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Equity Incentive Plans (Tables)
12 Months Ended
Dec. 31, 2023
Equity Incentive Plans [Abstract]  
Stock Option Plan Activity
Activity under the stock option plans was as follows:
 
          Weighted  
          average  
    Number of     exercise  
   
options
   
price
 
Outstanding at December 31, 2021
   
689,995
   
$
3.58
 
Granted
   
367,670
     
5.33
 
Exercised
   
(9,445
)
   
1.71
 
Expired
   
(10,558
)
   
27.00
 
Forfeited
   
(106,112
)
   
4.09
 
Outstanding at December 31, 2022
   
931,550
   
$
3.97
 
Granted
   
1,301,200
     
0.59
 
Forfeited
   
(130,720
)
   
1.97
 
Outstanding at December 31, 2023
   
2,102,030
   
$
2.00
 
                 
Vested and exercisable at December 31, 2023
    1,226,458     $
2.65  

Stock options granted under the 2021 Plan for the years ended December 31 2023 and 2022 were as follows:

 
 
2023
   
2022
 
Employee
   
1,211,200
     
299,670
 
Nonemployee
   
90,000
     
68,000
 
Total
   
1,301,200
     
367,670
 
Black-Scholes Weighted Average Assumptions
The Black-Scholes weighted average assumptions for all stock option awards granted during 2023 and 2022 were as follows:

    2023
   
2022
 
 
 
2021 Plan
   
2021 Plan
   
Inducement
Grants
 
Fair Value of Awards
  $ 0.48      
2.06
     
2.01
 
Grant Price
  $ 0.59      
5.33
     
2.42
 
 
   
                 
Expected term (in years)
    5.63      
6.28
     
6.25
 
Risk‑free interest rate
    4.09 %    
2.13
%
   
2.52
%
Dividend yield
    %    
%
   
%
Expected volatility
    105.33 %    
107.98
%
   
107.70
%
Options Outstanding and Vested and Currently Exercisable by Exercise Prices
The options outstanding and vested and currently exercisable by exercise prices as of December 31, 2023 were as follows:
 
Options outstanding
   
Options vested and exercisable
 
            Weighted           Weighted
    Weighted  
            average     Number of     average
    average  
Exercise     Outstanding     remaining     options     Exercise     remaining  
price
   
(in shares)
   
life years
   
vested
   
price
   
life years
 
$
0.47 - 0.48
     
3,200
     
9.50
     
   
$
     
 
 
0.49 - 0.53
     
1,061,600
     
9.50
     
601,400
     
0.49
     
9.51
 
 
0.54 - 1.61
     
186,000
     
9.15
     
51,725
     
1.50
     
8.44
 
 
1.62 - 1.74
     
193,335
     
2.21
     
82,224
     
1.71
     
2.21
 
 
1.75 - 3.14
     
196,242
     
8.61
     
29,456
     
2.96
     
8.10
 
 
3.15 - 3.6
     
259,836
     
3.50
     
259,836
     
3.24
     
3.50
 
 
3.61 - 13.00
     
201,817
     
6.52
     
201,817
     
8.97
     
6.52
 
         
2,102,030
     
7.69
     
1,226,458
      2.65      
7.17
 
Share-based Compensation Expense
The following table shows the stock-based compensation expense related to vested stock option grants to employees and non-employees awarded under the stock plans and inducement grants by financial statement line item on the accompanying statements of comprehensive loss:

   
2023
   
2022
 
Research and development
 
$
159,816
     
95,484
 
Sales and marketing
   
(948
)
   
6,680
 
General and administrative
   
516,832
     
122,775
 
Total share-based compensation expense
 
$
675,700
     
224,939