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Stock-Based Compensation (Tables)
6 Months Ended
Jun. 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 June 30,
   
Six months ended June 30,
 
   
2023
   
2022
   
2023
   
2022
 
   
(unaudited)
   
(unaudited)
 
Stock-Based Compensation
                       
Research and development
 
$
806,548
   
$
487,532
   
$
1,607,312
   
$
856,582
 
General and administrative
   
1,298,990
     
861,069

   
2,578,545
     
1,620,992
 
Total
 
$
2,105,538
   
$
1,348,601
   
$
4,185,857
   
$
2,477,574
 
Assumptions Used to Value Stock Options Granted

The fair value of options granted during the three and six months ended June 30, 2023 and 2022 was estimated using the Black-Scholes option valuation model utilizing the following assumptions. There were 29,900 and 1,154,500 of options granted during the three and six month periods ended June 30, 2023, respectively and 494,000 and 1,439,005 of options granted during the three and six month period ended June 30, 2022, respectively.


   
Three Months Ended June 30
   
Six Months Ended June 30,
 
   
2023
   
2022
   
2023
   
2022
 
   
Weighted
Average
   
Weighted
Average
   
Weighted
Average
   
Weighted
Average
 
   
(unaudited)
   
(unaudited)
 
Volatility
   
143.87
%
   
100.05
%
   
142.07
%
   
99.45
%
Risk-Free Interest Rate
   
3.59
%
   
2.60
%
   
4.05
%
   
11.62
%
Expected Term in Years
   
6.08
     
6.02
     
6.08
     
6.43
 
Dividend Rate
   
     
     
     
 
Fair Value of Option on Grant Date
 
$
5.09
   
$
4.01
   
$
10.64
   
$
4.59
 
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
   
1,154,500
     
11.45
     

   


 
Exercised
   
(1,409
)
   
-
     
   


 
Forfeited and expired
   
-

   
-
     

   


 
Options outstanding at June 30, 2023
   
5,324,402
   
$
6.85
     
7.86
   
$
4,645,635
 
Vested and expected to vest at June 30, 2023
   
5,324,402
   
$
6.85
     
7.86
   
$
4,645,635
 
Exercisable at June 30, 2023
   
2,513,595
   
$
5.80
     
6.83
   
$
2,901,233