I don't think you need to concatenate or group the time series in any way.

Just train your NNet on the 10 data sets, with [PPG, ECG] as inputs and [ABP] as the outputs. Then use it to predict the [ABP] for the eleventh data set.

So your data should look like:

Patient #.    Input       Target 
    1      [PPG1, ECG1]   [ABP1]
    2      [PPG2, ECG2]   [ABP2]
   ...          ...         ...
   10      [PPG10,ECG10]  [ABP10]

You only have 10 data sets for training so you should use cross validation.

Then feed

[PPG11, ECG11] to predict your new [ABP].

I don't think you need to concatenate or group the time series in any way.

Just train your NNet on the 10 data sets, with [PPG, ECG] as inputs and [ABP] as the outputs. Then use it to predict the [ABP] for the eleventh data set.

So your data should look like:

Patient #.    Input       Target 
    1      [PPG1, ECG1]   [ABP1]
    2      [PPG2, ECG2]   [ABP2]
   ...          ...         ...
   10      [PPG10,ECG10]  [ABP10]

You only have 10 data sets for training so you should use cross validation.

Then feed

[PPG11, ECG11] to your NNet to predict your new [ABP].