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Equity Incentive Plans (Tables)
12 Months Ended
Dec. 31, 2022
Equity Incentive Plans [Abstract]  
Stock Option Plan Activity
Activity under the stock option plans was as follows:
 
          Weighted  
          average  
    Number of     exercise  
   
options
   
price
 
Balances at December 31, 2020
   
743,627
   
$
3.60
 
Granted
   
     
 
Exercised
   
(44,698
)
   
2.83
 
Expired
   
(556
)
   
27.00
 
Forfeited
   
(8,378
)
   
5.43
 
Balances 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
 
Balances at December 31, 2022
   
931,550
   
$
3.97
 

Stock options granted under the stock option plans for the years ended December 31 2022 and 2021 were as follows:

 
 
2022
   
2021
 
Employee
   
299,670
     
 
Nonemployee
   
68,000
     
 
Total
   
367,670
     
 
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, 2022 were as follows:
 
Option 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
 
$
1.13 - 1.67
     
91,100
     
9.59
     
   
$
     
 
 
1.68 - 1.86
     
193,335
     
3.21
     
82,224
     
1.71
     
3.21
 
 
1.87 - 3.14
     
166,850
     
9.09
     
     
     
 
 
3.15 - 3.60
     
259,836
     
4.50
     
259,836
     
3.24
     
4.50
 
 
3.61 - 5.31
     
68,616
     
5.23
     
68,616
     
3.97
     
5.23
 
 
5.32 - 9.56
     
51,813
     
6.95
     
38,765
     
6.12
     
6.95
 
 
9.57 - 13.00
     
100,000
     
9.07
     
     
     
 
         
931,550
     
6.23
     
449,441
      3.32      
4.58
 
Black-Scholes Weighted Average Assumptions
The Black-Scholes weighted average assumptions for all stock option awards granted during 2022 were as follows:


  2022  
 
 
2021 Equity Plan
   
Inducement Grants
 
Fair Value of Awards
 
$
2.06
     
2.01
 
Grant Price
 
$
5.33
     
2.42
 
 
               
Expected term (in years)
   
6.28
     
6.25
 
Risk‑free interest rate
   
2.13
%
   
2.52
%
Dividend yield
   
%
   
%
Expected volatility
   
107.98
%
   
107.70
%
Share-based Compensation Expense
The following table shows the stock-based compensation expense related to vested stock option grants to employees and nonemployees awarded under the stock plans and inducement grants by financial statement line item on the accompanying statement of comprehensive loss:

   
2022
   
2021
 
Research and development
 
$
95,484
     
106,469
 
Sales and marketing
   
6,680
     
3,759
 
General and administrative
   
122,775
     
83,138
 
Total share-based compensation expense
 
$
224,939
     
193,366