Fair value measurements are market-based measurements, not entity-specific measurements. Therefore, fair value measurements are determined based on the assumptions that market participants would use in pricing the asset or liability. We follow a three-level hierarchy to prioritize the inputs used in the valuation techniques to derive fair values. The basis for fair value measurements for each level within the hierarchy is described below:

Warrants issued by the Company in connection with the sale of common stock in a registration offering in September 2019 (“Series U Warrants”) were classified as liabilities at issuance. The Series U warrants were marked to market at each subsequent reporting date as non-operating income or loss in the statement of operations. As described in more detail in Note 12, during 2020 the Company amended the terms of 3,522,500 Series U Warrants such that those amended Series U Warrants met the requirements to be classified within stockholders’ equity and were no longer required to be re-measured at fair value at each balance sheet date.

Expected volatility was computed using daily pricing observations of traded shares of the Company for recent periods that correspond to the expected term of the warrants. The Company believes this method produces an estimate that is representative of our expectations of future volatility over the expected term of these warrants. The Company currently has no reason to believe future volatility over the expected remaining life of these warrants is likely to differ materially from historical volatility. The expected life is based on the remaining contractual term of the warrants. The risk-free interest rate is the U.S. Treasury bond rate as of the valuation date. Because some of the inputs to our valuation model are either not observable or are not derived principally from or corroborated by observable market data by correlation or other means, the warrant liability is classified as Level 3 in the fair value hierarchy. Fluctuations in the fair value of the warrants are impacted by unobservable inputs. Significant increases (decreases) in this input in isolation would result in a significantly higher (lower) fair value measurement.

The Company estimated the fair value of the liability-classified Series U Warrants on the issuance date as well as at each subsequent balance sheet date with the Black Scholes model. The assumptions used in the Black Scholes option pricing model to determine the fair value of the Series U warrants were as follows:

	As of December 31, 2021			As of December 31, 2020
Expected term		2.75 years		3.75 years
Common stock market price	$	1.05		$	2.02
Risk-free interest rate		0.91	%		0.24	%
Expected volatility		143.2	%		149.0	%
Resulting fair value (per warrant)	$	0.58		$	1.56

The following table summarizes the change in our Level 3 warrant liability value (in thousands):

	Years ended December 31,
Warrant liability	2021			2020
Beginning balance	$	7		$	6,929
Change in fair value of warrants		(6	)		(2,418	)
Reclassification to equity		—			(4,504	)
Ending balance	$	1		$	7

On September 30, 2020, the Company committed to issue 180,701 shares to Lincoln Park as a committee fee (“Commitment Shares”) in connection with the 2020 Purchase Agreement, and these shares were issued on October 2, 2020. The change in fair value of the Commitment Shares between September 30, 2020 and the issuance date, in the amount of $18,000 and calculated using the closing stock prices on respective dates, was recorded in change in fair value of liability-classified instruments on the statement of operations and comprehensive income/loss for the year ended December 31, 2020.

The Company applies fair value techniques on a non-recurring basis, if and when necessary, associated with: (1) valuing potential impairment losses related to goodwill which are accounted for pursuant to the authoritative guidance for intangibles—goodwill and other; and (2) valuing potential impairment losses related to long-lived assets which are accounted for pursuant to the authoritative guidance for property, plant and equipment.