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Stock-Based Compensation (Tables)
 6 Months Ended
Jun. 30, 2021
Stock-Based Compensation [Abstract]  
Stock-Based Compensation Expense

The Company’s stock-based compensation expense related to stock options was recognized in operating expense as follows:
   
Three Months Ended June 30,
    
Six Months Ended June 30,
  
   
2021
    
2020
    
2021
    
2020
  
   
(unaudited)
    
(unaudited)
  
Stock-Based Compensation
                        
Research and development
  
$
167,432
    
$
53,842
    
$
227,817
    
$
106,526
  
General and administrative
    
274,166
      
(7,728
)
    
471,401
      
64,580
  
Total
  
$
441,598
    
$
46,113
    
$
699,219
    
$
171,106
  
Assumptions Used to Value Stock Options Granted

The fair value of options granted during the three and six months ended June 30, 2021 and the three and six months ended June 30, 2020 was estimated using the Black-Scholes option valuation model utilizing the following assumptions. There was 1,391,130 and 1,658,930 of options granted during the three and six month period ended June 30, 2021.
   
Three Months Ended June 30,
    
Six Months Ended June 30,
  
   
2021
    
2020
    
2021
    
2020
  
   
Weighted Average
    
Weighted Average
    
Weighted Average
    
Weighted Average
  
   
(unaudited)
    
(unaudited)
  
Volatility
    
100.63
%
    
97.13
%
    
100.59
%
    
97.00
%
Risk-Free Interest Rate
    
0.79
%
    
0.34
%
    
0.72
%
    
0.38
%
Expected Term in Years
    
6.38
      
6.07
      
6.28
      
6.07
  
Dividend Rate
    
–
      
–
      
–
      
–
  
Fair Value of Option on Grant Date
  
$
7.28
    
$
1.11
    
$
6.39
    
$
1.11
  
Stock Option Activity

The following table summarizes the number of options outstanding and the weighted average exercise price:
   
Number
of Shares
    
Weighted
Average
Exercise Price
    
Weighted Average
Remaining
Contractual
Life in Years
    
Aggregate
Intrinsic Value
  
Options outstanding at December 31, 2020
    
1,650,897
    
$
11.87
      
7.03
    
$
226,731
  
Granted
    
1,658,930
      
2.89
      
9.50
    
$
–
  
Exercised
    
(78,579
)
    
7.25
      
3
    
$
414,306
  
Forfeited
    
(22,000
)
    
21.40
      
–
    
$
141,978
  
Options outstanding at June 30, 2021
    
3,209,248
    
$
7.28
      
8.12
    
$
25,359,866
  
Vested and expected to vest at June 30, 2021
    
3,209,248
    
$
7.28
      
8.12
    
$
25,359,866
  
Exercisable at June 30, 2021
    
1,204,185
    
$
14.43
      
5.77
    
$
6,173,912