diff --git a/starlette/middleware/base.py b/starlette/middleware/base.py
index 718387395..7df6161b9 100644
--- a/starlette/middleware/base.py
+++ b/starlette/middleware/base.py
@@ -3,7 +3,7 @@
 import typing
 
 import anyio
-from anyio.abc import ObjectReceiveStream, ObjectSendStream
+from anyio.streams.memory import MemoryObjectReceiveStream, MemoryObjectSendStream
 
 from starlette._utils import collapse_excgroups
 from starlette.requests import ClientDisconnect, Request
@@ -105,8 +105,8 @@ async def __call__(self, scope: Scope, receive: Receive, send: Send) -> None:
         wrapped_receive = request.wrapped_receive
         response_sent = anyio.Event()
 
-        send_stream: ObjectSendStream[typing.MutableMapping[str, typing.Any]]
-        recv_stream: ObjectReceiveStream[typing.MutableMapping[str, typing.Any]]
+        send_stream: MemoryObjectSendStream[Message]
+        recv_stream: MemoryObjectReceiveStream[Message]
         send_stream, recv_stream = anyio.create_memory_object_stream()
 
         async def call_next(request: Request) -> Response: