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Equity Incentive Plans (Tables)
12 Months Ended
Dec. 31, 2024
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]  
Black-Scholes Weighted Average Assumptions
The Black-Scholes weighted average assumptions for all stock option awards granted during 2024 and 2023 were as follows:

   
2024
   
2023
 
   
2021 Plan
   
Inducement
Grants
   
2021 Plan
 
Fair Value of Awards
 
$
0.91
     
0.94
     
0.48
 
Grant Price
 
$
1.07
     
1.1
     
0.59
 
                         
Expected term (in years)
   
6.20
     
6.25
     
5.63
 
Risk‑free interest rate
   
4.04
%
   
4.10
%
   
4.09
%
Dividend yield
   
%
   
%
   
%
Expected volatility
   
109.61
%
   
109.64
%
   
105.33
%
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, 2024 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 - 0.49
     
1,063,600
     
8.50
     
716,950
   
$
0.49
     
8.50
 
 
0.50 - 0.80
     
565,321
     
9.05
     
22,867
     
0.59
     
8.47
 
 
0.81 - 1.33
     
564,450
     
9.40
     
20,325
     
0.88
     
8.42
 
 
1.34 - 1.74
     
210,846
     
2.26
     
85,335
     
1.67
     
2.45
 
 
1.75 - 3.14
     
164,325
     
7.70
     
57,225
     
2.64
     
7.53
 
 
3.15 - 3.60
     
237,614
     
2.49
     
237,614
     
3.24
     
2.49
 
 
3.61 - 13.00
     
168,063
     
5.75
     
168,063
     
9.68
     
5.74
 
         
2,974,219
     
7.65
     
1,308,379
      2.35      
6.62
 
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:

   
2024
   
2023
 
Research and development
 
$
179,911
     
159,816
 
Sales and marketing
   
48,379
     
(948
)
General and administrative
   
215,857
     
516,832
 
Total share-based compensation expense
 
$
444,147
     
675,700
 
2021 Stock Option Plan [Member]  
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]  
Stock Option Plan Activity
Activity under the stock option plans was as follows:
 
   
Number of
options
   
Weighted
average
exercise
price
   
Aggregate
Intrinsic Value
 
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
       
Granted
   
1,359,821
     
1.07
       
Forfeited
   
(487,632
)
   
1.84
       
Outstanding at December 31, 2024
   
2,974,219
   
$
1.60
      847,758
 
                         
Vested and exercisable at December 31, 2024
    1,308,379     $ 2.35       453,514
 

Stock options granted under the 2021 Plan for the years ended December 31 2024 and 2023 were as follows:

 
 
2024
   
2023
 
Employee
   
1,286,921
     
1,211,200
 
Nonemployee
   
72,900
     
90,000
 
Total
   
1,359,821
     
1,301,200
 
Inducement Grants [Member]  
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]  
Stock Option Plan Activity
The inducement grants are summarized as follows:

         
Weighted
   
Weighted
 
         
average
   
average
 
   
Number of
   
exercise
   
remaining
 
   
options
   
price
   
life years
 
Outstanding at December 31, 2023
   
150,000
   
$
2.42
     
8.40
 
Granted
   
100,000
     
1.10
     
9.12
 
Outstanding at December 31, 2024
   
250,000
   
$
1.89
     
8.07
 
                         
Vested and exercisable at December 31, 2024     75,000     $
2.42
      7.36