Saying that Karen's not important to Frank because he also saved Madani is so misguided.
Frank saved Madani because he doesn't hurt innocents, and she was never meant to get hurt. It's why he was so angry with Lieberman for hitting her and why he went back to save her. But that is not the same as him saving Karen because she's his family and he loves her. It's not the same as the absolute fear and dread on his face when Karen's in danger. When Karen's in danger, Frank can't even form words to express how worried he is and he has to resort to slamming his hand down on a table to convey what he's feeling.
When he saved Madani, there was no risk of him getting injured, but when he needed to rescue Karen? He willfully injured himself because it was the fastest way to get to her. Because his pain is secondary to hers. Frank can handle pain. What he can't handle is the thought of Karen in pain and agony.