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Stockholders' Equity - Stock-Based Compensation Expense (Details) - USD ($)
3 Months Ended
Mar. 31, 2019
Mar. 31, 2018
Stock-based compensation expense    
Total stock-based compensation expense $ 1,382,443 $ 1,115,830
Research and Development    
Stock-based compensation expense    
Total stock-based compensation expense 507,822 425,209
General and Administrative Expense.    
Stock-based compensation expense    
Total stock-based compensation expense $ 874,621 $ 690,621