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Equity Incentive Plans and Warrants (Tables)
6 Months Ended
Jun. 30, 2024
Equity Incentive Plans and Warrants [Abstract]  
Stock Option Plan Activity
Activity under the Company’s stock option plans for the six months ended June 30, 2024 was as follows:

   
Number of
options
   
Weighted
average
exercise
price
 
Outstanding at December 31, 2023     2,102,030     $ 2.00  
Granted     1,062,421       1.06  
Forfeited     (243,312 )     2.09  
Outstanding at June 30, 2024     2,921,139     $ 1.65  
                 
Vested and exercisable at June 30, 2024     1,207,595     $ 2.53  
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 condensed statement of comprehensive loss:

    Three Months Ended June 30,     Six Months Ended June 30,  
   
2024
   
2023
    2024     2023  
Research and development
 
$
34,629
     
27,192
      64,637       52,251  
Sales and marketing
   
18,246
     
602
      24,764       (1,942 )
General and administrative
   
51,138
     
37,422
      92,197       71,861  
Total share-based compensation expense
 
$
104,013
     
65,216
      181,598       122,170  

Share-based Compensation Arrangement by Share-based Payment Award [Line Items]  
Warrants Valuation Assumptions
The common stock was valued at $1,133,480, based on the Company’s stock price. The pre-funded warrants and common warrants were valued at $1,615,701 and $1,854,099, respectively, using the following Black-Scholes assumptions:

   
Pre-funded
warrants
   
Common
warrants
 
Expected term (in years)
 

4
     
4
 
Risk‑free interest rate
   
3.83
%
   
3.83
%
Dividend yield
   
%    
%
Expected volatility
   
100.25
%
   
100.25
%
Exercise price
 
$
0.0001
   
$
1.095
 
Stock price
 
$
0.86
   
$
0.86
 
Black-Scholes value
  $ 0.86     $ 0.58  
2021 Stock Option Plan [Member]  
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]  
Estimated Using Assumptions
Options granted under our 2021 Stock Option Plan for the six months ended June 30, 2024 to employees and nonemployees were 1,059,921 and 2,500, respectively and the weighted average exercise prices were $1.06 and $0.79, respectively. The weighted-average fair values of the options granted to employees and nonemployees were $0.90 and $0.39, respectively and were estimated using the following Black-Scholes assumptions:

    Employee
    Nonemployee  
Expected term (in years)
 

6.25
      1.50  
Risk‑free interest rate
   
4.06
%
    4.53 %
Dividend yield
   
%
    %
Expected volatility
   
110.40
%
    105.34 %
Inducement Grant [Member]  
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]  
Estimated Using Assumptions
On February 12, 2024, the Company awarded, outside the 2021 Plan, our Chief Commercial Officer a stock option grant for the right to purchase 100,000 shares of common stock at an exercise price of $1.10 per share (inducement grant), which was approved by the Compensation committee. The inducement grant will vest in equal installments over four years provided the employee remains employed by the Company on the vesting date. The fair value of the inducement grant was $0.94 and was estimated using the following assumptions:

 
 
Inducement
 
Expected term (in years)
 

6.25
 
Risk‑free interest rate
   
4.10
%
Dividend yield
   
%
Expected volatility
   
109.64
%