Well bless my long grey whiskers, but YGBSM!!!! This neurologist is either thinking pure thoughts or he's suffering from a severe case of cerebral flatulence...
I've heard a lot of lame-ass excuses from neurologists who didn't want to prescribe oxygen therapy to patients suffering from CH, but not prescribing an oxygen flow rate above 10 liters/minute because it would collapse the heart's left and right ventricles takes the cake

...
If you quoted his exact words and he made this statement with a straight face and there was no apparent lengthening of his nose as he made it... I would strongly consider looking for another neurologist...
Either that or throw the BS flag and ask for the medical evidence that oxygen therapy at flow rates greater than 10 liters/minute can cause the heart's ventricles to collapse...
I'm very confident that if such medical evidence exists... oxygen regulators capable of delivering flow rates greater than 10 liters/minute would be banned worldwide.
Good people of Clusterville... using oxygen therapy at 12 to 15 liters/minute is the safest, most effective and least expensive method of aborting a cluster headache... It works even more effectively at flow rates between 25 and 40 liters/minute with much shorter abort times.
Navy and Marine Corps pilots flying tactical fighter and attack aircraft have been breathing 100% oxygen from takeoff to landing on missions lasting 2 hours or more since 1943... That was shortly after US engineers cockaroached the oxygen regulator design from a Bf-109 that landed by mistake in the UK.
I can also assure you after over 3000 hours as a pilot of Navy jet fighter aircraft, breathing 100% oxygen from take of to landing on every flight, that I routinely sucked down that oxygen at flow rates well in excess of 40 liters/minute during air combat maneuvering... or whenever things got hairy-scary... my heart never collapsed... and I'm still here more than 30 years later...
Moreover, OPNAV 3710.7U, the Naval Aviator's bible of General Flight and Operating Instructions, signed by the Chief of Naval Operations, states:
"8.2.4.3 Tactical Jet and Tactical Jet Training Aircraft
Oxygen shall be used by all occupants from takeoff to landing. Emergency bailout bottles, when provided, shall be connected prior to takeoff."
You've got to ask yourself... Why would a 4-Star Admiral mandate pilots and NFOs flying a National Treasure worth of jet aircraft, breathe oxygen from takeoff to landing on all flights... day and night, on and off aircraft carriers... if it could cause hearts to collapse?.
The good Dr. Peter Goadsby, MD, completed a Level A RCT on oxygen therapy a few years back... The conclusion clearly calls for the acute treatment for cluster headache to start with oxygen therapy at flow rates up to 12 liters/minute.
Even Wikipedia has a section on the use of oxygen therapy as an acute treatment for cluster headache... "During the onset of a cluster headache, many people respond to inhalation of 100% oxygen (12-15 liters per minute in a non-re-breathing mask). Some people have found better results with 25 liters per minute. There is also a study (commenced 2011) using an "on-demand" valve that can deliver up to 160 liters per minute. When oxygen is used at the onset this can abort the attack in as little as 1 minute or as long as 10 minutes. Once an attack is at its peak, oxygen therapy appears to have little effect so many people keep an oxygen tank close at hand to use at the very first sign of an attack."
Many of us have said the following in the past and it still holds true today... Cluster headache sufferers need to be their own best advocate when it comes to methods of cluster headache intervention that work effectively...
Take care,
V/R, Batch