Formal Verification of Cardiorenal-Metabolic Guidelines
Abstract
An undergraduate thesis proposal modeling and formally verifying polypharmacy clinical guidelines across cardiovascular, renal, and metabolic co-morbidities using first-order logic and Z3 SMT solver.
Theoretical Methodology & Specifications
Academic Notice: This research initiative is an ongoing Undergraduate Bachelor’s Thesis Proposal at Daffodil International University. It represents active theoretical formulation and formal modeling rather than a defended dissertation or clinical trial.
Proposal Overview
Patients suffering from comorbid Type 2 Diabetes (T2D), Chronic Kidney Disease (CKD), and Heart Failure (HF) exist at the epicenter of therapeutic conflict. Clinical guidelines are historically authored in disease silos:
- KDIGO (Kidney Disease: Improving Global Outcomes) dictates renoprotective targets.
- ADA (American Diabetes Association) prescribes glycemic thresholds and SGLT2i indications.
- ACC/AHA (American College of Cardiology) specifies neurohormonal blockade.
When co-prescribed, pharmacodynamic interactions (e.g., ACE inhibitors combined with ARBs and mineralocorticoid receptor antagonists) create perilous risks of hyperkalemia and acute kidney injury. This thesis proposes a formal verification framework encoding heterogeneous guideline propositions into Satisfiability Modulo Theories (SMT).
Research Questions & Formal Objectives
- Formal Encoding: Can heterogeneous multi-society guidelines expressed in natural language be translated into decidable First-Order Logic (FOL) fragments without loss of clinical intent?
- Automated Conflict Detection: Can an SMT solver (Microsoft Z3) deterministically uncover latent contradictions between concurrent guideline recommendations for multimorbid patient states in sub-second runtime?
- Counterexample Generation: In cases of unsatisfiable regimens (
UNSAT), can the solver automatically generate minimally disruptive alternative dosing parameters?
Methodological Framework
The project constructs a formalization pipeline:
- Predicate Extraction: Isolating biomarker boundary domains (eGFR, serum creatinine, potassium, ejection fraction, HbA1c).
- SMT Axiomatization: Encoding guideline logic as conjunctions of implications over non-linear real and integer arithmetic.
- Solver Integration: Verifying global satisfiability using the Z3 solver backend.
# Formal Representation of Polypharmacy Conflict (Sample Theory)
from z3 import *
egfr = Real('egfr')
serum_k = Real('serum_k')
ras_inhibitor = Bool('ras_inhibitor')
mra = Bool('mra')
solver = Solver()
# Patient Context: Advanced CKD with Hyperkalemia
solver.add(egfr < 30.0)
solver.add(serum_k > 5.2)
# ACC Guideline: Indication for Heart Failure
solver.add(mra == True)
# KDIGO Safety Invariant: MRA + RASi contraindication when K+ > 5.0 or eGFR < 30
safety_invariant = Implies(
And(mra, serum_k > 5.0),
Not(ras_inhibitor)
)
solver.add(safety_invariant)
# Verifying if dual therapy is satisfiable
solver.add(ras_inhibitor == True)
# Returns UNSAT: Proves formal incompatibility of simultaneous therapy
assert solver.check() == unsatAcademic Supervision & Milestones
- Supervision: Supervised under Assistant Professor, Department of Computer Science and Engineering, Daffodil International University (DIU).
- Current Status: Thesis Proposal Scaffolding & SMT Axiom Cataloging.
- Expected Deliverables: Verified benchmark test suite, formalized SMT-LIB2 guideline library, and reproducible CLI analysis harness.
Formal Verification (SMT-LIB2 & Z3) & Architecture
Formal pipeline illustrating the translation of medical propositions into SMT constraints.
; SMT-LIB2 Multi-Guideline Encoding
(set-logic QF_LRA)
(declare-fun egfr () Real)
(declare-fun k_serum () Real)
(declare-fun rasi_indicated () Bool)
(declare-fun mra_indicated () Bool)
; Patient Comorbidity Parameter Set
(assert (< egfr 30.0))
(assert (> k_serum 5.2))
(assert (= rasi_indicated true))
(assert (= mra_indicated true))
; Dual Blockade Invariant Check
(assert (not (and rasi_indicated mra_indicated)))
(check-sat)
; Result: unsat (Conflict Formally Proven)