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Warrants (Tables) | 12 Months Ended
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Dec. 31, 2021
Class of Warrant or Right [Line Items] |
Summary of the company's warrant activity and related information | A summary of the Company’s warrant activity and related information is as follows: ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | Warrants | ​ | Pre-Funded Warrants
​ |  | ​ |  | Weighted |  | ​ |  | Weighted
​ | ​ | ​ | ​ | Average | ​ | ​ | ​ | Average
​ | ​ | ​ | ​ | Exercise | ​ | ​ | ​ | Exercise
​ | ​ | Warrants | ​ | Price | ​ | Warrants | ​ | Price
Outstanding at December 31, 2019 |  | 2,463,063 | ​ | $ | 7.96 |  | 868,443 | ​ | $ | 0.001
Issued |  | 705,688 | ​ | $ | 8.90 |  | — | ​ | $ | —
Exercised |  | (589,941) | ​ | $ | 2.39 |  | (548,242) | ​ | $ | 0.001
Held in abeyance | ​ | (803,300) | ​ | $ | 2.32 | ​ | — | ​ | $ | —
Expired | ​ | (625,642) | ​ | $ | 24.44 | ​ | — | ​ | $ | —
Outstanding at December 31, 2020 | ​ | 1,149,868 | ​ | $ | 6.36 | ​ | 320,201 | ​ | $ | 0.001
Exercised | ​ | (363,448) | ​ | $ | 8.90 | ​ | (66,373) | ​ | $ | 0.001
Outstanding at December 31, 2021 | ​ | 786,420 | ​ | $ | 5.19 | ​ | 253,828 | ​ | $ | 0.001
Warrants. |
Class of Warrant or Right [Line Items] |
Schedule of assumptions used in the black-scholes model | The assumptions used in the Black-Scholes model for these warrants are as follows: ​
​ | ​ | ​ | ​
Average risk-free interest rate |  | 0.22 | %
Expected dividend yield |  | — | %
Expected life |  | 5 years | ​
Expected volatility |  | 90 | %

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- Definition Tabular disclosure of warrant activity. + References No definition available. + Details
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- Definition Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table. + References No definition available. + Details
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- Definition Tabular disclosure of the significant assumptions used during the year to estimate the fair value of stock options, including, but not limited to: (a) expected term of share options and similar instruments, (b) expected volatility of the entity's shares, (c) expected dividends, (d) risk-free rate(s), and (e) discount for post-vesting restrictions. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (f)(2) -URI http://asc.fasb.org/extlink&oid=120381028&loc=d3e5070-113901 + Details
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