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Stock-Based Compensation | 12 Months Ended
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Dec. 31, 2023
Stock-Based Compensation |
Stock-Based Compensation | (8) Stock-Based Compensation Effective upon the closing of the Company’s IPO on January 31, 2020, the Company’s 2019 Equity Incentive Plan (the “2019 Plan”) became effective, succeeding the Company’s previous equity incentive plan. No new options may be issued under the previous plan, although shares subject to grants which are cancelled or forfeited will again be available under the 2019 Plan. Effective June 1, 2021, the 2019 Plan was amended to increase the number of shares authorized to be issued from 1,000,000 to 2,000,000. As of December 31, 2023, 35,545 shares were available for future grants. The 2019 Plan provides for grants to employees, members of the Board, consultants and advisors to the Company, in the form of stock options, stock awards and other equity-based awards. The amount and terms of grants are determined by the Board, except when they are below previously approved thresholds allowing the Company’s CEO to grant awards on a discretionary basis. Stock options generally have a maximum term of 10 years after date of grant and are exercisable in cash or as otherwise determined by the Board. Stock-based compensation expense in the statements of operations, including the fair value of stock awards to consultants and advisors for services rendered, for the years ended December 31, 2023 and 2022 was as follows:
​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | Year Ended
​ | ​ | December 31,
​ |  | 2023 |  | 2022
General and administrative | ​ | $ | 2,414,867 | ​ | $ | 5,778,117
Research and development | ​ |  | 2,213,539 | ​ | ​ | 3,374,403
​ | ​ | $ | 4,628,406 | ​ | $ | 9,152,520
​ Stock option activity for the years ended December 31, 2023, and 2022, was as follows: ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ |  | ​ |  | ​ | ​ |  | Weighted | ​ | ​ | ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | Average | ​ | ​ | ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | Remaining | ​ | ​ | ​
​ | ​ | ​ | ​ | Weighted | ​ | Contractual | ​ | Aggregate
​ | ​ | Number of | ​ | Average | ​ | Term | ​ | Intrinsic
​ | ​ | Shares | ​ | Exercise Price | ​ | (Years) |  | Value
Outstanding at December 31, 2021 |  | 1,489,748 | ​ | $ | 13.82 | ​ |  | ​ |  |
Granted |  | 348,294 | ​ | $ | 15.90 | ​ |  | ​ |  |
Exercised |  | (70,101) | ​ | $ | 1.97 | ​ |  | ​ |  |
Forfeited |  | (110,599) | ​ | $ | 25.93 | ​ |  | ​ |  |
Outstanding at December 31, 2022 |  | 1,657,342 | ​ | $ | 13.95 | ​ | ​ | ​ | ​ | ​
Granted | ​ | 367,329 | ​ | $ | 8.57 | ​ | ​ | ​ | ​ | ​
Exercised | ​ | (59,897) | ​ | $ | 0.14 | ​ | ​ | ​ | ​ | ​
Forfeited | ​ | (10,000) | ​ | $ | 4.39 | ​ | ​ | ​ | ​ | ​
Outstanding at December 31, 2023 |  | 1,954,774 | ​ | $ | 13.41 | ​ | 6.10 | ​ | $ | 17,862,936
Exercisable at December 31, 2023 | ​ | 1,600,577 | ​ | $ | 14.30 | ​ | 5.39 | ​ | $ | 14,532,422
​ The aggregate intrinsic value of options exercised during the years ended December 31, 2023 and 2022 was $1,111,688 and $803,357, respectively. As of December 31, 2023, there was $2,177,110 unrecognized compensation expense related to unvested options. That cost is expected to be recognized over a weighted-average period of 0.92 years. During the years ended December 31, 2023 and 2022, the Company issued 367,329 and 348,294 options, respectively. Under the grant agreements for the 2023 stock option grants, 94,624 of the options vested immediately and 272,705 of the options vest in substantially equal quarterly installments over two years from the date of grant. Under the grant agreements for the 2022 stock option grants, 10,000 of the options vested immediately, 9,947 of the options vested on March 29, 2022, 9,947 of the options vest on March 31, 2023, 43,333 of the options vest on August 29, 2023, and 255,067 of the options vest in substantially equal quarterly installments over two years from the date of grant. 20,000 of the options have performance-based vesting conditions. As of December 31, 2022, it was not considered probable that the performance conditions would be achieved, and no compensation expense was recognized during the period related to these options. All of the options have a 10-year term prior to expiration. ​ The weighted average grant date fair value of options issued during the years ended December 31, 2023 and 2022 was $7.39 per share and $13.24 per share, respectively. The fair value was estimated using the Black Sholes option pricing model. The expected life of options was estimated using the simplified method, as the Company has limited historical information to develop reasonable expectations about future exercise patterns and post-vesting employment. The risk-free rate was based on the interest rate payable on U.S. Treasury securities at the time of grant for a period that is commensurate with the expected term of the option. Given the lack of a public market for the Company’s common stock prior to the IPO, the expected stock price volatility was based on a weighted approach that incorporates the historic daily volatility of the Company’s common stock since the IPO and the historic daily volatility of similar companies that have been publicly traded for a period commensurate with the expected term of the option. The expected dividend yield is 0% because the Company has not historically paid and does not expect for the foreseeable future to pay a dividend on its common stock. The weighted average assumptions used in the valuation of options granted were as follows: ​
​ | ​ | ​ | ​ | ​ | ​
​ |  | Year Ended |  | Year Ended |
​ | ​ | December 31, 2023 |  | December 31, 2022 |
Risk-free interest rate |  | 4.17 | % | 2.24 | %
Expected life |  | 5.5 | ​ | 5.9 | ​
Expected volatility |  | 120 | % | 112 | %
Expected dividend yield |  | — | ​ | — | ​
​ Related Party Transaction ​ During the year ended December 31, 2023, the Company issued 4,068 non-qualified stock options to a member of its Board of Directors in consideration for the member’s agreement to serve as a consultant of the Company. The options were issued in two separate tranches, at grant prices of $9.56 per share and $7.39 per share, respectively. ​

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