperature dependent perfusion the maximum is 42.3 °C, located in one shoulder. In both cases, maximum temperature increases exceed the maximum allowable local temperature of 40 °C. Fig.1 shows the comparisons between the temperature distribution obtained with a Finite Difference temperature solver and the method presented here, with and without the thermoregulatory corrections. When no thermoregulatory effects are considered the maximum temperature in the two methods differ by less than 1%, while when thermoregulatory effects are considered the maximum temperature differ by less than 8% with the fast method being more conservative. For a time interval Δt=30s, the method presented here requires a computation time about 30 times shorter than the Finite Difference method. Increasing Δt to 120s results in a very similar temperature distribution with approximately a 120-fold acceleration over the finite difference method. The method is stable and accurate even for large accelerations, though temporal resolution may be lost (Fig. 2).The advance presented in this work overcomes the main limitation of a previous extremely fast method² by approximating the effects of local temperature-dependent perfusion rates without affecting the speed of the method. This allows real-time safety prediction and assurance for an entire MRI exam, useful in rapid determination of pulses, sequences, and series of sequences that will not exceed limits on temperature or thermal dose.