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Stock-Based Compensation (Tables)
9 Months Ended
Sep. 30, 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
September 30,
   
Nine Months Ended
September 30,
 
   
2023
   
2022
   
2023
   
2022
 
   
(unaudited)
   
(unaudited)
 
Stock-Based Compensation
                       
Research and development
 
$
782,249
   
$
493,083
   
$
2,389,561
   
$
1,349,664
 
General and administrative
   
1,291,358
     
851,267

   
3,869,903
     
2,472,259
 
Total
 
$
2,073,607
   
$
1,344,350
   
$
6,259,464
   
$
3,821,923
 
Assumptions Used to Value Stock Options Granted

There were 59,500 and 1,214,000 of options granted during the three and nine month periods ended September 30, 2023, respectively and 87,000 and 1,526,005 of options granted during the three and nine month period ended September 30, 2022, respectively. The fair value of options granted during the three and nine months ended September 30, 2023 and 2022 was estimated using the Black-Scholes option valuation model utilizing the following assumptions.


   
Three Months Ended
September 30,
   
Nine Months Ended
September 30,
 
   
2023
   
2022
   
2023
   
2022
 
   
Weighted
Average
   
Weighted
Average
   
Weighted
Average
   
Weighted
Average
 
   
(unaudited)
   
(unaudited)
 
Volatility
   
150.26
%
   
101.43
%
   
142.47
%
   
99.56
%
Risk-Free Interest Rate
   
3.92
%
   
3.03
%
   
4.04
%
   
1.70
%
Expected Term in Years
   
5.59
     
6.08
     
6.06
     
6.41
 
Dividend Rate
   
     
     
     
 
Fair Value of Option on Grant Date
 
$
4.77
   
$
2.58
   
$
10.35
   
$
4.80
 
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
   
$
32,779,920
 
Granted
   
1,214,000
     
11.14
     

   


 
Exercised
   
(1,409
)
   
-
     
   


 
Forfeited and expired
   
-

   
-
     

   


 
Options outstanding at September 30, 2023
   
5,383,902
   
$
6.82
     
7.63
   
$
4,685,828
 
Vested and expected to vest at September 30, 2023
   
5,383,902
   
$
6.82
     
7.63
   
$
4,685,828
 
Exercisable at September 30, 2023
   
2,722,797
   
$
5.72
     
6.67
   
$
3,225,309