Multivariate Regression & Cerebral Blood Flow Modeling

Multivariate Regression and Cerebral Blood Flow Module to Computationally Model Dopaminergic Cell Loss in Basal Ganglia Introduction Parkinson’s Disease: ● Neurodegenerative disease caused by loss of dopamine-producing neurons ● Dopamine: neurotransmitter involved in motor control ● 80% dopamine loss → PD symptoms ● Symptoms: Tremor, bradykinesia, stiffness, balance/posture impairment Results Predicted Mitochondrial Stress Level Basal Ganglia: ● group of subcortical nuclei in charge of motor control ● Substantia Nigra pars compacta (SNc): storage for dopamine neurons ● Subthalamic Nucleus (STN): contains circuits that prevent unwanted movement ● Globus Pallidus Externa (GPe): controls inhibition of STN Energy Deficiency: ● Dopamine neurons have large axonal arbors ● Relatively sparsely insulated by myelin ○ Require more energy to send a signal ● Stressors that disrupt energy production lead to cell death because energy demand exceeds supply ● Curve models intracellular calcium accumulation in mitochondria in SNc, STN, and GPe. ● Root Mean Squared Error: 0.0454. ● 100% of variance can be explained by regression. Actual Mitochondrial Stress Level in SNc Calcium Dynamics: ● Calcium concentration is normally regulated by pumps, transporters, and binding proteins. ● Due to ATP deficits, calcium homeostasis is disrupted and calcium builds up in the endoplasmic reticulum and mitochondria ● Result: ER-induced and MT-induced apoptosis Purpose: ● Assess the energy deficiency theory and its role in dopaminergic cell death by investigating calcium dynamics in STN and GPe and modelling the ischemic condition. Predicted Endoplasmic Reticulum Stress Level Methods ● Adapted multiscale model of excitotoxic loss in SNc5. Blood Vessel Module ● Adapted differential and kinetic equations from Cloutier et al 2009 modelling the dynamics of extracellular glucose(GLCe) exchange between capillary, extracellular fluid, and neurons3. Discussion Our model builds upon the future directions provided by Muddapu and Chakravarty 2020. By implementing a more realistic glucose variable that incorporates cerebral blood flow, cell energy and stress levels are better modeled. Furthermore, our model was able to show calcium accumulated in the ER and MT, which is in support of the energy deficiency theory. While both ensemble learners were able to explain most of the variance of the data, the endoplasmic reticulum regression model had a lower r squared value meaning it could only explain 89% of variance. Additionally, this value could be lower when running the prediction on data not in the training set since the regression was created and tested on the membrane potentials of the same cell. A notable limitation is that calcium concentration graph shapes change based on the time interval. As time intervals increase, graphs look more logarithmic which may require a different regression model. Future work should determine parameters using a 50000 ms interval using the given regression models. Muddapu and Chakravarty 2020 model SNC and GPE using Izhikevich cells ● Curve models calcium concentration in endoplasmic reticulum in SNc, STN, and GPe. ● Root Mean Squared Error: 0.01266. ● 89.09% of variance can be explained by regression. Actual Endoplasmic Reticulum Stress Level in SNc Our model predicts calcium levels based on membrane potential given from Izhikevich model Predictions gives a baseline for fine-tuning parameters in conductance-based GPE and SNC ● Solved for change in GLCe over time used to calculate next GLCe at each time step. Intracellular Calcium Dynamics ● Create input data consisting of simulation time vector and SNc membrane potential(V) trajectory and output data of SNc Mt trajectory. ● Fit ensemble of 100 regression trees on input and output data. ● Make predictions for Mt Ca2+ trajectory in STN and GPe. ● Create input data consisting of simulation time vector and SNc V trajectory and output data of SNc ER Ca2+ trajectory. ● Fit ensemble of 100 regression trees on input and output data. ● Make predictions for ER Ca2+ trajectory in STN and GPe. Shared Trends ● Higher calcium levels signify increased stress on neurons and energy deficiency because there is a lack of ATP that is required to remove calcium from ER and MT leading to apoptosis. ● Calcium accumulates rapidly and then levels off. ● STN, SNc and GPe predictions had similar calcium trajectories likely due to the synaptic connections between the nuclei.