<?php

$string = 'Diabetes, Nutrition, Dietician';
$array = explode(',', $string);
$result = array();
foreach ($array as $part) {
    if (substr(strtolower(trim($part)),0,1) == 'd') {
        array_push($result, trim($part));
    }
}

var_dump($result);

array(2) {
  [0]=>
  string(8) "Diabetes"
  [1]=>
  string(9) "Dietician"
}