Engine shudder on slow take off

I have a 2013 Prius with 180k miles. When I take off after idling for any time (Traffic light or drive through) as I start to accelerate rather easy- the motor starts to shudder and make all kinds of rattling sounds. I can accelerate hard and it clears up. When I get up to speed and maintain-it runs as if nothing is wrong until I go back down on speed and have to set a light and idle. The check engine light did come on and it showed a plug misfire. I changed plugs and the code cleared but still shudders when taking off from an idle? Code did come back after a couple slow take offs. Thanks ahead of time for your guess work

 

Update* swapped around coil pack using diagnostic reading showing #4 misfire and #1 showing nothing. Took manifold and EGR pipe off, smaller manifold holes slugged up - med/ carbon on manifold and pipe. Soaked and pressure washed and replaced PCV (spring pressure next to non-existing) on my second can of fuel injector cleaner with no codes and no issues. Fuel economy showing 12-15 mpg better

 

Can you clean the cooler (and how) or do you have to replace it?

 

Yes, gonna have to go further. Yet to clean the cooler and such. The engine light came on again showing a misfire on 4 even after the plugs replaced and swapped 1 over to 4 and 4 to 1? The engine light on again showing a #4 misfire and the shudder is infrequent now on a slow take off - but none the less....still there. Will go further and do a complete clean out - from manifold to exhaust and see what happens....... things were so much easier in the 80’s......lol!

 

Ok, went through and cleaned it all from intake manifold and to include the exhaust cooler. It still has the engine shudder when feathering the gas, but no shudder if I get into the gas a little heavy. MPG has increased @ about 6. I’ve replaced plugs, pcv valve, air filter and cleaned from intake manifold to exhaust cooler ( was heavy carbon built up) I have not replaced the coils. Do not know what else I could do to get rid of the horrendous shudder. Runs great with no issues when up to speed except going through towns , cruising at slow speeds like 25-35 and having to feather the gas- shudder is present but not bad, horrible sitting at lights and having to take off again easily- if I am heavy in the gas- no problems.....

 

Yes, but I thought that was from the first tear down when I didn’t include the exhaust cooler....?

 

I've never had any bad looking deposits in my oil....I will check further. Thanks!

 

Hmmmm, never did I think that would be it. Oil always looked great. I will get it checked. Thanks everyone.

 

Head gasket is blown, providing I can locate someone to check the head out, is it something that can be done in a backyard garage? I’ve never been a deep engine repair guy, but have changed many motors and transmissions.