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Warrants (Tables)
3 Months Ended
Mar. 31, 2023
Equity [Abstract]  
Schedule of Share-based Compensation Arrangements by Share-based Payment Award
The following table summarizes the Company’s stock-based compensation expense by line item for the three months ended March 31, 2023 and 2022 (in thousands):
Three months ended
March 31,
20232022
Research and development$4,135 $6,980 
Selling, general and administrative5,70113,700
Total $9,836 $20,680 
The fair value of the Warrants at the issuance date was measured using the Black-Scholes-Merton option pricing model. The key inputs used in the valuation were as follows:

Expected term (years)10
Risk free interest rate3.0 %
Expected volatility91.3 %
Dividend yield— %
Exercise price$2.15 
Stock price$3.63 
The fair value of the warrants upon the expiration of the option period was measured using the Black-Scholes-Merton option pricing model. The key inputs used in the valuation were as follows:
Expected term (year)0.9
Expected volatility116.4 %
Expected dividend rate— %
Risk free rate4.7 %
Estimated fair value per warrant$0.57 
Exercise price$1.05 
Stock price$1.20 
The fair value of the warrants at the issuance date was measured using the Black-Scholes-Merton option pricing model. The key inputs used in the valuation were as follows:
Expected term (years)5.0
Expected volatility106.8 %
Expected dividend rate— %
Risk free rate3.78 %
Estimated fair value per warrant$0.80 
Exercise price$1.30 
Stock price$1.05