Meth math: modeling temperature responses to methamphetamine

Abstract

Methamphetamine (Meth) can evoke extreme hyperthermia, which correlates with neurotoxicity and death in laboratory animals and humans. The objective of this study was to uncover the mechanisms of a complex dose dependence of temperature responses to Meth by mathematical modeling of the neuronal circuitry. On the basis of previous studies, we composed an artificial neural network with the core comprising three sequentially connected nodes: excitatory, medullary, and sympathetic preganglionic neuronal (SPN). Meth directly stimulated the excitatory node, an inhibitory drive targeted the medullary node, and, in high doses, an additional excitatory drive affected the SPN node. All model parameters (weights of connections, sensitivities, and time constants) were subject to fitting experimental time series of temperature responses to 1, 3, 5, and 10 mg/kg Meth. Modeling suggested that the temperature response to the lowest dose of Meth, which caused an immediate and short hyperthermia, involves neuronal excitation at a supramedullary level. The delay in response after the intermediate doses of Meth is a result of neuronal inhibition at the medullary level. Finally, the rapid and robust increase in body temperature induced by the highest dose of Meth involves activation of high-dose excitatory drive. The impairment in the inhibitory mechanism can provoke a life-threatening temperature rise and makes it a plausible cause of fatal hyperthermia in Meth users. We expect that studying putative neuronal sites of Meth action and the neuromediators involved in a detailed model of this system may lead to more effective strategies for prevention and treatment of hyperthermia induced by amphetamine-like stimulants.

Keywords: amphetamines; artificial neural network; body temperature; hyperthermia; modeling.

Fig. 1.

Neuronal circuitry involved in responses to amphetamines. A: actual anatomic structures. B: simplified conceptual network. Lines with arrows, excitatory projections (source is white); lines with circles, inhibitory projections (source is gray). MPOA, medial preoptic area; vlPAG and dlPAG, ventrolateral and dorsolateral periaqueductal gray; RVLM, rostral ventrolateral medulla; DMH, dorsomedial hypothalamus; RP, raphe pallidus; SC, superior colliculus.

Fig. 2.

Dose dependence of temperature responses to methamphetamine (Meth). Meth was injected intraperitoneally at 0 min (t = 0) in a volume of 1 ml/kg.

Fig. 3.

“Three-arrow” (circuitry-based) model. A: model schematic. Each circle represents a neural population. Meth-sensitive populations (“Meth”-labeled arrows) are modeled as an artificial neuron with sigmoidal activation function applied to its input (see text for a detailed description). Circuitry is a compilation of data from the literature. Exc, excitatory; Inhib, inhibitory; HD, high dose; Mdl, medulla; SPN, sympathetic preganglionic (or premotor) neuron; TEMP, temperature. B: activation functions of Meth-sensitive populations. Vertical lines show half-activation concentrations. C: reconstructed activity of neuronal populations included in the model, together with comparison of reconstructed dynamics of body temperature, after various doses of Meth, with actual experimental data used in fitting procedures. All reconstructed values of body temperature were within 1 SD of actual experimental data within the time period used for fitting procedures (220 min, gray bar). au, Arbitrary units.

Fig. 4.

A and B: excitatory and inhibitory components of thermogenic activity in three- and two-arrow models as a function of Meth concentration in the blood. C: reconstructed time courses of Meth concentration in the blood for 1, 3, 5, and 10 mg/kg Meth. Vertical lines show maximal Meth concentrations in the blood for each dose in A and B.

Fig. 5.

Two-arrow model. See Fig. 3 legend for details.

Fig. 6.

One-arrow model. See Fig. 3 legend for details.

Fig. 7.

Variability of temperature responses to 1, 3, 5, and 10 mg/kg Meth due to model parameter perturbation. A: two-arrow model. B: three-arrow model. ● with error bars represent average and SD of experimentally measured core body temperature. Top and bottom solid lines are maximal and minimal temperature responses produced by the models after 3% change in key model parameters.

Fig. 8.

Modeling temperature responses to Meth (1 and 3 mg/kg) if inhibitory component is suppressed. ● with error bars represent experimental data. Thin solid line, best-fitting three-arrow model; dashed line, model with all parameters of thin solid line, except weight of inhibitory projection is considered 50% of the original value; thick solid line, model with all parameters of thin solid line, except weight of inhibitory projection is considered equal to 0.