Unable to sign a file with nodejs crypto

I've created a private Key with nodejs crypto and want to sign a file with this key. My code is following:

var ecdh = crypto.createECDH('brainpoolP512t1');
        ecdh.generateKeys();
        var key = ecdh.getPrivateKey('buffer');

        var data= fs.readFileSync(req.file.path);
        var sign = crypto.createSign('sha512');
        sign.update(data);
        var signature = sign.sign(key, 'hex');

But I get the error:

Error: error:0906D06C:PEM routines:PEM_read_bio:no start line
    at Error (native)
    at Sign.sign (crypto.js:283:26)
    at /....js:32:27
    at Immediate.<anonymous> (/.../node_modules/multer/lib/make-middleware.js:52:37)
    at runCallback (timers.js:578:20)
    at tryOnImmediate (timers.js:554:5)
    at processImmediate [as _immediateCallback] (timers.js:533:5)

I know it has something to do with the key format, but I don't know how to fix this. Can anyone help?

UPDATE: I edited the privateKey to fit the pem format:

var KEY_START = '-----BEGIN EC PRIVATE KEY-----\n';
var KEY_END = '\n-----END EC PRIVATE KEY-----';

const ecdh = crypto.createECDH('brainpoolP512t1');
            ecdh.generateKeys();
            var key =KEY_START + ecdh.getPrivateKey('base64') + KEY_END;        
            var data= fs.readFileSync(req.file.path);
            const sign = crypto.createSign('sha512');
            sign.update(data);
            var signature = sign.sign(key, 'hex');

And now I geht a different error:

Error: error:0D07207B:asn1 encoding routines:ASN1_get_object:header too long
    at Error (native)
    at Sign.sign (crypto.js:283:26)
    at /...js:37:27
    at Immediate.<anonymous> (/.../node_modules/multer/lib/make-middleware.js:52:37)
    at runCallback (timers.js:578:20)
    at tryOnImmediate (timers.js:554:5)
    at processImmediate [as _immediateCallback] (timers.js:533:5)

The key you sign the data with needs to be a valid PEM-encoded private key. The DH getPrivateKey() function does not return a key in this format, it returns the bare private key data.

Your options include:

Generating a private key via the OpenSSL key generator utility or similar

Using third-party node modules to properly encode the private key as outlined in RFC 5915. Full example using the asn1.js and bn.js modules:

var crypto = require('crypto');

var asn1 = require('asn1.js');
var BN = require('bn.js');

function toOIDArray(oid) {
  return oid.split('.').map(function(s) {
    return parseInt(s, 10)
  });
}

// Define ECPrivateKey from RFC 5915
var ECPrivateKey = asn1.define('ECPrivateKey', function() {
  this.seq().obj(
    this.key('version').int(),
    this.key('privateKey').octstr(),
    this.key('parameters').explicit(0).objid().optional(),
    this.key('publicKey').explicit(1).bitstr().optional()
  );
});

// Generate the DH keys
var ecdh = crypto.createECDH('brainpoolP512t1');
ecdh.generateKeys();

// Generate the PEM-encoded private key
var pemKey = ECPrivateKey.encode({
  version: new BN(1),
  privateKey: ecdh.getPrivateKey(),
  // OID for brainpoolP512t1
  parameters: toOIDArray('1.3.36.3.3.2.8.1.1.14')
}, 'pem', { label: 'EC PRIVATE KEY' });

// Sign data
var sign = crypto.createSign('sha512');
sign.update('hello world');
var signature = sign.sign(pemKey, 'hex');

console.log('signature', signature);