Quantum Mechanical Mechanisms in the Therapeutic Effects of Spinal Cord Stimulation to Treat Chronic Neuropathic Pain: A Quantum Computational Model

Mahmoud Abdallat,1 Abdallah Barjas Qaswal,2 Ahmad Quzli,3 Moustafa Hassan,4 Sondos Alkhatib,3 Yazan Khraim,5 Ghufran Alkhateeb,6 Omar Alsmadi,7 Zaid Abdulqader,4 Jehad Shitawi,4 Hala Raed Miqdadi,2 Mariana Nuseir,8 Hussam IA Alzeerelhouseini,8 Sehrish Hanif,9 Omar Essa,10 Dima Yousef,10 Fatima Alsoub,10 Maram Okour,10 Ayham Alzubaidi,11 Omar Alsahli,12 Hasan El-Isa,13 Hussam Alsaddi,14 Mohamad Osama Al-Rashdan2 1Department of Neurosurgery, University of Jordan, Amman, 11942, Jordan; 2Department of Psychiatry, Jordan University Hospital, Amman, 11942, Jordan; 3West Suffolk NHS Foundation Trust, Suffolk, UK; 4United Lincolnshire Hospital NHS Trust, Grantham, Lincolnshire, NG31 8JE, UK; 5Hull University Teaching Hospital NHS Trust, Hull, HU3 2JZ, UK; 6School of Medicine, University of Jordan, Amman, 11942, Jordan; 7Colchester General Hospital, Colchester, CO4 5JL, UK; 8Department of Internal Medicine, School of Medicine, University of Jordan, Amman, 11942, Jordan; 9Bahria University, Islamabad, Islamabad Capital Territory, Pakistan; 10Department of Family Medicine, School of Medicine, University of Jordan, Amman, 11942, Jordan; 11School of Medicine, Jordan University of Science and Technology, Irbid, 22110, Jordan; 12Alabdali Clemenceau Hospital, Amman, 11190, Jordan; 13Jordanian Royal Medical Services, Amman, 11855, Jordan; 14School of Medicine, Al-Baath University, Homs, SyriaCorrespondence: Abdallah Barjas Qaswal, Email [email protected]: Spinal cord stimulation (SCS) is an emerging intervention used to treat neuropathic pain by inducing depolarization mediated by ion channels. According to the principles of classical electrophysiology, SCS will fail to induce depolarization if the barrier height of potassium channels is lower than that of sodium channels; moreover, the SCS seems to add more energetic burden on the neurons which may worsen the neuropathic pain. Therefore, our research question is “does quantum physics offer an alternative mechanism that may solve these two problematic concerns?”.Methods: In the present study, a mathematical model of quantum tunneling is applied on two-pore domain potassium channel K2P and sodium leak channel NALCN channels. The equations that describe the relationship between the external electric field produced from SCS and the membrane potential are stated clearly. Then, these equations are inserted in the MATLAB software to be solved for the membrane potential.Results and discussion: Our results indicate that quantum tunneling model predicts the occurrence of depolarization induced by SCS even in the case that potassium channels have lower barrier height because the quantum model predicts that extracellular potassium ions have higher kinetic energy and higher tunneling probability compared to the intracellular potassium ions. As a result, net inward potassium current is generated and is able to depolarize the membrane potential. Hyperpolarization is predicted by the quantum model only in the case in which the influence of the external electric field on the kinetic energy of ions is considered and its direction is opposite to the direction of the electric field of the neuronal membrane. In addition, quantum tunneling-assisted depolarization utilizes lower energy compared to the depolarization induced by the classical opening of closed channels because the quantum tunneling of ions requires lower energy than the barrier height for the transport to occur.Keywords: quantum tunneling, chronic pain, ion channels, spinal cord stimulation