Arnold and Edna are the couple that helps Adam out of the ditch he's been pushed into by the bullies. They drive him for a while on his journey. Arnold is described as being "kind and concerned," with "an old face, a grandfather kind of face" (21.2). Edna is a "white-haired woman" with a "worried expression" (21.10), who, we learn from Arnold, has had a stroke.
Notice the words Arnold uses to describe his wife, Edna. He says, more than once, that "[s]he's not herself these days" (21.33). What does this tell us? Perhaps nothing when we're reading it the first time. But once we realize that everyone Adam meets on his bike ride is somehow part of his life in the hospital, we think she's probably a patient there, too. It tells us that the patients are there because they're not themselves – Adam isn't alone in this respect.
One other thing: Shmoop wonders if maybe Arnold is Dr. Dupont. We don't explicitly meet Arnold's counterpart in the hospital at the end of the book. It would make sense for Adam to imagine Dr. Dupont carrying around a woman who just had a stroke and helping him out when he fell off his bike. Also, the first words Arnold says to Adam are, "You all right, son?" (21.1), and back at the hospital Dr. Dupont keeps telling Adam that everything is going to be "all right." Maybe this is supposed to be ambiguous, or maybe it doesn't matter at all, but it's fun to speculate. What do you think?