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Goodwill and Intangible Assets
6 Months Ended
Jun. 30, 2023
Goodwill and Intangible Assets Disclosure [Abstract]  
Goodwill and Intangible Assets Goodwill and Intangible Assets
There were no changes in the carrying amount of goodwill for the periods ended June 30, 2023 and December 31, 2022.
Intangible assets as of June 30, 2023 and December 31, 2022 consisted of the following:
Useful LivesJune 30,
2023
December 31,
2022
Patent application costs3 Years$420,002 $382,285 
Trade name and trademarks3 Years69,556 68,356 
Intangible assets, gross489,558 450,641 
Less: Accumulated amortization(274,735)(198,955)
Intangible assets, net$214,823 $251,686 
Intangible asset amortization expense is recognized on a straight-line basis and intangible asset amortization expense for the three months ended June 30, 2023 and 2022 totaled $38 thousand and $22 thousand, respectively. Intangible asset amortization expense is recognized on a straight-line basis and intangible asset amortization expense for the six months ended June 30, 2023 and 2022 totaled $75 thousand and $46 thousand, respectively.
Estimated future amortization expense of intangible assets is as follows:
Years Ending December 31,Amount
2023$76,048 
202493,545 
202542,884 
20262,346 
$214,823