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Equity Incentive Plans (Tables)
6 Months Ended
Jun. 30, 2022
Equity Incentive Plans [Abstract]  
Stock Option Plan Activity
Activity under the stock option plans was as follows:

   
Number of
options
   
Weighted
average
exercise price
   
Weighted
average
remaining
contracted
term in
years
   
Aggregate
intrinsic
value
 
Outstanding at December 31, 2021
   
689,995
   
$
3.58
          $ 683,531  
Granted
   
270,170
     
6.71
               
Expired
   
(3,334
)
   
27.00
               
Forfeited
   
(834
)
   
6.12
               
Outstanding at March 31, 2022
   
955,997
   
$
4.38
      6.47     $ 125,279  
Granted
    51,000       1.50                  
Exercised
    (9,445 )     1.71                  
Expired
    (278 )     27.00                  
Forfeited
    (46,668 )     3.27                  
Outstanding at June 30, 2022
    950,606     $ 4.30       6.55     $ 181,745  
                                 
Vested and exercisable at June 30, 2022
    476,941     $ 3.71       5.08     $ 57,557  
Estimated Using Assumptions The weighted-average fair values of the options granted to employees and nonemployees were $2.34 and $1.55, respectively and were estimated using the following weighted-average assumptions:

    Employee     Nonemployee  
Expected term (in years)
   
6.47
     
5.63
 
Risk‑free interest rate
   
1.74
%
   
2.67
%
Dividend yield
   
%
   
%
Expected volatility
   
107.23
%
   
109.67
%
 
The fair value of the inducement grant was $2.46 and was estimated using the following assumptions:

   
Inducement
 
Expected term (in years)
   
6.25
 
Risk‑free interest rate
   
1.76
%
Dividend yield
   
%
Expected volatility
   
106.76
%
Share-based Compensation Expense
The following table shows the share-based compensation expense related to vested stock option grants to employees and nonemployees by financial statement line item on the accompanying statement of comprehensive loss:
 
    Three Months Ended June 30,
    Six Months Ended June 30,  
   
2022
   
2021
    2022
    2021
 
Research and development
 
$
33,436
     
29,205
      62,575       64,702  
Sales and marketing
   
1,216
     
936
      2,342       1,861  
General and administrative
   
27,515
     
27,905
      41,609       63,973  
Total share-based compensation expense
 
$
62,167
     
58,046
      106,526       130,536