Strength-duration time constants, rheobase currents, and recovery cycles allow the nerve adaptive processes to single or pairs of depolarizing stimuli to be assessed. This study investigates the temperature dependence of these excitability indices of human motor nerve fibers with one of three increasingly-severe type of amyotrophic lateral sclerosis pathology, referred to as ALS1, ALS2, and ALS3. The temperature dependence of the excitability indices was investigated during hypothermia (
Amyotrophic lateral sclerosis (ALS) is a usually fatal disorder causing progressive death of the motor neurons in both the cerebral cortex and the spinal cord. The pathological mechanisms of upper and lower motor neuron degeneration in this disorder have not been fully elucidated. ALS is a progressively debilitating disease characterized by increasing skeletal muscle atrophy starting in the limbs and spreading to the rest of the body [1, 2, 3], often accompanied by wide-spread fasciculations [4-12], possibly suggesting motor nerve axonal hyperexcitability [4, 7, 12, 13]. There is also the theory that these fasiculations are due the spreading of acetylcholine (ACh) receptors over the muscle surface: denervation hypersensitivity.
A threshold tracking technique [14-17] has been clinically employed to assess nerve adaptation in control subjects [18, 19] and patients with neurological disorders including and three progressively greater degrees of ALS severity (at or above a skin temperature of 32
Temperature effects on adaptive processes have also been examined in the range of 20-42
The simulations presented here were performed using a temperature-dependent multi-layered numerical model of human motor nerve fibres developed by the authors. The control (normal) temperature was 37
This temperature-dependent, multi-layered model was applied to the previously simulated ALS1, ALS2, and ALS3 cases [28, 29]. The uniform axonal dysfunctions of active parameters such as maximum permeabilities of nodal and internodal ion channels with their characteristic values follow those suggested by Bostock et al. [20]. Specifically they were: (i) nodal fast potassium
Temperatures were changed concurrently and equally in each segment along the fibre length. The strength-duration curves, charge-duration curves, strength-duration time constants, rheobase currents, and recovery cycles were investigated during hypothermia (
For a given temperature, the threshold stimulus duration was increased in 0.025 ms steps from 0.025 ms to 1 ms for constructing the strength-duration curves. These curves were not simple single-exponential functions, and thus the associated charge-duration curves were not linear. However, the following polynomial function of second degree (transfer parabola), which related the threshold charge (
For a given temperature, the test stimulus amplitude required to elicit a second action potential during the relative refractory period was either greater or less than the conditioning stimulus amplitude, depending on the conditioning test (CT) intervals. To obtain the time course of recovery of axonal excitability following a single stimulus (the recovery cycle), test threshold current stimuli of one ms duration were delivered at CT intervals of 2-100 ms after a suprathreshold conditioning current stimulus of one ms duration. The test stimulus thresholds were determined at 27 CT intervals, with the intervals being increased up to 100 ms in approximately geometric progression. Three stimulus combinations were tested: (i) conditioning (first) stimulus (duration one ms) was determined at threshold; (ii) suprathreshold conditioning stimulus (duration one ms) was calculated, which was increased by 5% of threshold, and (iii) the first suprathreshold (conditioning) plus the test (second) threshold stimuli were used to obtained the recovery cycle.
Comparison of the strength-duration curves (Fig. 1, first column) and charge-duration curves (Fig. 1, last column) is shown for normal (Fig. 1a), ALS1 (Fig. 1b) and ALS2 (Fig. 1c) cases during hypothermia (20
Comparison between the strength-duration curves (first column) and charge-duration curves (last column) in the normal (a), ALS1 (b), and ALS2 Comparison between the strength-duration curves (first column) and charge-duration curves (last column) in the normal (a), ALS1 (b), and ALS2
In the almost superimposed strength-duration curves for the normal/ALS1/ALS2 cases at 30
Comparison between the strength-duration curves (first column) and charge-duration curves (last column) in the normal (a), ALS1 (b), and ALS2
Comparison between the strength-duration time constants (first column) and rheobase currents (last column) for normal (hatched first bars, from left to the right), ALS1 (white second bars), and ALS2
Consequently, with the increase of temperature from 20
Absolute temperature-dependent recovery cycles of the normal, ALS1, ALS2, and ALS3 cases are plotted in Fig. 4 on logarithmic
The absolute refractory period, relative refractory period, and axonal superexcitability in the 100 ms recovery cycle changed with increased temperature. The absolute refractory periods in the normal/ALS1/ALS2/ALS3 cases were 4.0/4.0/5.0/5.0, 2.8/2.8/2.9/2.9, 2.5/2.5/2.7/2.7, 2.4/2.4/2.5/2.5, 2.1/2.1/2.1/2.1 and 2.1/2.1/2.1/2.1 ms at 20
For the normal and ALS1 cases with increased temperature, the axonal superexcitability decreased during hypothermia and increased rapidly during hyperthermia. Also, the superexcitability period was followed by a late subexcitability period when the temperature was 37
Comparison between the absolute recovery cycles in the normal (first column), ALS1 (second column), ALS2 (third column), and ALS3 (last column) cases. The recovery cycles are numbered from 1 to 6 and each consecutive number corresponds to 20
The recovery cycles commented on above are normalized and presented together in Fig. 5. Each recovery cycle in the normal and abnormal cases for the given temperature is normalized to the control threshold current of its corresponding conditioning stimulus. The presented panel figures clearly show that the profile of recovery cycles is similar for the normal and ALS1 cases (Fig. 5, first row), and that the axonal superexcitabilities increase rapidly in the ALS2 case at 20
Comparison between the normalized recovery cycles in the normal, ALS1, ALS2 and ALS3 cases. The recovery cycles are numbered from 1 to 6 and each consecutive number corresponds to 20
Recovery cycles depend not only on the temperature, but also on the regenerative axonal membrane depolarization or hyperpolarization caused by the conditioning afterpotential and could be explained by the delay-dependent testing potential. The temporal distributions of testing potentials for the normal, ALS1, ALS2, and ALS3 cases as a function of CT intervals are given during hypothermia and hyperthermia (Fig. 6). During hypothermia at 20
Temporal distributions of action potentials when the test stimulus is applied as a function of CT interval, corresponding to: CT
The temporal distributions of testing potentials for the normal, ALS1, ALS2, and ALS3 cases as a function of CT intervals are also presented for the physiological temperature range at 30
Temporal distributions of action potentials when the test stimulus is applied as a function of the CT intervals, corresponding to: CT
Simulated excitability indices were studied, such as strength-duration time constants, rheobase currents, and recovery cycles of the ALS1, ALS2, and ALS3 cases during hypothermia, hyperthermia, and in the physiological temperature range. These parameters were compared to those of the normal case. The results presented here, as well as those from both clinical [20, 21, 22, 23, 24, 25, 26, 27] and previous studies [28, 29], conducted at normal temperature, showed that compared to the normal case, there is a characteristic: (i) longer strength-duration time constant and lower rheobase current, (ii) less refractoriness, and (iii) greater axonal superexcitability and reduced late subexcitability. Nevertheless, in the three ALS cases the strength-duration time constants gradually decreased with increased temperature from 20
As suggested from simulation results, it is proposed that the temperature-dependent strength-duration time constants, rheobase currents, and recovery cycles in the three ALS cases can be clinically interpreted as specific indicators for the motor neuron disease ALS. Results obtained are essential for the interpretation of mechanisms of excitability parameter measurements in healthy and ALS patients with symptoms of cooling, warming and fever, which can result from alteration in body temperature.
We thank the Institute of Biophysics and Biomedical Engineering for use of computational facilities.
All authors declare no conflict of interest.