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Warrants to Acquire Shares of Common Stock
 6 Months Ended
Jun. 30, 2021
Warrants and Rights Note Disclosure [Abstract]  
Warrants to Acquire Shares of Common Stock Warrants to Acquire Shares of Common Stock
Warrants Outstanding

The following is a summary of the activity of the Company's warrants to acquire shares of common stock for the six months ended June 30, 2021 (in thousands):
 
Warrant IssuanceOutstanding, December 31, 2020GrantedExercisedCanceled/ExpiredOutstanding, June 30, 2021Expiration
July 2020 PIPE Offering445 — (420)— 25 August 2025
January 2020 Offering719 — (410)— 309 July 2025
June 2019 Offering2 — (1)— 1 June 2024
March 2019 Exercise Agreement63 — — — 63 March 2024
July 2018 Offering141 — (1)— 140 July 2023
Other22 — — (1)21 November 2021 - November 2023
1,392 — (832)(1)559 

Warrants to acquire shares of common stock consist of warrants that may be settled in cash, which are liability-classified warrants, and equity-classified warrants.
Warrants Classified as Liabilities

Liability-classified warrants consist of warrants to acquire common stock issued in connection with certain previous equity financings. These warrants may be settled in cash and were determined not to be indexed to the Company’s common stock.

The estimated fair value of outstanding warrants accounted for as liabilities is determined at each balance sheet date. Any decrease or increase in the estimated fair value of the warrant liability since the most recent balance sheet date is recorded in the consolidated statement of operations as change in fair value of warrant liability. The fair value of the warrants is estimated using a Black-Scholes pricing model with the following inputs:

As of June 30, 2021
Warrant IssuanceOutstanding (in thousands)Strike price (per share)Expected term (years)Volatility %Risk-free rate %
Other warrants (liability-classified)13 $7.50 2.26151.45 %0.30 %
As of December 31, 2020
Warrant IssuanceOutstanding (in thousands)Strike price (per share)Expected term (years)Volatility %Risk-free rate %
Other warrants (liability-classified)13 $7.50 2.75150.38 %0.16 %

The expected volatility assumptions are based on the Company's implied volatility in combination with the implied volatilities of similar publicly traded entities. The expected life assumption is based on the remaining contractual terms of the warrants. The risk-free rate is based on the zero coupon rates in effect at the time of valuation. The dividend yield used in the pricing model is zero, because the Company has no present intention to pay cash dividends.

The changes in fair value of the warrant liability for the six months ended June 30, 2021 were as follows (in thousands):
 
Warrant IssuanceWarrant liability, December 31, 2020Change in fair value of warrantsWarrant liability, June 30, 2021
Other warrants (liability-classified)$55 $59 $114 
$55 $59 $114