	Number of options			Weighted average exercise price
Outstanding at December 31, 2023		2,102,030		$	2.00
Granted		1,062,421			1.06
Forfeited		(243,312	)		2.09
Outstanding at June 30, 2024		2,921,139		$	1.65

Vested and exercisable at June 30, 2024		1,207,595		$	2.53

Options granted under our 2021 Stock Option Plan for the six months ended June 30, 2024 to employees and nonemployees were 1,059,921 and 2,500, respectively and the weighted average exercise prices were $1.06 and $0.79, respectively. The weighted-average fair values of the options granted to employees and nonemployees were $0.90 and $0.39, respectively and were estimated using the following Black-Scholes assumptions:

	Employee			Nonemployee
Expected term (in years)		6.25			1.50
Risk‑free interest rate		4.06	%		4.53	%
Dividend yield		—	%		—	%
Expected volatility		110.40	%		105.34	%

As of June 30, 2024, the total number of shares of common stock reserved for future awards under the 2021 Stock Option Plan was 676,741.

On February 12, 2024, the Company awarded, outside the 2021 Plan, our Chief Commercial Officer a stock option grant for the right to purchase 100,000 shares of common stock at an exercise price of $1.10 per share (inducement grant), which was approved by the Compensation committee. The inducement grant will vest in equal installments over four years provided the employee remains employed by the Company on the vesting date. The fair value of the inducement grant was $0.94 and was estimated using the following assumptions:

As of June 30, 2024, inducement grant awards of 250,000 shares were outstanding with a weighted average exercise price of $1.89, and 62,500 shares were vested and exercisable with a weighted average exercise price of $2.64.

The following table shows the share-based compensation expense related to vested stock option grants to employees and nonemployees by financial statement line item on the accompanying condensed statement of comprehensive loss:

	Three Months Ended June 30,				Six Months Ended June 30,
	2024		2023		2024		2023
Research and development	$	34,629		27,192		64,637		52,251
Sales and marketing		18,246		602		24,764		(1,942	)
General and administrative		51,138		37,422		92,197		71,861
Total share-based compensation expense	$	104,013		65,216		181,598		122,170

As of June 30, 2024, the remaining share-based compensation expense that is expected to be recognized in future periods for employees and nonemployees is $1,516,737, which includes $155,222 of compensation expense to be recognized upon achieving certain performance conditions. For service-based awards, the $1,361,515 of unrecognized expense is expected to be recognized over a weighted average period of 3.3 years.

For the six months ended June 30, 2024, 12,081 shares of common stock were issued under the Company’s ESPP Plan at a fair value of $10,390. For the six months ended June 30, 2023, 3,858 shares of common stock were issued under the ESPP plan at a fair value of $1,697. As of June 30, 2024, the total number of shares of common stock reserved for future awards under the ESPP Plan was 591,437.

On April 20, 2023, the Company entered into a securities purchase agreement pursuant to which the Company sold (i) 1,318,000 shares of common stock (see Note 11, Stockholders’ Equity), (ii) pre-funded warrants to purchase 1,878,722 shares of common stock, (iii) common warrants to purchase 3,196,722 shares of common stock. Additionally, common warrants to purchase 191,803 shares of common stock were issued to the placement agent compensation for services performed.

The pre-funded warrants, common warrants and placement agent warrants were exercisable immediately following the closing date of the offering. The pre-funded warrants have an unlimited term and an exercise price of $0.0001 per share. The common warrants have a 5.5 year term and an exercise price of $1.095 per share. The placement agent warrants have a 5 year term and exercise price of $1.525 per share. The offering resulted in aggregate gross proceeds of $3,899,813, before $547,764 of transaction costs.

The pre-funded warrants and common warrants are classified as a component of permanent equity because they are freestanding financial instruments that are legally detachable and separately exercisable from the shares of common stock with which they were issued, are immediately exercisable, do not embody an obligation for the Company to repurchase its shares, and permit the holders to receive a fixed number of shares of common stock upon exercise.

The common stock was valued at $1,133,480, based on the Company’s stock price. The pre-funded warrants and common warrants were valued at $1,615,701 and $1,854,099, respectively, using the following Black-Scholes assumptions:

The net proceeds of $3,352,049 were allocated to the common stock, pre-funded warrants and common warrants using the relative fair value method. The valuations were recorded to stockholders’ equity.

In June 2023, all pre-funded warrants were exercised for shares of common stock. In September and October 2023, all common warrants and 122,994 placement agent warrants were exercised for cash proceeds of $3,687,976. As of June 30, 2024, 68,809 placement agent warrants remain outstanding.