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Stock-Based Compensation (Tables)
3 Months Ended
Mar. 31, 2023
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 March 31,
 
   
2023
   
2022
 
    (unaudited)
 
Stock-Based Compensation            
Research and development
  $
800,764
    $
369,050
 
General and administrative
   
1,279,555
     
759,923
 
Total
  $
2,080,319
    $
1,128,973
 
Assumptions Used to Value Stock Options and Warrants Granted

The fair value of options granted during the three months ended March 31, 2023 and 2022 was estimated using the Black-Scholes option valuation model utilizing the following assumptions:

   
Three Months Ended March 31,
 
   
2023
   
2022
 
   
Weighted Average
   
Weighted Average
 
   
(unaudited)
 
Volatility
   
142.02
%
   
99.13
%
Risk-Free Interest Rate
   
4.06
%
   
1.10
%
Expected Term in Years
   
6.08
     
6.64
 
Dividend Rate            
Fair Value of Option on Grant Date
 
$
10.79
   
$
4.88
 
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, 2022
   
4,171,311
   
$
5.56
     
7.89
   
$
10,839,589
 
Granted
   
1,124,600
     
11.61
      9.77        
Exercised
   
   
                 
Forfeited and expired
   
   
                 
Options outstanding at March 31, 2023
   
5,295,911
   
$
6.85
     
8.09
   
$
7,054,179
 
Vested and expected to vest at March 31, 2023
   
5,295,911
   
$
6.85
     
8.09
   
$
7,054,179
 
Exercisable at March 31, 2023
   
2,169,348
   
$
6.00
     
6.86
   
$
3,615,087